WorldWideScience

Sample records for media analytical solutions

  1. The analytical solution to the 1D diffusion equation in heterogeneous media

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Nigg, D.W.

    2011-01-01

    The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane cylindrical and spherical media is presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup solution as a series of one-group solutions which, when re-assembled, gives the analytical solution. Customized Eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a uniform spatial domain. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is then numerically implemented through recurrence. Finally, we apply the theory to assess the accuracy of a second order finite difference scheme and to a 1D slab BWR reactor in the four-group approximation. (author)

  2. The analytical benchmark solution of spatial diffusion kinetics in source driven systems for homogeneous media

    International Nuclear Information System (INIS)

    Oliveira, F.L. de; Maiorino, J.R.; Santos, R.S.

    2007-01-01

    This paper describes a closed form solution obtained by the expansion method for the general time dependent diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. Thus, first an analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent without precursors was also solved and the results inter compared with results obtained by the previous one group models for a given fast homogeneous media, and different types of source transients. The results are being compared with the obtained by numerical methods. (author)

  3. Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media

    Directory of Open Access Journals (Sweden)

    Yu Bai

    2015-01-01

    Full Text Available Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well.

  4. Reactive silica transport in fractured porous media: Analytical solutions for a system of parallel fractures

    Science.gov (United States)

    Yang, Jianwen

    2012-04-01

    A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.

  5. Contribution to analytical solution of neutron slowing down problem in homogeneous and heterogeneous media

    International Nuclear Information System (INIS)

    Stefanovic, D.B.

    1970-12-01

    The objective of this work is to describe the new analytical solution of the neutron slowing down equation for infinite monoatomic media with arbitrary energy dependence of cross section. The solution is obtained by introducing Green slowing down functions instead of starting from slowing down equations directly. The previously used methods for calculation of fission neutron spectra in the reactor cell were numerical. The proposed analytical method was used for calculating the space-energy distribution of fast neutrons and number of neutron reactions in a thermal reactor cell. The role of analytical method in solving the neutron slowing down in reactor physics is to enable understating of the slowing down process and neutron transport. The obtained results could be used as standards for testing the accuracy od approximative and practical methods

  6. From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

    Science.gov (United States)

    Bodin, Jacques

    2015-03-01

    In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

  7. A family of analytical solutions of a nonlinear diffusion-convection equation

    Science.gov (United States)

    Hayek, Mohamed

    2018-01-01

    Despite its popularity in many engineering fields, the nonlinear diffusion-convection equation has no general analytical solutions. This work presents a family of closed-form analytical traveling wave solutions for the nonlinear diffusion-convection equation with power law nonlinearities. This kind of equations typically appears in nonlinear problems of flow and transport in porous media. The solutions that are addressed are simple and fully analytical. Three classes of analytical solutions are presented depending on the type of the nonlinear diffusion coefficient (increasing, decreasing or constant). It has shown that the structure of the traveling wave solution is strongly related to the diffusion term. The main advantage of the proposed solutions is that they are presented in a unified form contrary to existing solutions in the literature where the derivation of each solution depends on the specific values of the diffusion and convection parameters. The proposed closed-form solutions are simple to use, do not require any numerical implementation, and may be implemented in a simple spreadsheet. The analytical expressions are also useful to mathematically analyze the structure and properties of the solutions.

  8. Semianalytical Solutions of Radioactive or Reactive Transport in Variably-Fractured Layered Media: 1. Solutes

    International Nuclear Information System (INIS)

    George J. Moridis

    2001-01-01

    In this paper, semianalytical solutions are developed for the problem of transport of radioactive or reactive solute tracers through a layered system of heterogeneous fractured media with misaligned fractures. The tracer transport equations in the non-flowing matrix account for (a) diffusion, (b) surface diffusion, (c) mass transfer between the mobile and immobile water fractions, (d) linear kinetic or equilibrium physical, chemical, or combined solute sorption or colloid filtration, and (e) radioactive decay or first-order chemical reactions. The tracer-transport equations in the fractures account for the same processes, in addition to advection and hydrodynamic dispersion. Any number of radioactive decay daughter products (or products of a linear, first-order reaction chain) can be tracked. The solutions, which are analytical in the Laplace space, are numerically inverted to provide the solution in time and can accommodate any number of fractured and/or porous layers. The solutions are verified using analytical solutions for limiting cases of solute and colloid transport through fractured and porous media. The effect of important parameters on the transport of 3 H, 237 Np and 239 Pu (and its daughters) is investigated in several test problems involving layered geological systems of varying complexity

  9. Finite volume approximation of the three-dimensional flow equation in axisymmetric, heterogeneous porous media based on local analytical solution

    KAUST Repository

    Salama, Amgad

    2013-09-01

    In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.

  10. Analytical solution of electrohydrodynamic flow and transport in rectangular channels: inclusion of double layer effects

    KAUST Repository

    Joekar-Niasar, V.

    2013-01-25

    Upscaling electroosmosis in porous media is a challenge due to the complexity and scale-dependent nonlinearities of this coupled phenomenon. "Pore-network modeling" for upscaling electroosmosis from pore scale to Darcy scale can be considered as a promising approach. However, this method requires analytical solutions for flow and transport at pore scale. This study concentrates on the development of analytical solutions of flow and transport in a single rectangular channel under combined effects of electrohydrodynamic forces. These relations will be used in future works for pore-network modeling. The analytical solutions are valid for all regimes of overlapping electrical double layers and have the potential to be extended to nonlinear Boltzmann distribution. The innovative aspects of this study are (a) contribution of overlapping of electrical double layers to the Stokes flow as well as Nernst-Planck transport has been carefully included in the analytical solutions. (b) All important transport mechanisms including advection, diffusion, and electromigration have been included in the analytical solutions. (c) Fully algebraic relations developed in this study can be easily employed to upscale electroosmosis to Darcy scale using pore-network modeling. © 2013 Springer Science+Business Media Dordrecht.

  11. Analytical solution of electrohydrodynamic flow and transport in rectangular channels: inclusion of double layer effects

    KAUST Repository

    Joekar-Niasar, V.; Schotting, R.; Leijnse, A.

    2013-01-01

    Upscaling electroosmosis in porous media is a challenge due to the complexity and scale-dependent nonlinearities of this coupled phenomenon. "Pore-network modeling" for upscaling electroosmosis from pore scale to Darcy scale can be considered as a promising approach. However, this method requires analytical solutions for flow and transport at pore scale. This study concentrates on the development of analytical solutions of flow and transport in a single rectangular channel under combined effects of electrohydrodynamic forces. These relations will be used in future works for pore-network modeling. The analytical solutions are valid for all regimes of overlapping electrical double layers and have the potential to be extended to nonlinear Boltzmann distribution. The innovative aspects of this study are (a) contribution of overlapping of electrical double layers to the Stokes flow as well as Nernst-Planck transport has been carefully included in the analytical solutions. (b) All important transport mechanisms including advection, diffusion, and electromigration have been included in the analytical solutions. (c) Fully algebraic relations developed in this study can be easily employed to upscale electroosmosis to Darcy scale using pore-network modeling. © 2013 Springer Science+Business Media Dordrecht.

  12. Generalized analytic solutions and response characteristics of magnetotelluric fields on anisotropic infinite faults

    Science.gov (United States)

    Bing, Xue; Yicai, Ji

    2018-06-01

    In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.

  13. Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

    KAUST Repository

    El-Amin, Mohamed; Radwan, Ahmed G.; Sun, Shuyu

    2017-01-01

    In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

  14. Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

    KAUST Repository

    El-Amin, Mohamed

    2017-07-06

    In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

  15. Contribution to analytical solution of neutron slowing down problem in homogeneous and heterogeneous media; Prilog analitickom resavanju problema usporavanja neutrona u homogenim i heterogenim sredinama

    Energy Technology Data Exchange (ETDEWEB)

    Stefanovic, D B [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)

    1970-07-01

    The objective of this work is to describe the new analytical solution of the neutron slowing down equation for infinite monoatomic media with arbitrary energy dependence of cross section. The solution is obtained by introducing Green slowing down functions instead of starting from slowing down equations directly. The previously used methods for calculation of fission neutron spectra in the reactor cell were numerical. The proposed analytical method was used for calculating the space-energy distribution of fast neutrons and number of neutron reactions in a thermal reactor cell. The role of analytical method in solving the neutron slowing down in reactor physics is to enable understating of the slowing down process and neutron transport. The obtained results could be used as standards for testing the accuracy od approximative and practical methods.

  16. Exact bright and dark spatial soliton solutions in saturable nonlinear media

    International Nuclear Information System (INIS)

    Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

    2009-01-01

    We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

  17. An analytic solution of the static problem of inclined risers conveying fluid

    KAUST Repository

    Alfosail, Feras

    2016-05-28

    We use the method of matched asymptotic expansion to develop an analytic solution to the static problem of clamped–clamped inclined risers conveying fluid. The inclined riser is modeled as an Euler–Bernoulli beam taking into account its self-weight, mid-plane stretching, an applied axial tension, and the internal fluid velocity. The solution consists of three parts: an outer solution valid away from the two boundaries and two inner solutions valid near the two ends. The three solutions are then matched and combined into a so-called composite expansion. A Newton–Raphson method is used to determine the value of the mid-plane stretching corresponding to each applied tension and internal velocity. The analytic solution is in good agreement with those obtained with other solution methods for large values of applied tensions. Therefore, it can be used to replace other mathematical solution methods that suffer numerical limitations and high computational cost. © 2016 Springer Science+Business Media Dordrecht

  18. Insight solutions are correct more often than analytic solutions

    Science.gov (United States)

    Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark

    2016-01-01

    How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960

  19. Three-dimensional solutions in media with spatial dependence of nonlinear refractive index

    International Nuclear Information System (INIS)

    Kovachev, L.M.; Kaymakanova, N.I.; Dakova, D.Y.; Pavlov, L.I.; Donev, S.G.; Pavlov, R.L.

    2004-01-01

    We investigate a nonparaxial vector generalization of the scalar 3D+1 Nonlinear Schrodinger Equation (NSE). Exact analytical 3D+1 soliton solutions are obtained for the first time in media of spatial dependence of the nonlinear refractive index

  20. Analytical modeling of pressure transient behavior for coalbed methane transport in anisotropic media

    International Nuclear Information System (INIS)

    Wang, Lei; Wang, Xiaodong

    2014-01-01

    Resulting from the nature of anisotropy of coal media, it is a meaningful work to evaluate pressure transient behavior and flow characteristics within coals. In this article, a complete analytical model called the elliptical flow model is established by combining the theory of elliptical flow in anisotropic media and Fick's laws about the diffusion of coalbed methane. To investigate pressure transient behavior, analytical solutions were first obtained through introducing a series of special functions (Mathieu functions), which are extremely complex and are hard to calculate. Thus, a computer program was developed to establish type curves, on which the effects of the parameters, including anisotropy coefficient, storage coefficient, transfer coefficient and rate constant, were analyzed in detail. Calculative results show that the existence of anisotropy would cause great pressure depletion. To validate new analytical solutions, previous results were used to compare with the new results. It is found that a better agreement between the solutions obtained in this work and the literature was achieved. Finally, a case study is used to explain the effects of the parameters, including rock total compressibility coefficient, coal medium porosity and anisotropic permeability, sorption time constant, Langmuir volume and fluid viscosity, on bottom-hole pressure behavior. It is necessary to coordinate these parameters so as to reduce the pressure depletion. (paper)

  1. Analytic solutions of hydrodynamics equations

    International Nuclear Information System (INIS)

    Coggeshall, S.V.

    1991-01-01

    Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

  2. Semianalytical solutions of radioactive or reactive tracer transport in layered fractured media

    International Nuclear Information System (INIS)

    Moridis, G.J.; Bodvarsson, G.S.

    2001-01-01

    In this paper, semianalytical solutions are developed for the problem of transport of radioactive or reactive tracers (solutes or colloids) through a layered system of heterogeneous fractured media with misaligned fractures. The tracer transport equations in the matrix account for (a) diffusion, (b) surface diffusion (for solutes only), (c) mass transfer between the mobile and immobile water fractions, (d) linear kinetic or equilibrium physical, chemical, or combined solute sorption or colloid filtration, and (e) radioactive decay or first order chemical reactions. Any number of radioactive decay daughter products (or products of a linear, first-order reaction chain) can be tracked. The tracer-transport equations in the fractures account for the same processes, in addition to advection and hydrodynamic dispersion. Additionally, the colloid transport equations account for straining and velocity adjustments related to the colloidal size. The solutions, which are analytical in the Laplace space, are numerically inverted to provide the solution in time and can accommodate any number of fractured and/or porous layers. The solutions are verified using analytical solutions for limiting cases of solute and colloid transport through fractured and porous media. The effect of important parameters on the transport of 3 H, 237 Np and 239 Pu (and its daughters) is investigated in several test problems involving layered geological systems of varying complexity. 239 Pu colloid transport problems in multilayered systems indicate significant colloid accumulations at straining interfaces but much faster transport of the colloid than the corresponding strongly sorbing solute species

  3. Analytical solution for multi-species contaminant transport in finite media with time-varying boundary conditions

    Science.gov (United States)

    Most analytical solutions available for the equations governing the advective-dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this work we present an ...

  4. Analytic solutions for colloid transport with time- or depth-dependent retention in porous media

    Science.gov (United States)

    Elucidating and quantifying the transport of industrial nanoparticles (e.g. silver, carbon nanotubes, and graphene oxide) and other colloid-size particles such as viruses and bacteria is important to safeguard and manage the quality of the subsurface environment. Analytic solutions were derived for...

  5. Analytical solution of spatial kinetics of the diffusion model for subcritical homogeneous systems driven by external source

    International Nuclear Information System (INIS)

    Oliveira, Fernando Luiz de

    2008-01-01

    This work describes an analytical solution obtained by the expansion method for the spatial kinetics using the diffusion model with delayed emission for source transients in homogeneous media. In particular, starting from simple models, and increasing the complexity, numerical results were obtained for different types of source transients. An analytical solution of the one group without precursors was solved, followed by considering one precursors family. The general case of G-groups with R families of precursor although having a closed form solution, cannot be solved analytically, since there are no explicit formulae for the eigenvalues, and numerical methods must be used to solve such problem. To illustrate the general solution, the multi-group (three groups) time-dependent problem without precursors was solved and the numerical results of a finite difference code were compared with the exact results for different transients. (author)

  6. Social media analytics and research testbed (SMART: Exploring spatiotemporal patterns of human dynamics with geo-targeted social media messages

    Directory of Open Access Journals (Sweden)

    Jiue-An Yang

    2016-06-01

    Full Text Available The multilevel model of meme diffusion conceptualizes how mediated messages diffuse over time and space. As a pilot application of implementing the meme diffusion, we developed the social media analytics and research testbed to monitor Twitter messages and track the diffusion of information in and across different cities and geographic regions. Social media analytics and research testbed is an online geo-targeted search and analytics tool, including an automatic data processing procedure at the backend and an interactive frontend user interface. Social media analytics and research testbed is initially designed to facilitate (1 searching and geo-locating tweet topics and terms in different cities and geographic regions; (2 filtering noise from raw data (such as removing redundant retweets and using machine learning methods to improve precision; (3 analyzing social media data from a spatiotemporal perspective; and (4 visualizing social media data in diagnostic ways (such as weekly and monthly trends, trend maps, top media, top retweets, top mentions, or top hashtags. Social media analytics and research testbed provides researchers and domain experts with a tool that can efficiently facilitate the refinement, formalization, and testing of research hypotheses or questions. Three case studies (flu outbreaks, Ebola epidemic, and marijuana legalization are introduced to illustrate how the predictions of meme diffusion can be examined and to demonstrate the potentials and key functions of social media analytics and research testbed.

  7. Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir

    Directory of Open Access Journals (Sweden)

    Junfeng Ding

    2018-04-01

    Full Text Available Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions.

  8. Semi-analytic solution to planar Helmholtz equation

    Directory of Open Access Journals (Sweden)

    Tukač M.

    2013-06-01

    Full Text Available Acoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costs.

  9. Towards Secure and Trustworthy Cyberspace: Social Media Analytics on Hacker Communities

    Science.gov (United States)

    Li, Weifeng

    2017-01-01

    Social media analytics is a critical research area spawned by the increasing availability of rich and abundant online user-generated content. So far, social media analytics has had a profound impact on organizational decision making in many aspects, including product and service design, market segmentation, customer relationship management, and…

  10. A development of simulation and analytical program for through-diffusion experiments for a single layer of diffusion media

    International Nuclear Information System (INIS)

    Sato, Haruo

    2001-01-01

    A program (TDROCK1. FOR) for simulation and analysis of through-diffusion experiments for a single layer of diffusion media was developed. This program was made by Pro-Fortran language, which was suitable for scientific and technical calculations, and relatively easy explicit difference method was adopted for an analysis. In the analysis, solute concentration in the tracer cell as a function of time that we could not treat to date can be input and the decrease in the solute concentration as a function of time by diffusion from the tracer cell to the measurement cell, the solute concentration distribution in the porewater of diffusion media and the solute concentration in the measurement cell as a function of time can be calculated. In addition, solution volume in both cells and diameter and thickness of the diffusion media are also variable as an input condition. This simulation program could well explain measured result by simulating solute concentration in the measurement cell as a function of time for case which apparent and effective diffusion coefficients were already known. Based on this, the availability and applicability of this program to actual analysis and simulation were confirmed. This report describes the theoretical treatment for the through-diffusion experiments for a single layer of diffusion media, analytical model, an example of source program and the manual. (author)

  11. Analytical solution to the diffusion, sorption and decay chain equation in a saturated porous medium between two reservoirs

    International Nuclear Information System (INIS)

    Guzman, Juan; Maximov, Serguei; Escarela-Perez, Rafael; López-García, Irvin; Moranchel, Mario

    2015-01-01

    The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain

  12. A Social Media Practicum: An Action-Learning Approach to Social Media Marketing and Analytics

    Science.gov (United States)

    Atwong, Catherine T.

    2015-01-01

    To prepare students for the rapidly evolving field of digital marketing, which requires more and more technical skills every year, a social media practicum creates a learning environment in which students can apply marketing principles and become ready for collaborative work in social media marketing and analytics. Using student newspapers as…

  13. Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations

    Science.gov (United States)

    Wagenmaker, Timothy Roger

    This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of

  14. Heat as a groundwater tracer in shallow and deep heterogeneous media: Analytical solution, spreadsheet tool, and field applications

    Science.gov (United States)

    Kurylyk, Barret L.; Irvine, Dylan J.; Carey, Sean K.; Briggs, Martin A.; Werkema, Dale D.; Bonham, Mariah

    2017-01-01

    Groundwater flow advects heat, and thus, the deviation of subsurface temperatures from an expected conduction‐dominated regime can be analysed to estimate vertical water fluxes. A number of analytical approaches have been proposed for using heat as a groundwater tracer, and these have typically assumed a homogeneous medium. However, heterogeneous thermal properties are ubiquitous in subsurface environments, both at the scale of geologic strata and at finer scales in streambeds. Herein, we apply the analytical solution of Shan and Bodvarsson (2004), developed for estimating vertical water fluxes in layered systems, in 2 new environments distinct from previous vadose zone applications. The utility of the solution for studying groundwater‐surface water exchange is demonstrated using temperature data collected from an upwelling streambed with sediment layers, and a simple sensitivity analysis using these data indicates the solution is relatively robust. Also, a deeper temperature profile recorded in a borehole in South Australia is analysed to estimate deeper water fluxes. The analytical solution is able to match observed thermal gradients, including the change in slope at sediment interfaces. Results indicate that not accounting for layering can yield errors in the magnitude and even direction of the inferred Darcy fluxes. A simple automated spreadsheet tool (Flux‐LM) is presented to allow users to input temperature and layer data and solve the inverse problem to estimate groundwater flux rates from shallow (e.g., regimes.

  15. Analytic solution for a quartic electron mirror

    Energy Technology Data Exchange (ETDEWEB)

    Straton, Jack C., E-mail: straton@pdx.edu

    2015-01-15

    A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z{sup 2}−r{sup 2}/2) to which we add a quartic term (kλz{sup 4}). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile. - Highlights: • We find the analytical solution for electron mirrors whose curvature has z4 dependence added to the usual z{sup 2} – r{sup 2}/2 terms. • The resulting Jacobi cosine-amplitude function reduces to the well-known cosh solution in the limit where the new term is 0. • This quartic term gives a mirror designer additional flexibility for eliminating spherical and chromatic aberrations. • The possibility of using these analytical results to approximately model spherical tetrode mirrors close to axis is noted.

  16. Transport Visualization for Studying Mass Transfer and Solute Transport in Permeable Media

    International Nuclear Information System (INIS)

    Roy Haggerty

    2004-01-01

    Understanding and predicting mass transfer coupled with solute transport in permeable media is central to several energy-related programs at the US Department of Energy (e.g., CO 2 sequestration, nuclear waste disposal, hydrocarbon extraction, and groundwater remediation). Mass transfer is the set of processes that control movement of a chemical between mobile (advection-dominated) domains and immobile (diffusion- or sorption-dominated) domains within a permeable medium. Consequences of mass transfer on solute transport are numerous and may include (1) increased sequestration time within geologic formations; (2) reduction in average solute transport velocity by as much as several orders of magnitude; (3) long ''tails'' in concentration histories during removal of a solute from a permeable medium; (4) poor predictions of solute behavior over long time scales; and (5) changes in reaction rates due to mass transfer influences on pore-scale mixing of solutes. Our work produced four principle contributions: (1) the first comprehensive visualization of solute transport and mass transfer in heterogeneous porous media; (2) the beginnings of a theoretical framework that encompasses both macrodispersion and mass transfer within a single set of equations; (3) experimental and analytical tools necessary for understanding mixing and aqueous reaction in heterogeneous, granular porous media; (4) a clear experimental demonstration that reactive transport is often not accurately described by a simple coupling of the convection-dispersion equation with chemical reaction equations. The work shows that solute transport in heterogeneous media can be divided into 3 regimes--macrodispersion, advective mass transfer, and diffusive mass transfer--and that these regimes can be predicted quantitatively in binary media. We successfully predicted mass transfer in each of these regimes and verified the prediction by completing quantitative visualization experiments in each of the regimes, the

  17. New analytic solutions of stochastic coupled KdV equations

    International Nuclear Information System (INIS)

    Dai Chaoqing; Chen Junlang

    2009-01-01

    In this paper, firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures.

  18. Contaminant transport in fractured porous media: analytical solution for a two-member decay chain in a single fracture

    International Nuclear Information System (INIS)

    Sudicky, E.A.; Frind, E.O.

    1984-01-01

    An analytical solution is presented for the problem of radionuclide chain decay during transport through a discrete fracture situated in a porous rock matrix. The solution takes into account advection along the fracture, molecular diffusion from the fracture to the porous matrix, adsorption on the fracture face, adsorption in the rock matrix, and radioactive decay. The solution for the daughter product is in the form of a double integral which is evaluated by Gauss-Legendre quadrature. Results show that the daughter product tends to advance ahead of the parent nuclide even when the half-life of the parent is larger. This is attributed to the effect of chain decay in the matrix, which tends to reduce the diffusive loss of the daughter along the fracture. The examples also demonstrate that neglecting the parent nuclide and modeling its daughter as a single species can result in significant overestimation of arrival times at some point along the fracture. Although the analytical solution is restricted to a two-member chain for practical reasons, it represents a more realistic description of nuclide transport along a fracture than available single-species models. The solution may be of use for application to other contaminants undergoing different types of first-order transformation reactions

  19. An algorithm for analytical solution of basic problems featuring elastostatic bodies with cavities and surface flaws

    Science.gov (United States)

    Penkov, V. B.; Levina, L. V.; Novikova, O. S.; Shulmin, A. S.

    2018-03-01

    Herein we propose a methodology for structuring a full parametric analytical solution to problems featuring elastostatic media based on state-of-the-art computing facilities that support computerized algebra. The methodology includes: direct and reverse application of P-Theorem; methods of accounting for physical properties of media; accounting for variable geometrical parameters of bodies, parameters of boundary states, independent parameters of volume forces, and remote stress factors. An efficient tool to address the task is the sustainable method of boundary states originally designed for the purposes of computerized algebra and based on the isomorphism of Hilbertian spaces of internal states and boundary states of bodies. We performed full parametric solutions of basic problems featuring a ball with a nonconcentric spherical cavity, a ball with a near-surface flaw, and an unlimited medium with two spherical cavities.

  20. Analytic Solution to Shell Boundary – Value Problems

    Directory of Open Access Journals (Sweden)

    Yu. I. Vinogradov

    2015-01-01

    Full Text Available Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.

  1. Triangular dislocation: an analytical, artefact-free solution

    Science.gov (United States)

    Nikkhoo, Mehdi; Walter, Thomas R.

    2015-05-01

    Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

  2. Analytic solution of integral equations for molecular fluids

    International Nuclear Information System (INIS)

    Cummings, P.T.

    1984-01-01

    We review some recent progress in the analytic solution of integral equations for molecular fluids. The site-site Ornstein-Zernike (SSOZ) equation with approximate closures appropriate to homonuclear diatomic fluids both with and without attractive dispersion-like interactions has recently been solved in closed form analytically. In this paper, the close relationship between the SSOZ equation for homonuclear dumbells and the usual Ornstein-Zernike (OZ) equation for atomic fluids is carefully elucidated. This relationship is a key motivation for the analytic solutions of the SSOZ equation that have been obtained to date. (author)

  3. Analytic solutions of a class of nonlinearly dynamic systems

    International Nuclear Information System (INIS)

    Wang, M-C; Zhao, X-S; Liu, X

    2008-01-01

    In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently

  4. An analytical solution for improved HIFU SAR estimation

    International Nuclear Information System (INIS)

    Dillon, C R; Vyas, U; Christensen, D A; Roemer, R B; Payne, A

    2012-01-01

    Accurate determination of the specific absorption rates (SARs) present during high intensity focused ultrasound (HIFU) experiments and treatments provides a solid physical basis for scientific comparison of results among HIFU studies and is necessary to validate and improve SAR predictive software, which will improve patient treatment planning, control and evaluation. This study develops and tests an analytical solution that significantly improves the accuracy of SAR values obtained from HIFU temperature data. SAR estimates are obtained by fitting the analytical temperature solution for a one-dimensional radial Gaussian heating pattern to the temperature versus time data following a step in applied power and evaluating the initial slope of the analytical solution. The analytical method is evaluated in multiple parametric simulations for which it consistently (except at high perfusions) yields maximum errors of less than 10% at the center of the focal zone compared with errors up to 90% and 55% for the commonly used linear method and an exponential method, respectively. For high perfusion, an extension of the analytical method estimates SAR with less than 10% error. The analytical method is validated experimentally by showing that the temperature elevations predicted using the analytical method's SAR values determined for the entire 3D focal region agree well with the experimental temperature elevations in a HIFU-heated tissue-mimicking phantom. (paper)

  5. Quasi-three-dimensional analysis of ground water flow and dissolved multicomponent solute transport in saturated porous media

    International Nuclear Information System (INIS)

    Tang, Yi.

    1991-01-01

    A computational procedure was developed in this study to provide flexibility needed in the application of three-dimensional groundwater flow and dissolved multicomponent solute transport simulations. In the first part of this study, analytical solutions were proposed for the dissolved single-component solute transport problem. These closed form solutions were developed for homogeneous but stratified porous media. This analytical model took into account two-dimensional diffusion-advection in the main aquifer layer and one-dimensional diffusion-advection in the adjacent aquitards, as well as first order radioactive decay and linear adsorption isotherm in both aquifer and aquitards. The associated analytical solutions for solute concentration distributions in the aquifer and aquitards were obtained using Laplace Transformation and Method of Separation of Variables techniques. Next, in order to analyze the problem numerically, a quasi-three-dimensional finite element algorithm was developed based on the multilayer aquifer concept. In this phase, advection, dispersion, adsorption and first order multi-species chemical reaction terms were included to the analysis. Employing this model, without restriction on groundwater flow pattern in the multilayer aquifer system, one may analyze the complex behavior of the groundwater flow and solute movement pattern in the system. These numerical models may be utilized as calibration tools in site characterization studies, or as predictive models during the initial stages of a typical site investigation study. Through application to several test and field problems, the usefulness, accuracy and efficiency of the proposed models were demonstrated. Comparison of results with analytical solution, experimental data and other numerical methods were also discussed

  6. Analytical solutions of one-dimensional advection–diffusion

    Indian Academy of Sciences (India)

    Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal finite initially solute free domain,for two dispersion problems.In the first one,temporally dependent solute dispersion along uniform flow in homogeneous domain is studied.In the second problem the ...

  7. 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.

  8. 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.

  9. Teaching Social Media Analytics: An Assessment Based on Natural Disaster Postings

    Science.gov (United States)

    Goh, Tiong T.; Sun, Pei-Chen

    2015-01-01

    Unstructured data in social media is as part of the "big data" spectrum. Unstructured data in Social media can provide useful insights into social phenomena and citizen opinions, both of which are critical to government policy and businesses decisions. Teachers of business intelligence and analytics commonly use quantitative data from…

  10. Big Data on a Smaller Scale: A Social Media Analytics Assignment

    Science.gov (United States)

    Fischbach, Sarah; Zarzosa, Jennifer

    2018-01-01

    It is truly important for students to understand how to monitor online marketing buzz. This assignment, social media analytics, utilizes the content analysis research method to build student's in-depth understanding on how to evaluate and interpret user-generated content (UGC) to create social media campaigns. The authors adapted Resnik and…

  11. Klasifikasi Daya Tarik Konten Artikel Media Daring Dari Data Google Analytics Dengan C-FDT

    Directory of Open Access Journals (Sweden)

    Erlin Windia Ambarsari

    2018-05-01

    Full Text Available Information of article which had attractive contains as Trending Topics, although this is article hoax or not. The frequency of article's content which created by online media, it can be monitored by Google Analytics. One of the reasons for using Google Analytics is to understand the content of a site which leads to the change and behavior of behind the content. Google Analytics can be regarded as web analytics software with ease of installation. Classification of Google Analytics data with C-Fuzzy Decision Tree (C-FDT, aims to get the attraction of article content, which means having special attention from visitors and the article can be interesting or not, and observed whether C-FDT can recognize patterns from metric data Google Analytics. The purpose of this study is the results of FDT are expected to facilitate online media managers to analyze the content of articles and evaluate content groups tend to potentially gain traffic for getting promotional or marketing advertising as revenue from online media sites. The results obtained are C-FDT can recognize the pattern of Google Analytics metrics thus as facilitating the search of the article content into a simple form that is the reduction of attributes by grouping data with the same object and the data had Pruning. Online media managers can focus on certain attributes that have a big effect on Content Articles. However C-FDT is having trouble dealing with data sync due to system errors when retrieving data from Google Analytics. Therefore it is necessary to monitor data in time series.

  12. Surface solitons in waveguide arrays: Analytical solutions.

    Science.gov (United States)

    Kominis, Yannis; Papadopoulos, Aristeidis; Hizanidis, Kyriakos

    2007-08-06

    A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear or nonlinear homogeneous medium as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of each part in order to assure existence of solutions with specific profile characteristics. The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations and interesting features are presented such as their remarkable robustness which could facilitate their experimental observation.

  13. Analytical solution of population balance equation involving ...

    Indian Academy of Sciences (India)

    This paper presents an effective analytical simulation to solve population .... considering spatial dependence and growth, based on the so-called LPA formulation as .... But the particle size distribution is defined so that n(v,t) dx is the number of ..... that was made beforehand in the construction of the analytical solutions ...

  14. Analytical solutions for one-dimensional advection–dispersion ...

    Indian Academy of Sciences (India)

    We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0.

  15. A nonequilibrium model for reactive contaminant transport through fractured porous media: Model development and semianalytical solution

    Science.gov (United States)

    Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.

    2012-10-01

    In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.

  16. Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

    Science.gov (United States)

    Ding, Xiao-Li; Nieto, Juan J.

    2017-11-01

    In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

  17. Analytical Solution of General Bagley-Torvik Equation

    Directory of Open Access Journals (Sweden)

    William Labecca

    2015-01-01

    Full Text Available Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomogeneous case is solved without restrictions in boundary and initial conditions. The generalized Mittag-Leffler functions with three parameters are used and the solutions presented are expressed in terms of Wiman’s functions and their derivatives.

  18. Applicability of the Analytical Solution to N-Person Social Dilemma Games

    Directory of Open Access Journals (Sweden)

    Ugo Merlone

    2018-05-01

    Full Text Available The purpose of this study is to present an analysis of the applicability of an analytical solution to the N−person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent based simulation. However, no discussion has been offered for the applicability of this result in all Prisoners' Dilemma game scenarios or in other N−person social dilemma games such as Chicken or Stag Hunt. In this paper it is shown that the analytical solution works in all social games where the linear payoff functions are such that each agent's cooperating probability fluctuates around the analytical solution without cooperating or defecting with certainty. The social game regions where this determination holds are explored by varying payoff function parameters. It is found by both simulation and a special method that the analytical solution applies best in Chicken when the payoff parameter S is slightly negative and then the analytical solution slowly degrades as S becomes more negative. It turns out that the analytical solution is only a good estimate for Prisoners' Dilemma games and again becomes worse as S becomes more negative. A sensitivity analysis is performed to determine the impact of different initial cooperating probabilities, learning factors, and neighborhood size.

  19. An analytical solution for the Marangoni mixed convection boundary layer flow

    DEFF Research Database (Denmark)

    Moghimi, M. A.; Kimiaeifar, Amin; Rahimpour, M.

    2010-01-01

    In this article, an analytical solution for a Marangoni mixed convection boundary layer flow is presented. A similarity transform reduces the Navier-Stokes equations to a set of nonlinear ordinary differential equations, which are solved analytically by means of the homotopy analysis method (HAM...... the convergence of the solution. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on the HAM....

  20. Exact analytical solutions for nonlinear reaction-diffusion equations

    International Nuclear Information System (INIS)

    Liu Chunping

    2003-01-01

    By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

  1. Analytical solution of one dimensional temporally dependent ...

    African Journals Online (AJOL)

    user

    transfer of heat in fluids, flow through porous media, and the spread of ... In present paper, advection-dispersion equation is considered one dimensional longitudinal initially solute free semi- .... free. Thus initial and boundary conditions for eq.

  2. Analytical Solution of General Bagley-Torvik Equation

    OpenAIRE

    William Labecca; Osvaldo Guimarães; José Roberto C. Piqueira

    2015-01-01

    Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomoge...

  3. Analytic Solutions of Special Functional Equations

    Directory of Open Access Journals (Sweden)

    Octav Olteanu

    2013-07-01

    Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.

  4. Cloud-Based Social Media Visual Analytics Disaster Response System, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — We propose a next-generation cloud-based social media visual analytics disaster response system that will enable decision-makers and first-responders to obtain...

  5. Approximate analytical solution of two-dimensional multigroup P-3 equations

    International Nuclear Information System (INIS)

    Matausek, M.V.; Milosevic, M.

    1981-01-01

    Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)

  6. Analytical Solutions of the KDV-KZK Equation

    Science.gov (United States)

    Gan, W. S.

    The KdV-KZK equation for fluids developed by me was presented at the ICSV 11 in St. Petersburg in July 2004. In this paper, I made an attempt on the analytical solutions of this equation using the perturbation method. Some physical interpretation of the solutions is given. A brief introduction to KdV-KZK equation for solids is given

  7. Analytic solutions of nonlinear Cournot duopoly game

    Directory of Open Access Journals (Sweden)

    Akio Matsumoto

    2005-01-01

    Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.

  8. Analytical solution for Van der Pol-Duffing oscillators

    International Nuclear Information System (INIS)

    Kimiaeifar, A.; Saidi, A.R.; Bagheri, G.H.; Rahimpour, M.; Domairry, D.G.

    2009-01-01

    In this paper, the problem of single-well, double-well and double-hump Van der Pol-Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the 'Homotopy Analysis Method' (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. This method is a capable tool for solving this kind of nonlinear problems.

  9. Approximate analytical solution of two-dimensional multigroup P-3 equations

    International Nuclear Information System (INIS)

    Matausek, M.V.; Milosevic, M.

    1981-01-01

    Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de

  10. Analytic plane wave solutions for the quaternionic potential step

    International Nuclear Information System (INIS)

    De Leo, Stefano; Ducati, Gisele C.; Madureira, Tiago M.

    2006-01-01

    By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in the presence of a quaternionic step potential. The analytic solution for the stationary states allows one to explicitly show the qualitative and quantitative differences between this quaternionic quantum dynamical system and its complex counterpart. A brief discussion on reflected and transmitted times, performed by using the stationary phase method, and its implication on the experimental evidence for deviations of standard quantum mechanics is also presented. The analytic solution given in this paper represents a fundamental mathematical tool to find an analytic approximation to the quaternionic barrier problem (up to now solved by numerical method)

  11. On the General Analytical Solution of the Kinematic Cosserat Equations

    KAUST Repository

    Michels, Dominik L.

    2016-09-01

    Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

  12. On the General Analytical Solution of the Kinematic Cosserat Equations

    KAUST Repository

    Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.

    2016-01-01

    Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

  13. Measurement of Solute Diffusion Behavior in Fractured Waste Glass Media

    International Nuclear Information System (INIS)

    Saripalli, Kanaka P.; Lindberg, Michael J.; Meyer, Philip D.

    2008-01-01

    Determination of aqueous phase diffusion coefficients of solutes through fractured media is essential for understanding and modeling contaminants transport at many hazardous waste disposal sites. No methods for earlier measurements are available for the characterization of diffusion in fractured glass blocks. We report here the use of time-lag diffusion experimental method to assess the diffusion behavior of three different solutes (Cs, Sr and Pentafluoro Benzoic Acid or PFBA) in fractured, immobilized low activity waste (ILAW) glass forms. A fractured media time-lag diffusion experimental apparatus that allows the measurement of diffusion coefficients has been designed and built for this purpose. Use of time-lag diffusion method, a considerably easier experimental method than the other available methods, was not previously demonstrated for measuring diffusion in any fractured media. Hydraulic conductivity, porosity and diffusion coefficients of a solute were experimentally measured in fractured glass blocks using this method for the first time. Results agree with the range of properties reported for similar rock media earlier, indicating that the time-lag experimental method can effectively characterize the diffusion coefficients of fractured ILAW glass media

  14. On the Partial Analytical Solution of the Kirchhoff Equation

    KAUST Repository

    Michels, Dominik L.

    2015-09-01

    We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.

  15. On the Partial Analytical Solution of the Kirchhoff Equation

    KAUST Repository

    Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Sobottka, Gerrit A.; Weber, Andreas G.

    2015-01-01

    We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.

  16. Analytic solutions of QCD motivated Hamiltonians at low energy

    International Nuclear Information System (INIS)

    Yepez, T.; Amor, A.; Hess, P.O.; Szczepaniak, A.; Civitarese, O.

    2011-01-01

    A model Hamiltonian, motivated by QCD, is investigated in order to study only the quark sector, then only the gluon sector and finally both together. Restricting to the pure quark sector and setting the mass of the quarks to zero, we find analytic solutions, involving two to three orbitals. Allowing the mass of the quarks to be different to zero, we find semi-analytic solutions involving an arbitrary number of orbitals. Afterwards, we indicate on how to incorporate gluons. (author)

  17. Analytical Solution for Time-drawdown Response to Constant Pumping from a Homogeneous, Confined Horizontal Aquifer with Unidirectional Flow

    Science.gov (United States)

    Parrish, K. E.; Zhang, J.; Teasdale, E.

    2007-12-01

    An exact analytical solution to the ordinary one-dimensional partial differential equation is derived for transient groundwater flow in a homogeneous, confined, horizontal aquifer using Laplace transformation. The theoretical analysis is based on the assumption that the aquifer is homogeneous and one-dimensional (horizontal); confined between impermeable formations on top and bottom; and of infinite horizontal extent and constant thickness. It is also assumed that there is only a single pumping well penetrating the entire aquifer; flow is everywhere horizontal within the aquifer to the well; the well is pumping with a constant discharge rate; the well diameter is infinitesimally small; and the hydraulic head is uniform throughout the aquifer before pumping. Similar to the Theis solution, this solution is suited to determine transmissivity and storativity for a two- dimensional, vertically confined aquifer, such as a long vertically fractured zone of high permeability within low permeable rocks or a long, high-permeability trench inside a low-permeability porous media. In addition, it can be used to analyze time-drawdown responses to pumping and injection in similar settings. The solution can also be used to approximate the groundwater flow for unconfined conditions if (1) the variation of transmissivity is negligible (groundwater table variation is small in comparison to the saturated thickness); and (2) the unsaturated flow is negligible. The errors associated with the use of the solution to unconfined conditions depend on the accuracies of the above two assumptions. The solution can also be used to assess the impacts of recharge from a seasonal river or irrigation canal on the groundwater system by assuming uniform, time- constant recharge along the river or canal. This paper presents the details for derivation of the analytical solution. The analytical solution is compared to numerical simulation results with example cases. Its accuracy is also assessed and

  18. Analytical solutions in the two-cavity coupling problem

    International Nuclear Information System (INIS)

    Ayzatsky, N.I.

    2000-01-01

    Analytical solutions of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases.For their derivation we have used the method of solution of an infinite set of linear algebraic equations,based on its transformation into dual integral equations

  19. A comprehensive analytical solution of the nonlinear pendulum

    International Nuclear Information System (INIS)

    Ochs, Karlheinz

    2011-01-01

    In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions and starts with the solution of a pendulum that swings over. Due to a meticulous sign correction term, this solution is also valid if the pendulum does not swing over.

  20. Analytic continuation of solutions of some nonlinear convolution partial differential equations

    Directory of Open Access Journals (Sweden)

    Hidetoshi Tahara

    2015-01-01

    Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.

  1. Analytical solutions of advection-dispersion equation for varying ...

    African Journals Online (AJOL)

    Analytical solutions are obtained for a one-dimensional advection–dispersion equation with variable coefficients in a longitudinal domain. Two cases are considered. In the first one the solute dispersion is time dependent along a uniform flow in a semi-infinite domain while in the second case the dispersion and the velocity ...

  2. Homogenized blocked arcs for multicriteria optimization of radiotherapy: Analytical and numerical solutions

    International Nuclear Information System (INIS)

    Fenwick, John D.; Pardo-Montero, Juan

    2010-01-01

    Purpose: Homogenized blocked arcs are intuitively appealing as basis functions for multicriteria optimization of rotational radiotherapy. Such arcs avoid an organ-at-risk (OAR), spread dose out well over the rest-of-body (ROB), and deliver homogeneous doses to a planning target volume (PTV) using intensity modulated fluence profiles, obtainable either from closed-form solutions or iterative numerical calculations. Here, the analytic and iterative arcs are compared. Methods: Dose-distributions have been calculated for nondivergent beams, both including and excluding scatter, beam penumbra, and attenuation effects, which are left out of the derivation of the analytic arcs. The most straightforward analytic arc is created by truncating the well-known Brahme, Roos, and Lax (BRL) solution, cutting its uniform dose region down from an annulus to a smaller nonconcave region lying beyond the OAR. However, the truncation leaves behind high dose hot-spots immediately on either side of the OAR, generated by very high BRL fluence levels just beyond the OAR. These hot-spots can be eliminated using alternative analytical solutions ''C'' and ''L,'' which, respectively, deliver constant and linearly rising fluences in the gap region between the OAR and PTV (before truncation). Results: Measured in terms of PTV dose homogeneity, ROB dose-spread, and OAR avoidance, C solutions generate better arc dose-distributions than L when scatter, penumbra, and attenuation are left out of the dose modeling. Including these factors, L becomes the best analytical solution. However, the iterative approach generates better dose-distributions than any of the analytical solutions because it can account and compensate for penumbra and scatter effects. Using the analytical solutions as starting points for the iterative methodology, dose-distributions almost as good as those obtained using the conventional iterative approach can be calculated very rapidly. Conclusions: The iterative methodology is

  3. Analytical solution to the hybrid diffusion-transport equation

    International Nuclear Information System (INIS)

    Nanneh, M.M.; Williams, M.M.R.

    1986-01-01

    A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)

  4. General analytical shakedown solution for structures with kinematic hardening materials

    Science.gov (United States)

    Guo, Baofeng; Zou, Zongyuan; Jin, Miao

    2016-09-01

    The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.

  5. Analytical solution of dispersion relations for the nuclear optical model

    Energy Technology Data Exchange (ETDEWEB)

    VanderKam, J.M. [Center for Communications Research, Thanet Road, Princeton, NJ 08540 (United States); Weisel, G.J. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States); Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 (United States); Tornow, W. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States)

    2000-12-01

    Analytical solutions of dispersion integral relations, linking the real and imaginary parts of the nuclear optical model, have been derived. These are displayed for some widely used forms of the volume- and surface-absorptive nuclear potentials. When the analytical solutions are incorporated into the optical-model search code GENOA, replacing a numerical integration, the code runs three and a half to seven times faster, greatly aiding the analysis of direct-reaction, elastic scattering data. (author)

  6. Analytical solution for heat conduction problem in composite slab and its implementation in constructal solution for cooling of electronics

    International Nuclear Information System (INIS)

    Kuddusi, Luetfullah; Denton, Jesse C.

    2007-01-01

    The constructal solution for cooling of electronics requires solution of a fundamental heat conduction problem in a composite slab composed of a heat generating slab and a thin strip of high conductivity material that is responsible for discharging the generated heat to a heat sink located at one end of the strip. The fundamental 2D heat conduction problem is solved analytically by applying an integral transform method. The analytical solution is then employed in a constructal solution, following Bejan, for cooling of electronics. The temperature and heat flux distributions of the elemental heat generating slabs are assumed to be the same as those of the analytical solution in all the elemental volumes and the high conductivity strips distributed in the different constructs. Although the analytical solution of the fundamental 2D heat conduction problem improves the accuracy of the distributions in the elemental slabs, the results following Bejan's strategy do not affirm the accuracy of Bejan's constructal solution itself as applied to this problem of cooling of electronics. Several different strategies are possible for developing a constructal solution to this problem as is indicated

  7. Analytical SN solutions in heterogeneous slabs using symbolic algebra computer programs

    International Nuclear Information System (INIS)

    Warsa, J.S.

    2002-01-01

    A modern symbolic algebra computer program, MAPLE, is used to compute solutions to the well-known analytical discrete ordinates, or S N , solutions in one-dimensional, slab geometry. Symbolic algebra programs compute the solutions with arbitrary precision and are free of spatial discretization error so they can be used to investigate new discretizations for one-dimensional slab, geometry S N methods. Pointwise scalar flux solutions are computed for several sample calculations of interest. Sample MAPLE command scripts are provided to illustrate how easily the theory can be translated into a working solution and serve as a complete tool capable of computing analytical S N solutions for mono-energetic, one-dimensional transport problems

  8. Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis

    Directory of Open Access Journals (Sweden)

    Przemysław Korohoda

    2013-01-01

    Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.

  9. Modeling and analytical simulation of a smouldering carbonaceous ...

    African Journals Online (AJOL)

    Modeling and analytical simulation of a smouldering carbonaceous rod. A.A. Mohammed, R.O. Olayiwola, M Eseyin, A.A. Wachin. Abstract. Modeling of pyrolysis and combustion in a smouldering fuel bed requires the solution of flow, heat and mass transfer through porous media. This paper presents an analytical method ...

  10. Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

    Science.gov (United States)

    Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

    2017-11-01

    There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

  11. Analytical solutions to orthotropic variable thickness disk problems

    Directory of Open Access Journals (Sweden)

    Ahmet N. ERASLAN

    2016-02-01

    Full Text Available An analytical model is developed to estimate the mechanical response of nonisothermal, orthotropic, variable thickness disks under a variety of boundary conditions. Combining basic mechanical equations of disk geometry with the equations of orthotropic material, the elastic equation of the disk is obtained. This equation is transformed into a standard hypergeometric differential equation by means of a suitable transformation. An analytical solution is then obtained in terms of hypergeometric functions. The boundary conditions used to complete the solutions simulate rotating annular disks with two free surfaces, stationary annular disks with pressurized inner and free outer surfaces, and free inner and pressurized outer surfaces. The results of the solutions to each of these cases are presented in graphical forms. It is observed that, for the three cases investigated the elastic orthotropy parameter turns out to be an important parameter affecting the elastic behaviorKeywords: Orthotropic disk, Variable thickness, Thermoelasticity, Hypergeometric equation

  12. Big Data Analytics: Challenges And Applications For Text, Audio, Video, And Social Media Data

    OpenAIRE

    Jai Prakash Verma; Smita Agrawal; Bankim Patel; Atul Patel

    2016-01-01

    All types of machine automated systems are generating large amount of data in different forms like statistical, text, audio, video, sensor, and bio-metric data that emerges the term Big Data. In this paper we are discussing issues, challenges, and application of these types of Big Data with the consideration of big data dimensions. Here we are discussing social media data analytics, content based analytics, text data analytics, audio, and video data analytics their issues and expected applica...

  13. Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

    International Nuclear Information System (INIS)

    Pappas, George

    2009-01-01

    We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R ISCO ), the rotation frequency and the epicyclic frequencies Ω ρ , Ω z . Finally we present some results of the comparison.

  14. Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

    Energy Technology Data Exchange (ETDEWEB)

    Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

    2009-10-01

    We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.

  15. Quantum decay model with exact explicit analytical solution

    Science.gov (United States)

    Marchewka, Avi; Granot, Er'El

    2009-01-01

    A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

  16. An analytical solution to assess the SH seismoelectric response of the vadose zone

    Science.gov (United States)

    Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.

    2018-03-01

    We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a one-dimensional soil constituted by a single layer on top of a half space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than

  17. An analytical solution to assess the SH seismoelectric response of the vadose zone

    Science.gov (United States)

    Monachesi, L. B.; Zyserman, F. I.; Jouniaux, L.

    2018-06-01

    We derive an analytical solution of the seismoelectric conversions generated in the vadose zone, when this region is crossed by a pure shear horizontal (SH) wave. Seismoelectric conversions are induced by electrokinetic effects linked to relative motions between fluid and porous media. The considered model assumes a 1D soil constituted by a single layer on top of a half-space in contact at the water table, and a shearing force located at the earth's surface as the wave source. The water table is an interface expected to induce a seismoelectric interfacial response (IR). The top layer represents a porous rock in which porous space is partially saturated by water and air, while the half-space is completely saturated with water, representing the saturated zone. The analytical expressions for the coseismic fields and the interface responses, both electric and magnetic, are derived by solving Pride's equations with proper boundary conditions. An approximate analytical expression of the solution is also obtained, which is very simple and applicable in a fairly broad set of situations. Hypothetical scenarios are proposed to study and analyse the dependence of the electromagnetic fields on various parameters of the medium. An analysis of the approximate solution is also made together with a comparison to the exact solution. The main result of the present analysis is that the amplitude of the interface response generated at the water table is found to be proportional to the jump in the electric current density, which in turn depends on the saturation contrast, poro-mechanical and electrical properties of the medium and on the amplitude of the solid displacement produced by the source. This result is in agreement with the one numerically obtained by the authors, which has been published in a recent work. We also predict the existence of an interface response located at the surface, and that the electric interface response is several orders of magnitude bigger than the

  18. Radionuclide transport in fractured porous media -- Analytical solutions for a system of parallel fractures with a constant inlet flux

    International Nuclear Information System (INIS)

    Chen, C.T.; Li, S.H.

    1997-01-01

    Analytical solutions are developed for the problem of radionuclide transport in a system of parallel fractures situated in a porous rock matrix. A constant flux is used as the inlet boundary condition. The solutions consider the following processes: (a) advective transport along the fractures; (b) mechanical dispersion and molecular diffusion along the fractures; (c) molecular diffusion from a fracture to the porous matrix; (d) molecular diffusion within the porous matrix in the direction perpendicular to the fracture axis; (e) adsorption onto the fracture wall; (f) adsorption within the porous matrix, and (g) radioactive decay. The solutions are based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. The steady-state solutions are also provided. A number of examples are given to illustrate the effects of various important parameters, including: (a) fracture spacing; (b) fracture dispersion coefficient; (c) matrix diffusion coefficient; (d) fracture width; (e) groundwater velocity; (f) matrix retardation factor; and (g) matrix porosity

  19. Solution standards for quality control of nuclear-material analytical measurements

    International Nuclear Information System (INIS)

    Clark, J.P.

    1981-01-01

    Analytical chemistry measurement control depends upon reliable solution standards. At the Savannah River Plant Control Laboratory over a thousand analytical measurements are made daily for process control, product specification, accountability, and nuclear safety. Large quantities of solution standards are required for a measurement quality control program covering the many different analytical chemistry methods. Savannah River Plant produced uranium, plutonium, neptunium, and americium metals or oxides are dissolved to prepare stock solutions for working or Quality Control Standards (QCS). Because extensive analytical effort is required to characterize or confirm these solutions, they are prepared in large quantities. These stock solutions are diluted and blended with different chemicals and/or each other to synthesize QCS that match the matrices of different process streams. The target uncertainty of a standard's reference value is 10% of the limit of error of the methods used for routine measurements. Standard Reference Materials from NBS are used according to special procedures to calibrate the methods used in measuring the uranium and plutonium standards so traceability can be established. Special precautions are required to minimize the effects of temperature, radiolysis, and evaporation. Standard reference values are periodically corrected to eliminate systematic errors caused by evaporation or decay products. Measurement control is achieved by requiring analysts to analyze a blind QCS each shift a measurement system is used on plant samples. Computer evaluation determines whether or not a measurement is within the +- 3 sigma control limits. Monthly evaluations of the QCS measurements are made to determine current bias correction factors for accountability measurements and detect significant changes in the bias and precision statistics. The evaluations are also used to plan activities for improving the reliability of the analytical chemistry measurements

  20. 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.

  1. Explicit analytical solution of the nonlinear Vlasov Poisson system

    International Nuclear Information System (INIS)

    Skarka, V.; Mahajan, S.M.; Fijalkow, E.

    1993-10-01

    In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

  2. From digital positivism and administrative big data analytics towards critical digital and social media research!

    OpenAIRE

    Fuchs, Christian

    2017-01-01

    This essay argues for a paradigm shift in the study of the Internet and digital/social media. Big data analytics is the dominant paradigm. It receives large amounts of funding, is administrative and a form of digital positivism. Critical social media research is an alternative approach that combines critical social media theory, critical digital methods and critical-realist social media research ethics. Strengthening the second approach is a material question of power in academia.

  3. A Study of Analytical Solution for the Special Dissolution Rate Model of Rock Salt

    Directory of Open Access Journals (Sweden)

    Xin Yang

    2017-01-01

    Full Text Available By calculating the concentration distributions of rock salt solutions at the boundary layer, an ordinary differential equation for describing a special dissolution rate model of rock salt under the assumption of an instantaneous diffusion process was established to investigate the dissolution mechanism of rock salt under transient but stable conditions. The ordinary differential equation was then solved mathematically to give an analytical solution and related expressions for the dissolved radius and solution concentration. Thereafter, the analytical solution was fitted with transient dissolution test data of rock salt to provide the dissolution parameters at different flow rates, and the physical meaning of the analytical formula was also discussed. Finally, the influential factors of the analytical formula were investigated. There was approximately a linear relationship between the dissolution parameters and the flow rate. The effects of the dissolution area and initial volume of the solution on the dissolution rate equation of rock salt were computationally investigated. The results showed that the present analytical solution gives a good description of the dissolution mechanism of rock salt under some special conditions, which may provide a primary theoretical basis and an analytical way to investigate the dissolution characteristics of rock salt.

  4. Comparison of NMR simulations of porous media derived from analytical and voxelized representations.

    Science.gov (United States)

    Jin, Guodong; Torres-Verdín, Carlos; Toumelin, Emmanuel

    2009-10-01

    We develop and compare two formulations of the random-walk method, grain-based and voxel-based, to simulate the nuclear-magnetic-resonance (NMR) response of fluids contained in various models of porous media. The grain-based approach uses a spherical grain pack as input, where the solid surface is analytically defined without an approximation. In the voxel-based approach, the input is a computer-tomography or computer-generated image of reconstructed porous media. Implementation of the two approaches is largely the same, except for the representation of porous media. For comparison, both approaches are applied to various analytical and digitized models of porous media: isolated spherical pore, simple cubic packing of spheres, and random packings of monodisperse and polydisperse spheres. We find that spin magnetization decays much faster in the digitized models than in their analytical counterparts. The difference in decay rate relates to the overestimation of surface area due to the discretization of the sample; it cannot be eliminated even if the voxel size decreases. However, once considering the effect of surface-area increase in the simulation of surface relaxation, good quantitative agreement is found between the two approaches. Different grain or pore shapes entail different rates of increase of surface area, whereupon we emphasize that the value of the "surface-area-corrected" coefficient may not be universal. Using an example of X-ray-CT image of Fontainebleau rock sample, we show that voxel size has a significant effect on the calculated surface area and, therefore, on the numerically simulated magnetization response.

  5. Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

    Science.gov (United States)

    Rúa Taborda, María. Isabel

    2014-05-01

    In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.

  6. Hierarchically sinergistical integration of Social Media Analytics/Social CRM with Business Intelligence and with the Geographic Information System

    OpenAIRE

    Круковський, Ігор Анатолійович; Хомів, Богдан Арсенович; Гаврилюк, Всеволод Леонідович

    2014-01-01

    The actuality of integration of Social Media Analytics/Social CRM with Decision Support Systems on the basis of Business Intelligence 2.0 (DSS/BI 2.0) and with the Geographic Information System is presented. On the basis of their integration a new type of DSS is offered - Social Media Spatial DSS/BI. The variant is shown of this system realization on the programmatic platform of Social Media Analytics of the SemanticForce Company, which has its own semantic analyzer Blueberry. The suitability...

  7. An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

    DEFF Research Database (Denmark)

    Larsen, Niels Vesterdal; Breinbjerg, Olav

    2004-01-01

    Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

  8. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Ji Juan-Juan

    2017-01-01

    Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

  9. Analytic solutions of the multigroup space-time reactor kinetics equations

    International Nuclear Information System (INIS)

    Lee, C.E.; Rottler, S.

    1986-01-01

    The development of analytical and numerical solutions to the reactor kinetics equations is reviewed. Analytic solutions of the multigroup space-time reactor kinetics equations are developed for bare and reflected slabs and spherical reactors for zero flux, zero current and extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but spatially-dependent source terms and initial conditions are investigated. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method. These equations are solved by matrix Green's functions yielding a general matrix solution for the neutron flux and precursor concentration in the Laplace transform space. The detailed pole structure of the Laplace transform matrix solutions is investigated. The temporally- and spatially-dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, the theorem of Frobenius, a knowledge of the detailed pole structure and matrix operators. (author)

  10. Analytic vortex solutions on compact hyperbolic surfaces

    International Nuclear Information System (INIS)

    Maldonado, Rafael; Manton, Nicholas S

    2015-01-01

    We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations. (paper)

  11. Analytical study in 1D nuclear waste migration

    International Nuclear Information System (INIS)

    Perez Guerrero, Jesus S.; Heilbron Filho, Paulo L.; Romani, Zrinka V.

    1999-01-01

    The simulation of the nuclear waste migration phenomena are governed mainly by diffusive-convective equation that includes the effects of hydrodynamic dispersion (mechanical dispersion and molecular diffusion), radioactive decay and chemical interaction. For some special problems (depending on the boundary conditions and when the domain is considered infinite or semi-infinite) an analytical solution may be obtained using classical analytical methods such as Laplace Transform or variable separation. The hybrid Generalized Integral Transform Technique (GITT) is a powerful tool that can be applied to solve diffusive-convective linear problems to obtain formal analytical solutions. The aim of this work is to illustrate that the GITT may be used to obtain an analytical formal solution for the study of migration of radioactive waste in saturated flow porous media. A case test considering 241 Am radionuclide is presented. (author)

  12. Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations

    Energy Technology Data Exchange (ETDEWEB)

    Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares

    2015-07-01

    This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)

  13. Cell culture media impact on drug product solution stability.

    Science.gov (United States)

    Purdie, Jennifer L; Kowle, Ronald L; Langland, Amie L; Patel, Chetan N; Ouyang, Anli; Olson, Donald J

    2016-07-08

    To enable subcutaneous administration of monoclonal antibodies, drug product solutions are often needed at high concentrations. A significant risk associated with high drug product concentrations is an increase in aggregate level over the shelf-life dating period. While much work has been done to understand the impact of drug product formulation on aggregation, there is limited understanding of the link between cell culture process conditions and soluble aggregate growth in drug product. During cell culture process development, soluble aggregates are often measured at harvest using cell-free material purified by Protein A chromatography. In the work reported here, cell culture media components were evaluated with respect to their impact on aggregate levels in high concentration solution drug product during accelerated stability studies. Two components, cysteine and ferric ammonium citrate, were found to impact aggregate growth rates in our current media (version 1) leading to the development of new chemically defined media and concentrated feed formulations. The new version of media and associated concentrated feeds (version 2) were evaluated across four cell lines producing recombinant IgG4 monoclonal antibodies and a bispecific antibody. In all four cell lines, the version 2 media reduced aggregate growth over the course of a 12 week accelerated stability study compared with the version 1 media, although the degree to which aggregate growth decreased was cell line dependent. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:998-1008, 2016. © 2016 American Institute of Chemical Engineers.

  14. Solution of the porous media equation by Adomian's decomposition method

    International Nuclear Information System (INIS)

    Pamuk, Serdal

    2005-01-01

    The particular exact solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer, and in biological systems are obtained using Adomian's decomposition method. Also, numerical comparison of particular solutions in the decomposition method indicate that there is a very good agreement between the numerical solutions and particular exact solutions in terms of efficiency and accuracy

  15. Analytical solution for a coaxial plasma gun: Weak coupling limit

    International Nuclear Information System (INIS)

    Dietz, D.

    1987-01-01

    The analytical solution of the system of coupled ODE's which describes the time evolution of an ideal (i.e., zero resistance) coaxial plasma gun operating in the snowplow mode is obtained in the weak coupling limit, i.e, when the gun is fully influenced by the driving (RLC) circuit in which it resides but the circuit is negligibly influenced by the gun. Criteria for the validity of this limit are derived and numerical examples are presented. Although others have obtained approximate, asymptotic and numerical solutions of the equations, the present analytical results seem not to have appeared previously in the literature

  16. Analytic solutions for marginal deformations in open superstring field theory

    International Nuclear Information System (INIS)

    Okawa, Y.

    2007-04-01

    We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular. (orig.)

  17. On Analytic Solution of resonant Mixing for Solar Neutrino Oscillations

    OpenAIRE

    Masatoshi, ITO; Takao, KANEKO; Masami, NAKAGAWA; Department of Physics, Meijo University; Department of Physics, Meijo University; Department of Physics, Meijo University

    1988-01-01

    Behavior of resonant mixing in matter-enhancing region for solar neutrino oscillation, the Mikheyev-Smirnov-Wolfenstein mechanism, is reanalyzed by means of an analytic treatment recently proposed. We give solutions in terms of confluent hypergeometric functions, which agree with "exact" solutions of coupled differential equations.

  18. Computation of potentials from current electrodes in cylindrically stratified media: A stable, rescaled semi-analytical formulation

    Science.gov (United States)

    Moon, Haksu; Teixeira, Fernando L.; Donderici, Burkay

    2015-01-01

    We present an efficient and robust semi-analytical formulation to compute the electric potential due to arbitrary-located point electrodes in three-dimensional cylindrically stratified media, where the radial thickness and the medium resistivity of each cylindrical layer can vary by many orders of magnitude. A basic roadblock for robust potential computations in such scenarios is the poor scaling of modified-Bessel functions used for computation of the semi-analytical solution, for extreme arguments and/or orders. To accommodate this, we construct a set of rescaled versions of modified-Bessel functions, which avoids underflows and overflows in finite precision arithmetic, and minimizes round-off errors. In addition, several extrapolation methods are applied and compared to expedite the numerical evaluation of the (otherwise slowly convergent) associated Sommerfeld-type integrals. The proposed algorithm is verified in a number of scenarios relevant to geophysical exploration, but the general formulation presented is also applicable to other problems governed by Poisson equation such as Newtonian gravity, heat flow, and potential flow in fluid mechanics, involving cylindrically stratified environments.

  19. Analytical exact solution of the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

    2011-01-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  20. The big bang and inflation united by an analytic solution

    International Nuclear Information System (INIS)

    Bars, Itzhak; Chen, Shih-Hung

    2011-01-01

    Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index, and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the big bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Friedmann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in the 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow-roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time; rather, it oscillates around the potential minimum while settling down, unlike the slow-roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.

  1. Causality and analyticity in optics

    International Nuclear Information System (INIS)

    Nussenzveig, H.M.

    In order to provide an overall picture of the broad range of optical phenomena that are directly linked with the concepts of causality and analyticity, the following topics are briefly reviewed, emphasizing recent developments: 1) Derivation of dispersion relations for the optical constants of general linear media from causality. Application to the theory of natural optical activity. 2) Derivation of sum rules for the optical constants from causality and from the short-time response function (asymptotic high-frequency behavior). Average spectral behavior of optical media. Applications. 3) Role of spectral conditions. Analytic properties of coherence functions in quantum optics. Reconstruction theorem.4) Phase retrieval problems. 5) Inverse scattering problems. 6) Solution of nonlinear evolution equations in optics by inverse scattering methods. Application to self-induced transparency. Causality in nonlinear wave propagation. 7) Analytic continuation in frequency and angular momentum. Complex singularities. Resonances and natural-mode expansions. Regge poles. 8) Wigner's causal inequality. Time delay. Spatial displacements in total reflection. 9) Analyticity in diffraction theory. Complex angular momentum theory of Mie scattering. Diffraction as a barrier tunnelling effect. Complex trajectories in optics. (Author) [pt

  2. Analytic solution for one-dimensional diffusion of radionuclides from a waste package

    International Nuclear Information System (INIS)

    Oliver, D.L.

    1985-01-01

    This work implements an analytical solution for diffusion of radionuclides from a cylindrical waste form through the packing material into the surrounding host rock. Recent interest in predicting the performance of a proposed geological repository for nuclear waste has led to the development of several computer programs to predict the performance of such a repository for the next several millenia. These numerical codes are generally designed to accommodate a broad spectrum of geometrical configurations and repository conditions in order to accurately predict the behavior of the radionuclides in the repository environment. Confidence in such general purpose codes is gained by verifying the numerical modeling and the software through comparison of the numerical predictions generated by these computer codes with analytical solutions to reasonably complex problems. The analysis discussed herein implements the analytic solution, proposed by J.C. Jaeger in 1941 for radial diffusion through two concentric circular cylinders. Jaeger's solution was applied to the problem of diffusional mass transfer from a long cylindrical waste form and subsequently into the surrounding geological formation. Analytic predictions of fractional release rates, including the effects of sorption, were generated

  3. Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

    KAUST Repository

    Icardi, Matteo

    2014-07-31

    In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed. © 2014 American Physical Society.

  4. Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback

    Science.gov (United States)

    Al Noufaey, K. S.

    2018-06-01

    This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.

  5. A globally convergent and closed analytical solution of the Blasius equation with beneficial applications

    Science.gov (United States)

    Zheng, Jun; Han, Xinyue; Wang, ZhenTao; Li, Changfeng; Zhang, Jiazhong

    2017-06-01

    For about a century, people have been trying to seek for a globally convergent and closed analytical solution (CAS) of the Blasius Equation (BE). In this paper, we proposed a formally satisfied solution which could be parametrically expressed by two power series. Some analytical results of the laminar boundary layer of a flat plate, that were not analytically given in former studies, e.g. the thickness of the boundary layer and higher order derivatives, could be obtained based on the solution. Besides, the heat transfer in the laminar boundary layer of a flat plate with constant temperature could also be analytically formulated. Especially, the solution of the singular situation with Prandtl number Pr=0, which seems impossible to be analyzed in prior studies, could be given analytically. The method for finding the CAS of Blasius equation was also utilized in the problem of the boundary layer regulation through wall injection and slip velocity on the wall surface.

  6. RANCH, Radionuclide Migration in Geological Media

    International Nuclear Information System (INIS)

    Patry, J.; Hadermann, J.

    1991-01-01

    1 - Description of problem or function: One-dimensional transport of radionuclide chains through layered geological media, taking into account longitudinal dispersion, convection and retention. 2 - Method of solution: Semi-analytical solution by Laplace transform. Convolution integrals. 3 - Restrictions on the complexity of the problem: Maximum 4 nuclides and 10 layers. Peclet number large compared to 1

  7. A Quantum Dot with Spin-Orbit Interaction--Analytical Solution

    Science.gov (United States)

    Basu, B.; Roy, B.

    2009-01-01

    The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.

  8. Bound dipole solitary solutions in anisotropic nonlocal self-focusing media

    DEFF Research Database (Denmark)

    Mamaev, A.V.; Zozulya, A.A.; Mezentsev, V.K.

    1997-01-01

    We find and analyze bound dipole solitary solutions in media with anisotropic nonlocal photorefractive material response. The dipole solutions consist of two elliptically shaped Gaussian-type beams separated by several diameters, and with a pi phase shift between their fields. Spatial evolution...

  9. Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers

    Directory of Open Access Journals (Sweden)

    Belkacem Meziane

    2008-01-01

    Full Text Available A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These solutions are shown to evolve in accordance with the driving frequency of the permanent solution that we recently reported to illustrate the system. The procedure amounts to analytically construct the signal Fourier transform by applying an iterative algorithm that reconstitutes the first few terms of its development.

  10. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

  11. Analytic solution of magnetic induction distribution of ideal hollow spherical field sources

    Science.gov (United States)

    Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

    2017-12-01

    The Halbach type hollow spherical permanent magnet arrays (HSPMA) are volume compacted, energy efficient field sources, and capable of producing multi-Tesla field in the cavity of the array, which have attracted intense interests in many practical applications. Here, we present analytical solutions of magnetic induction to the ideal HSPMA in entire space, outside of array, within the cavity of array, and in the interior of the magnet. We obtain solutions using concept of magnetic charge to solve the Poisson's and Laplace's equations for the HSPMA. Using these analytical field expressions inside the material, a scalar demagnetization function is defined to approximately indicate the regions of magnetization reversal, partial demagnetization, and inverse magnetic saturation. The analytical field solution provides deeper insight into the nature of HSPMA and offer guidance in designing optimized one.

  12. Analytical construction of peaked solutions for the nonlinear ...

    African Journals Online (AJOL)

    These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schrödinger type.

  13. Stochastic dynamics modeling solute transport in porous media modeling solute transport in porous media

    CERN Document Server

    Kulasiri, Don

    2002-01-01

    Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations (SPDE) come from the fact that we can integrate the variability of the system along with the scientific knowledge pertaining to the system. One of the aims of this book is to explaim some useufl concepts in stochastic dynamics so that the scientists and engineers with a background in undergraduate differential calculus could appreciate the applicability and appropriateness of these developments in mathematics. The ideas ...

  14. The effect of growing media and concentration of nutrient solution on growth, flowering and macroelement content of media and leaves of Tymophylla tenuiloba Small

    Directory of Open Access Journals (Sweden)

    Joanna Nowak

    2013-12-01

    Full Text Available Effects of growing media and concentration of nutrient solution on growth, flowering, evapotranspiration and macroelement content of media and leaves of Tymophylla tenuiloba were evaluated under ebb-and-flow conditions. Two media: peat and peat + perlite (3:l, v/v, and four concentrations of nutrient solution: 1.0, 1.5, 2.0, 2.5 mS cm-1 were applied. High quality plants were produced in both media and all concentration of nutrient solution. The lowest evapotranspiration was measured at the highest concentration of nutrient solution. N concentration of leaves was high in all treatments. Concentrations of K, Ca, and Mg decreased with increasing concentration of nutrient solution. Opposite was found for P. At the end of cultivation the lowest pH was measured in the upper layer of growing media. The highest total soluble salt level was measured in the upper layers. Upper layers accumulated more N-NO3, P, Ca, and Mg. Mineral element content of both media was high in all concentrations of nutrient solution. Low concentration of nutrient solution at 1.0 mS cm-1 is recommended, although -1Tymophylla tenuiloba-1 can be also cultivated at higher concentrations of nutrient solution up to 2.5mS cm-1, if placed on the same bench with other bedding plants requiring more nutrients.

  15. An Analytical Vacuum-Assisted Resin Transfer Molding (VARTM) Flow Model

    National Research Council Canada - National Science Library

    Fink, Bruce

    2000-01-01

    .... The analytical solution presented here provides insight into the scaling laws governing fill times and resin inlet placement as a function of the properties of the preform, distribution media, and resin...

  16. An analytical solution for Dean flow in curved ducts with rectangular cross section

    Science.gov (United States)

    Norouzi, M.; Biglari, N.

    2013-05-01

    In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.

  17. Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

    KAUST Repository

    Younis, Mohammad I.

    2014-01-01

    We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions

  18. On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

    International Nuclear Information System (INIS)

    Liu Hongzhun; Pan Zuliang; Li Peng

    2006-01-01

    In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.

  19. Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

    Directory of Open Access Journals (Sweden)

    Xiao-Ying Qin

    2014-01-01

    Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

  20. Analytical solutions for systems of partial differential-algebraic equations.

    Science.gov (United States)

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2014-01-01

    This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

  1. A single continuum approximation of the solute transport in fractured porous media

    International Nuclear Information System (INIS)

    Jeong, J.T.; Lee, K.J.

    1992-01-01

    Solute transport in fractured porous media is described by the single continuum model, i.e., equivalent porous medium model. In this model, one-dimensional solute transport in the fracture and two-dimensional solute transport in the porous rock matrix is considered. The network of fractures embedded in the porous rock matrix is idealized as two orthogonally intersecting families of equally spaced, parallel fractures directed at 45 o to the regional groundwater flow direction. Governing equations are solved by the finite element method, and an upstream weighting technique is used in order to prevent the oscillation of the solution in the case of highly advection dominated transport. Breakthrough curves, similar to those of the one-dimensional solute transport problem in ordinary porous media, are obtained as a function of time according to volume or flux averaging of the concentration profile across the width of the flow region. The equivalent parameters, i.e., porosity and overall coefficient of longitudinal dispersivity, are obtained by a trial-and-error method. Analyses for the non-sorbing solute transport case show that within the range of considered parameters, and except for the region very close to the source, application of the single continuum model in the idealized fracture system is sufficient for modeling solute transport in fractured porous media. This numerical scheme is shown to be applicable to a sorbing solute and radionuclide transport. (author)

  2. Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations

    Science.gov (United States)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2013-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad

  3. Radionuclide transport in fractured porous media -- Analytical solutions for a system of parallel fractures with a kinetic solubility-limited dissolution model

    International Nuclear Information System (INIS)

    Li, S.H.; Chen, C.T.

    1997-01-01

    Analytical solutions are developed for the problem of radionuclide transport in a system of parallel fractures situated in a porous rock matrix. A kinetic solubility-limited dissolution model is used as the inlet boundary condition. The solutions consider the following processes: (a) advective transport in the fractures, (b) mechanical dispersion and molecular diffusion along the fractures, (c) molecular diffusion from a fracture to the porous matrix, (d) molecular diffusion within the porous matrix in the direction perpendicular to the fracture axis, (e) adsorption onto the fracture wall, (f) adsorption within the porous matrix, and (g) radioactive decay. The solutions are based on the Laplace transform method. The general transient solution is in the form of a double integral that is evaluated using composite Gauss-Legendre quadrature. A simpler transient solution that is in the form of a single integral is also presented for the case that assumes negligible longitudinal dispersion along the fractures. The steady-state solutions are also provided. A number of examples are given to illustrate the effects of the following important parameters: (a) fracture spacings, (b) dissolution-rate constants, (c) fracture dispersion coefficient, (d) matrix retardation factor, and (e) fracture retardation factor

  4. Analytic, High-beta Solutions of the Helical Grad-Shafranov Equation

    International Nuclear Information System (INIS)

    Smith, D.R.; Reiman, A.H.

    2004-01-01

    We present analytic, high-beta (β ∼ O(1)), helical equilibrium solutions for a class of helical axis configurations having large helical aspect ratio, with the helix assumed to be tightly wound. The solutions develop a narrow boundary layer of strongly compressed flux, similar to that previously found in high beta tokamak equilibrium solutions. The boundary layer is associated with a strong localized current which prevents the equilibrium from having zero net current

  5. Interactions between butterfly-shaped pulses in the inhomogeneous media

    International Nuclear Information System (INIS)

    Liu, Wen-Jun; Huang, Long-Gang; Pan, Nan; Lei, Ming

    2014-01-01

    Pulse interactions affect pulse qualities during the propagation. Interactions between butterfly-shaped pulses are investigated to improve pulse qualities in the inhomogeneous media. In order to describe the interactions between butterfly-shaped pulses, analytic two-soliton solutions are derived. Based on those solutions, influences of corresponding parameters on pulse interactions are discussed. Methods to control the pulse interactions are suggested. - Highlights: • Interactions between butterfly-shaped pulses are investigated. • Methods to control the pulse interactions are suggested. • Analytic two-soliton solutions for butterfly-shaped pulses are derived

  6. Interactions between butterfly-shaped pulses in the inhomogeneous media

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Wen-Jun [State Key Laboratory of Information Photonics and Optical Communications, School of Science, P. O. Box 91, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Huang, Long-Gang; Pan, Nan [State Key Laboratory of Information Photonics and Optical Communications, School of Science, P. O. Box 91, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Lei, Ming, E-mail: mlei@bupt.edu.cn [State Key Laboratory of Information Photonics and Optical Communications, School of Science, P. O. Box 91, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

    2014-10-15

    Pulse interactions affect pulse qualities during the propagation. Interactions between butterfly-shaped pulses are investigated to improve pulse qualities in the inhomogeneous media. In order to describe the interactions between butterfly-shaped pulses, analytic two-soliton solutions are derived. Based on those solutions, influences of corresponding parameters on pulse interactions are discussed. Methods to control the pulse interactions are suggested. - Highlights: • Interactions between butterfly-shaped pulses are investigated. • Methods to control the pulse interactions are suggested. • Analytic two-soliton solutions for butterfly-shaped pulses are derived.

  7. Matisse: A Visual Analytics System for Exploring Emotion Trends in Social Media Text Streams

    Energy Technology Data Exchange (ETDEWEB)

    Steed, Chad A [ORNL; Drouhard, Margaret MEG G [ORNL; Beaver, Justin M [ORNL; Pyle, Joshua M [ORNL; BogenII, Paul L. [Google Inc.

    2015-01-01

    Dynamically mining textual information streams to gain real-time situational awareness is especially challenging with social media systems where throughput and velocity properties push the limits of a static analytical approach. In this paper, we describe an interactive visual analytics system, called Matisse, that aids with the discovery and investigation of trends in streaming text. Matisse addresses the challenges inherent to text stream mining through the following technical contributions: (1) robust stream data management, (2) automated sentiment/emotion analytics, (3) interactive coordinated visualizations, and (4) a flexible drill-down interaction scheme that accesses multiple levels of detail. In addition to positive/negative sentiment prediction, Matisse provides fine-grained emotion classification based on Valence, Arousal, and Dominance dimensions and a novel machine learning process. Information from the sentiment/emotion analytics are fused with raw data and summary information to feed temporal, geospatial, term frequency, and scatterplot visualizations using a multi-scale, coordinated interaction model. After describing these techniques, we conclude with a practical case study focused on analyzing the Twitter sample stream during the week of the 2013 Boston Marathon bombings. The case study demonstrates the effectiveness of Matisse at providing guided situational awareness of significant trends in social media streams by orchestrating computational power and human cognition.

  8. Solute transport in aggregated and layered porous media

    International Nuclear Information System (INIS)

    Koch, S.

    1993-01-01

    This work is a contribution to research in soil physics dealing with solute transport in porous media. The influence of structural inhomogeneities on solute transport is investigated. Detailed experiments at the laboratory scale are used to enlighten distinct processes which cannot be studied separately at field scale. Two main aspects are followed up: (i) to show the influence of aggregation of a porous medium on breakthrough time and spreading of an inert tracer and consequences on the estimation of parameter values of models describing solute transport in aggregated systems, (ii) to investigate the influences on the dispersion process when stratification is perpendicular to the direction of flow. Several concepts of modelling solute transport in soil are discussed. Models based on the convection-dispersion equation (CDE) are emphasized because they are used here to model solute transport experiments conducted with aggregated porous media. Stochastic concepts are introduced to show the limitations of the deterministic CDE approaches. Experiments are done in columns containing two kinds of solid phases and were saturated with water. The solid phases are porous and solid glass beads exhibiting a distinctly unimodal or bimodal pore size distribution. Experimental breakthrough curves (BTCs) are modelled with the CDE, a bicontinuum model with a phenomenological mass transfer rate and a bicontinuum spherical diffusion model. Experiments are also done in columns that are unsaturated containing porous materials that are layered. Flow is made at a steady rate. It is shown that layer boundaries have a severe influence on lateral mixing. They may force streamlines to converge or cause a lateral redistribution of solutes. (author) figs., tabs., 122 refs

  9. Auto-Baecklund Transformation and Analytic Solutions of (2+1)-Dimensional Boussinesq Equation

    International Nuclear Information System (INIS)

    Liu Guanting

    2008-01-01

    Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Baecklund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass wp function. Some of them are novel.

  10. Domains of analyticity for response solutions in strongly dissipative forced systems

    International Nuclear Information System (INIS)

    Corsi, Livia; Feola, Roberto; Gentile, Guido

    2013-01-01

    We study the ordinary differential equation εx ¨ +x . +εg(x)=εf(ωt), where g and f are real-analytic functions, with f quasi-periodic in t with frequency vector ω. If c 0 ∈R is such that g(c 0 ) equals the average of f and g′(c 0 ) ≠ 0, under very mild assumptions on ω there exists a quasi-periodic solution close to c 0 with frequency vector ω. We show that such a solution depends analytically on ε in a domain of the complex plane tangent more than quadratically to the imaginary axis at the origin

  11. Development of collaborative-creative learning model using virtual laboratory media for instrumental analytical chemistry lectures

    Science.gov (United States)

    Zurweni, Wibawa, Basuki; Erwin, Tuti Nurian

    2017-08-01

    The framework for teaching and learning in the 21st century was prepared with 4Cs criteria. Learning providing opportunity for the development of students' optimal creative skills is by implementing collaborative learning. Learners are challenged to be able to compete, work independently to bring either individual or group excellence and master the learning material. Virtual laboratory is used for the media of Instrumental Analytical Chemistry (Vis, UV-Vis-AAS etc) lectures through simulations computer application and used as a substitution for the laboratory if the equipment and instruments are not available. This research aims to design and develop collaborative-creative learning model using virtual laboratory media for Instrumental Analytical Chemistry lectures, to know the effectiveness of this design model adapting the Dick & Carey's model and Hannafin & Peck's model. The development steps of this model are: needs analyze, design collaborative-creative learning, virtual laboratory media using macromedia flash, formative evaluation and test of learning model effectiveness. While, the development stages of collaborative-creative learning model are: apperception, exploration, collaboration, creation, evaluation, feedback. Development of collaborative-creative learning model using virtual laboratory media can be used to improve the quality learning in the classroom, overcome the limitation of lab instruments for the real instrumental analysis. Formative test results show that the Collaborative-Creative Learning Model developed meets the requirements. The effectiveness test of students' pretest and posttest proves significant at 95% confidence level, t-test higher than t-table. It can be concluded that this learning model is effective to use for Instrumental Analytical Chemistry lectures.

  12. An analytic solution for one-dimensional diffusion of radionuclides from a waste package

    International Nuclear Information System (INIS)

    1985-01-01

    This work implements an analytical solution for diffusion of radionuclides from a cylindrical waste form through the packing material into the surrounding host rock. Recent interest in predicting the performance of a proposed geological repository for nuclear waste has led to the development of several computer programs to predict the performance of such a repository for the next several millenia. These numerical codes are generally designed to accommodate a broad spectrum of geometrical configurations and repository conditions in order to accurately predict the behavior of the radionuclides in the repository environment. Confidence in such general purpose codes is gained by verifying the numerical modeling and the software through comparison of the numerical predictions generated by these computer codes with analytical solutions to reasonably complex problems. The analysis discussed herein implements the analytic solution, proposed by J.C. Jaeger in 1941 for radial diffusion through two concentric circular cylinders. Jaeger's solution was applied to the problem of diffusional mass transfer from a long cylindrical waste form and subsequently into the surrounding geological formation. Analytic predictions of fractional release rates, including the effects of sorption, were generated. 6 refs., 2 figs., 2 tabs

  13. An accurate analytical solution of a zero-dimensional greenhouse model for global warming

    International Nuclear Information System (INIS)

    Foong, S K

    2006-01-01

    In introducing the complex subject of global warming, books and papers usually use the zero-dimensional greenhouse model. When the ratio of the infrared radiation energy of the Earth's surface that is lost to outer space to the non-reflected average solar radiation energy is small, the model admits an accurate approximate analytical solution-the resulting energy balance equation of the model is a quartic equation that can be solved analytically-and thus provides an alternative solution and instructional strategy. A search through the literature fails to find an analytical solution, suggesting that the solution may be new. In this paper, we review the model, derive the approximation and obtain its solution. The dependence of the temperature of the surface of the Earth and the temperature of the atmosphere on seven parameters is made explicit. A simple and convenient formula for global warming (or cooling) in terms of the percentage change of the parameters is derived. The dependence of the surface temperature on the parameters is illustrated by several representative graphs

  14. A Generic analytical solution for modelling pumping tests in wells intersecting fractures

    Science.gov (United States)

    Dewandel, Benoît; Lanini, Sandra; Lachassagne, Patrick; Maréchal, Jean-Christophe

    2018-04-01

    The behaviour of transient flow due to pumping in fractured rocks has been studied for at least the past 80 years. Analytical solutions were proposed for solving the issue of a well intersecting and pumping from one vertical, horizontal or inclined fracture in homogeneous aquifers, but their domain of application-even if covering various fracture geometries-was restricted to isotropic or anisotropic aquifers, whose potential boundaries had to be parallel or orthogonal to the fracture direction. The issue thus remains unsolved for many field cases. For example, a well intersecting and pumping a fracture in a multilayer or a dual-porosity aquifer, where intersected fractures are not necessarily parallel or orthogonal to aquifer boundaries, where several fractures with various orientations intersect the well, or the effect of pumping not only in fractures, but also in the aquifer through the screened interval of the well. Using a mathematical demonstration, we show that integrating the well-known Theis analytical solution (Theis, 1935) along the fracture axis is identical to the equally well-known analytical solution of Gringarten et al. (1974) for a uniform-flux fracture fully penetrating a homogeneous aquifer. This result implies that any existing line- or point-source solution can be used for implementing one or more discrete fractures that are intersected by the well. Several theoretical examples are presented and discussed: a single vertical fracture in a dual-porosity aquifer or in a multi-layer system (with a partially intersecting fracture); one and two inclined fractures in a leaky-aquifer system with pumping either only from the fracture(s), or also from the aquifer between fracture(s) in the screened interval of the well. For the cases with several pumping sources, analytical solutions of flowrate contribution from each individual source (fractures and well) are presented, and the drawdown behaviour according to the length of the pumped screened interval of

  15. Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

    KAUST Repository

    Davit, Y.

    2012-07-26

    In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (τ 1) for the relaxation of the effective macroscale parameters (i. e., when t ≤ τ 1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ 1) (i.e., when t≫τ 1); and (3) a one-equation, time-asymptotic formulation (1eq ∞). This model can be adopted when (t) is significantly larger than the timescale (τ 2) associated with exchange processes between the two regions (i. e., when t≫τ 2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ∞) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects. © 2012 Springer Science+Business Media B.V.

  16. New analytical methodology for analysing S(IV) species at low pH solutions by one stage titration method (bichromatometry) with a clear colour change. Could potentially replace the state-of-art-method iodometry at low pH analysis due higher accuracy.

    Science.gov (United States)

    Santasalo-Aarnio, Annukka; Galfi, Istvan; Virtanen, Jorma; Gasik, Michael M

    2017-01-01

    A new, faster and more reliable analytical methodology for S(IV) species analysis at low pH solutions by bichromatometry is proposed. For decades the state of the art methodology has been iodometry that is still well justified method for neutral solutions, thus at low pH media possess various side reactions increasing inaccuracy. In contrast, the new methodology has no side reactions at low pH media, requires only one titration step and provides a clear color change if S(IV) species are present in the solution. The method is validated using model solutions with known concentrations and applied to analyses of gaseous SO2 from purged solution in low pH media samples. The results indicate that bichromatometry can accurately analyze SO2 from liquid samples having pH even below 0 relevant to metallurgical industrial processes.

  17. Migration of radionuclide through two-layered geologic media

    International Nuclear Information System (INIS)

    Nakayama, Shinichi; Takagi, Ikuji; Nakai, Kunihiro; Higashi, Kunio

    1984-01-01

    For the safety assessment of geologic disposal of high-level radioactive wastes, an analytical solution was obtained for one-dimensional migration of radionuclide through two-layered geologic media without dispersion. By applying it to geologic media composed of granite and soil layers, the effect of interlayer boundary on the discharge profile of radionuclides in decay chains into biological environment is examined. The time-space profiles of radionuclides in the vicinity of interlayer boundary are much complicated as shown in the results of calculation. Those profiles in case that the groundwater flows through granite followed by soil are quite different from those in case that the groundwater flows through soil followed by granite. Each of complicated dependence of profiles on time and space can be physically explained. The characteristic profiles in the vicinity of interlayer boundary have not been discussed previously. Recently, numerical computer codes has been developed to apply to much more realistic geologic situations. However, the numerical accuracies of the codes are necessary to be confirmed. This is achieved by comparing computational results with results from analytical solutions. The analytical solution presented will serve as a bench-mark for numerical accuracy. (author)

  18. The use of physiological solutions or media in calcium phosphate synthesis and processing.

    Science.gov (United States)

    Tas, A Cuneyt

    2014-05-01

    This review examined the literature to spot uses, if any, of physiological solutions/media for the in situ synthesis of calcium phosphates (CaP) under processing conditions (i.e. temperature, pH, concentration of inorganic ions present in media) mimicking those prevalent in the human hard tissue environments. There happens to be a variety of aqueous solutions or media developed for different purposes; sometimes they have been named as physiological saline, isotonic solution, cell culture solution, metastable CaP solution, supersaturated calcification solution, simulated body fluid or even dialysate solution (for dialysis patients). Most of the time such solutions were not used as the aqueous medium to perform the biomimetic synthesis of calcium phosphates, and their use was usually limited to the in vitro testing of synthetic biomaterials. This review illustrates that only a limited number of research studies used physiological solutions or media such as Earle's balanced salt solution, Bachra et al. solutions or Tris-buffered simulated body fluid solution containing 27mM HCO3(-) for synthesizing CaP, and these studies have consistently reported the formation of X-ray-amorphous CaP nanopowders instead of Ap-CaP or stoichiometric hydroxyapatite (HA, Ca10(PO4)6(OH)2) at 37°C and pH 7.4. By relying on the published articles, this review highlights the significance of the use of aqueous solutions containing 0.8-1.5 mMMg(2+), 22-27mM HCO3(-), 142-145mM Na(+), 5-5.8mM K(+), 103-133mM Cl(-), 1.8-3.75mM Ca(2+), and 0.8-1.67mM HPO4(2-), which essentially mimic the composition and the overall ionic strength of the human extracellular fluid (ECF), in forming the nanospheres of X-ray-amorphous CaP. Copyright © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

  19. The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

    Science.gov (United States)

    Gai, Litao; Bilige, Sudao; Jie, Yingmo

    2016-01-01

    In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

  20. Light diffusion in N-layered turbid media: steady-state domain.

    Science.gov (United States)

    Liemert, André; Kienle, Alwin

    2010-01-01

    We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

  1. Social media and the social sciences: How researchers employ Big Data analytics

    Directory of Open Access Journals (Sweden)

    Mylynn Felt

    2016-04-01

    Full Text Available Social media posts are full of potential for data mining and analysis. Recognizing this potential, platform providers increasingly restrict free access to such data. This shift provides new challenges for social scientists and other non-profit researchers who seek to analyze public posts with a purpose of better understanding human interaction and improving the human condition. This paper seeks to outline some of the recent changes in social media data analysis, with a focus on Twitter, specifically. Using Twitter data from a 24-hour period following The Sisters in Spirit Candlelight Vigil, sponsored by the Native Women’s Association of Canada, this article compares three free-use Twitter application programming interfaces for capturing tweets and enabling analysis. Although recent Twitter data restrictions limit free access to tweets, there are many dynamic options for social scientists to choose from in the capture and analysis of Twitter and other social media platform data. This paper calls for critical social media data analytics combined with traditional, qualitative methods to address the developing ‘data gold rush.’

  2. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

    OpenAIRE

    Mehmet Ali Akinlar; Muhammet Kurulay

    2013-01-01

    A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...

  3. Analytic solution to verify code predictions of two-phase flow in a boiling water reactor core channel

    International Nuclear Information System (INIS)

    Chen, K.F.; Olson, C.A.

    1983-01-01

    One reliable method that can be used to verify the solution scheme of a computer code is to compare the code prediction to a simplified problem for which an analytic solution can be derived. An analytic solution for the axial pressure drop as a function of the flow was obtained for the simplified problem of homogeneous equilibrium two-phase flow in a vertical, heated channel with a cosine axial heat flux shape. This analytic solution was then used to verify the predictions of the CONDOR computer code, which is used to evaluate the thermal-hydraulic performance of boiling water reactors. The results show excellent agreement between the analytic solution and CONDOR prediction

  4. Analytic solution to variance optimization with no short positions

    Science.gov (United States)

    Kondor, Imre; Papp, Gábor; Caccioli, Fabio

    2017-12-01

    We consider the variance portfolio optimization problem with a ban on short selling. We provide an analytical solution by means of the replica method for the case of a portfolio of independent, but not identically distributed, assets. We study the behavior of the solution as a function of the ratio r between the number N of assets and the length T of the time series of returns used to estimate risk. The no-short-selling constraint acts as an asymmetric \

  5. In-core LOCA-s: analytical solution for the delayed mixing model for moderator poison concentration

    International Nuclear Information System (INIS)

    Firla, A.P.

    1995-01-01

    Solutions to dynamic moderator poison concentration model with delayed mixing under single pressure tube / calandria tube rupture scenario are discussed. Such a model is described by a delay differential equation, and for such equations the standard ways of solution are not directly applicable. In the paper an exact, direct time-domain analytical solution to the delayed mixing model is presented and discussed. The obtained solution has a 'marching' form and is easy to calculate numerically. Results of the numerical calculations based on the analytical solution indicate that for the expected range of mixing times the existing uniform mixing model is a good representation of the moderator poison mixing process for single PT/CT breaks. However, for postulated multi-pipe breaks ( which is very unlikely to occur ) the uniform mixing model is not adequate any more; at the same time an 'approximate' solution based on Laplace transform significantly overpredicts the rate of poison concentration decrease, resulting in excessive increase in the moderator dilution factor. In this situation the true, analytical solution must be used. The analytical solution presented in the paper may also serve as a bench-mark test for the accuracy of the existing poison mixing models. Moreover, because of the existing oscillatory tendency of the solution, special care must be taken in using delay differential models in other applications. (author). 3 refs., 3 tabs., 8 figs

  6. Large time behaviour of oscillatory nonlinear solute transport in porous media

    NARCIS (Netherlands)

    Duijn, van C.J.; Zee, van der S.E.A.T.M.

    2018-01-01

    Oscillations in flow occur under many different situations in natural porous media, due to tidal, daily or seasonal patterns. In this paper, we investigate how such oscillations in flow affect the transport of an initially sharp solute front, if the solute undergoes nonlinear sorption and,

  7. Two-dimensional analytical solutions for chemical transport in aquifers. Part 1. Simplified solutions for sources with constant concentration. Part 2. Exact solutions for sources with constant flux rate

    International Nuclear Information System (INIS)

    Shan, C.; Javandel, I.

    1996-05-01

    Analytical solutions are developed for modeling solute transport in a vertical section of a homogeneous aquifer. Part 1 of the series presents a simplified analytical solution for cases in which a constant-concentration source is located at the top (or the bottom) of the aquifer. The following transport mechanisms have been considered: advection (in the horizontal direction), transverse dispersion (in the vertical direction), adsorption, and biodegradation. In the simplified solution, however, longitudinal dispersion is assumed to be relatively insignificant with respect to advection, and has been neglected. Example calculations are given to show the movement of the contamination front, the development of concentration profiles, the mass transfer rate, and an application to determine the vertical dispersivity. The analytical solution developed in this study can be a useful tool in designing an appropriate monitoring system and an effective groundwater remediation method

  8. Analytical solution for a linearly graded-index-profile planar waveguide.

    Science.gov (United States)

    Touam, T; Yergeau, F

    1993-01-20

    An analytical solution is presented for the TE modes of a planar waveguide structure comprising a high-index guiding layer and a buried layer with a profile such that the square of the index varies linearly and matches the substrate and high-index guiding layer. The electric-field profiles and the dispersion relation are obtained and discussed, and a solution by the WKB method is compared.

  9. Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

    Directory of Open Access Journals (Sweden)

    Olaniyi Samuel Iyiola

    2014-09-01

    Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

  10. Analytic solution of pseudocolloid migration in fractured rock

    International Nuclear Information System (INIS)

    Hwang, Y.; Pigford, T.H.; Lee, W.W.L.; Chambre, P.L.

    1989-06-01

    A form of colloid migration that can enhance or retard the migration of a dissolved contaminant in ground water is the sorption of the contaminant on the moving colloidal particulate to form pseudocolloids. In this paper we develop analytical solutions for the interactive migration of radioactive species dissolved in ground water and sorbed as pseudocolloids. The solute and pseudocolloids are assumed to undergo advection and dispersion in a one-dimensional flow field in planar fractures in porous rock. Interaction between pseudocolloid and dissolved species is described by equilibrium sorption. Sorbed species on the pseudocolloids undergo radioactive decay, and pseudocolloids can sorb on fracture surfaces and sediments. Filtration is neglected. The solute can decay and sorb on pseudocolloids, on the fracture surfaces, and on sediments and can diffuse into the porous rock matrix. 1 fig

  11. A hybrid ICT-solution for smart meter data analytics

    DEFF Research Database (Denmark)

    Liu, Xiufeng; Nielsen, Per Sieverts

    2016-01-01

    data processing, and using the machine learning toolkit, MADlib, for doing in-database data analytics in PostgreSQL database. This paper evaluates the key technologies of the proposed ICT-solution, and the results show the effectiveness and efficiency of using the system for both batch and online...

  12. Analytical solution for the convectively-mixed atmospheric boundary layer

    NARCIS (Netherlands)

    Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.

    2013-01-01

    Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation

  13. Analytical solution of the PNP equations at AC applied voltage

    International Nuclear Information System (INIS)

    Golovnev, Anatoly; Trimper, Steffen

    2012-01-01

    A symmetric binary polymer electrolyte subjected to an AC voltage is considered. The analytical solution of the Poisson–Nernst–Planck equations (PNP) is found and analyzed for small applied voltages. Three distinct time regimes offering different behavior can be discriminated. The experimentally realized stationary behavior is discussed in detail. An expression for the external current is derived. Based on the theoretical result a simple method is suggested of measuring the ion mobility and their concentration separately. -- Highlights: ► Analytical solution of Poisson–Nernst–Planck equations. ► Binary polymer electrolyte subjected to an external AC voltage. ► Three well separated time scales exhibiting different behavior. ► The experimentally realized stationary behavior is discussed in detail. ► A method is proposed measuring the mobility and the concentration separately.

  14. Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean

    Energy Technology Data Exchange (ETDEWEB)

    Petrov, P.S., E-mail: petrov@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Prants, S.V., E-mail: prants@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Petrova, T.N., E-mail: petrova.tn@dvfu.ru [Far Eastern Federal University, 8 Sukhanova str., 690950, Vladivostok (Russian Federation)

    2017-06-21

    The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic equations are solved explicitly, and the analytical expressions for the modal coefficients are obtained using a Lie-algebraic technique. - Highlights: • A group-theoretical approach is applied to a problem of sound propagation in a shallow sea with variable bottom slope. • An analytical solution of this problem is obtained in the form of modal expansion with analytical expressions of the coefficients. • Our result is the only analytical solution of the 3D sound propagation problem with no translational invariance. • This solution can be used for the validation of the numerical propagation models.

  15. Foam for Enhanced Oil Recovery : Modeling and Analytical Solutions

    NARCIS (Netherlands)

    Ashoori, E.

    2012-01-01

    Foam increases sweep in miscible- and immiscible-gas enhanced oil recovery by decreasing the mobility of gas enormously. This thesis is concerned with the simulations and analytical solutions for foam flow for the purpose of modeling foam EOR in a reservoir. For the ultimate goal of upscaling our

  16. Small-scale engagement model with arrivals: analytical solutions

    International Nuclear Information System (INIS)

    Engi, D.

    1977-04-01

    This report presents an analytical model of small-scale battles. The specific impetus for this effort was provided by a need to characterize hypothetical battles between guards at a nuclear facility and their potential adversaries. The solution procedure can be used to find measures of a number of critical parameters; for example, the win probabilities and the expected duration of the battle. Numerical solutions are obtainable if the total number of individual combatants on the opposing sides is less than 10. For smaller force size battles, with one or two combatants on each side, symbolic solutions can be found. The symbolic solutions express the output parameters abstractly in terms of symbolic representations of the input parameters while the numerical solutions are expressed as numerical values. The input parameters are derived from the probability distributions of the attrition and arrival processes. The solution procedure reduces to solving sets of linear equations that have been constructed from the input parameters. The approach presented in this report does not address the problems associated with measuring the inputs. Rather, this report attempts to establish a relatively simple structure within which small-scale battles can be studied

  17. A Computer Library for Ray Tracing in Analytical Media

    International Nuclear Information System (INIS)

    Miqueles, Eduardo; Coimbra, Tiago A; Figueiredo, J J S de

    2013-01-01

    Ray tracing technique is an important tool not only for forward but also for inverse problems in Geophysics, which most of the seismic processing steps depends on. However, implementing ray tracing codes can be very time consuming. This article presents a computer library to trace rays in 2.5D media composed by stack of layers. The velocity profile inside each layer is such that the eikonal equation can be analitically solved. Therefore, the ray tracing within such profile is made fast and accurately. The great advantage of an analytical ray tracing library is the numerical precision of the quantities computed and the fast execution of the implemented codes. Although ray tracing programs already exist for a long time, for example the seis package by Cervený, with a numerical approach to compute the ray. Regardless of the fact that numerical methods can solve more general problems, the analytical ones could be part of a more sofisticated simulation process, where the ray tracing time is completely relevant. We demonstrate the feasibility of our codes using numerical examples.

  18. New Class of Solutions for Water Infiltration Problems in Unsaturated Soils

    DEFF Research Database (Denmark)

    Barari, Amin; Omidvar, M; Momeni, M

    2010-01-01

    This paper presents the results of approximate analytical solutions to Richards’ equation, which governs the problem of unsaturated flow in porous media. The existing methods generally fall within the category of numerical and analytical methods, often having many restrictions for practical situa...

  19. Analytical solution of point kinetic equations for sub-critical systems

    International Nuclear Information System (INIS)

    Henrice Junior, Edson; Goncalves, Alessandro C.

    2013-01-01

    This article presents an analytical solution for the set of point kinetic equations for sub-critical reactors. This solution stems from the ordinary, non-homogeneous differential equation that rules the neutron density and that presents the incomplete Gamma function in its functional form. The method used proved advantageous and allowed practical applications such as the linear insertion of reactivity, considering an external constant source or with both varying linearly. (author)

  20. On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem

    Directory of Open Access Journals (Sweden)

    Soheil Salahshour

    2015-02-01

    Full Text Available In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville or a solution with increasing length of their support (Hukuhara difference. Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.

  1. Analytic solution of the Starobinsky model for inflation

    Energy Technology Data Exchange (ETDEWEB)

    Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)

    2017-07-15

    We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lemaitre-Robertson-Walker metric constitute an integrable system. The analytical solution in terms of a Painleve series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature. In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory. (orig.)

  2. Periodical gas flow around a well in porous media

    International Nuclear Information System (INIS)

    Shnaid, I.; Olek, S.

    1996-01-01

    Analytical solutions of the linearized governing equation are presented for periodic gas flow around a well in porous media. Two cases are considered: a fully penetrating well and a partially penetrating well. For the first case, a closed form solution is obtained, whereas for the second case the solution is in the form of eigenfunctions expansions. The results have practical application in compressed air energy storage. (authors)

  3. The presentation of explicit analytical solutions of a class of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Feng Jinshun; Guo Mingpu; Yuan Deyou

    2009-01-01

    In this paper, we introduce a function set Ω m . There is a conjecture that an arbitrary explicit travelling-wave analytical solution of a real constant coefficient nonlinear evolution equation is necessarily a linear (or nonlinear) combination of the product of some elements in Ω m . A widespread applicable approach for solving a class of nonlinear evolution equations is established. The new analytical solutions to two kinds of nonlinear evolution equations are described with the aid of the guess.

  4. Biological and analytical studies of peritoneal dialysis solutions

    Directory of Open Access Journals (Sweden)

    N. Hudz

    2018-04-01

    Full Text Available The purpose of our work was to conduct biological and analytical studies of the peritoneal dialysis (PD solutions containing glucose and sodium lactate and establish correlations between cell viability of the Vero cell line and values of analytical indexes of the tested solutions. The results of this study confirm the cytotoxicity of the PD solutions even compared with the isotonic solution of sodium chloride, which may be due to the low pH of the solutions, presence of glucose degradation products (GDPs and high osmolarity of the solutions, and unphysiological concentrations of glucose and sodium lactate. However, it is not yet known what factors or their combination and to what extent cause the cytotoxicity of PD solutions. In the neutral red (NR test the weak, almost middle (r = -0.496 and 0.498, respectively and unexpected correlations were found between reduced viability of monkey kidney cells and increased pH of the PD solutions and between increased cell viability and increased absorbance at 228 nm of the tested PD solutions. These two correlations can be explained by a strong correlation (r = -0.948 between a decrease in pH and an increase in the solution absorbance at 228 nm. The opposite effect was observed in the MTT test. The weak, but expected correlations (r = 0.32 and -0.202, respectively were found between increased cell viability and increased pH in the PD solutions and between decreased cell viability and increased absorbance at 228 nm of the tested PD solutions. The middle and weak correlations (r = 0.56 and 0.29, respectively were detected between increased cell viability and increased lactate concentration in the NR test and MTT test. The data of these correlations can be partially explained by the fact that a correlation with a coefficient r = -0.34 was found between decreased pH in the solutions and increased lactate concentration. The very weak correlations (0.138 and 0.196, respectively were found between increased cell

  5. The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

    Science.gov (United States)

    Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

    2017-08-01

    This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

  6. Role of nanoparticles in analytical solid phase microextraction (SPME)

    NARCIS (Netherlands)

    Zielinska, K.; Leeuwen, van H.P.

    2013-01-01

    Solid phase microextraction (SPME) is commonly used to measure the free concentration of fairly hydrophobic substances in aqueous media on the basis of their partitioning between sample solution and a solid phase. Here we study the role of nanoparticles that may sorb the analyte in the sample

  7. Recovery of uranium from analytical waste solution

    International Nuclear Information System (INIS)

    Kumar, Pradeep; Anitha, M.; Singh, D.K.

    2016-01-01

    Dispersion fuels are considered as advance fuel for the nuclear reactor. Liquid waste containing significant quantity of uranium gets generated during chemical characterization of dispersion fuel. The present paper highlights the effort in devising a counter current solvent extraction process based on the synergistic mixture of D2EHPA and Cyanex 923 to recover uranium from such waste solutions. A typical analytical waste solution was found to have the following composition: U 3 O 8 (∼3 g/L), Al: 0.3 g/L, V: 15 ppm, Phosphoric acid: 3M, sulphuric acid : 1M and nitric acid : 1M. The aqueous solution is composed of mixture of either 3M phosphoric acid and 1M sulphuric acid or 1M sulphuric acid and 1M nitric acid, keeping metallic concentrations in the above mentioned range. Different organic solvents were tested. Based on the higher extraction of uranium with synergistic mixture of 0.5M D2EHPA + 0.125M Cyanex 923, it was selected for further investigation in the present work

  8. Employee participation in knowledge sharing and change solutions through enterprise social media

    DEFF Research Database (Denmark)

    Andersen, Mona Agerholm; Agerdal-Hjermind, Annette; Valentini, Chiara

    Purpose - This paper explores the relationship between the participative style of the immediate manager and employees’ motivation to participate on enterprise social media both in daily knowledge sharing activities and in relation to organizational change solutions. Methodology - This project.......046). Findings - The data shows a positive relationship between the participative style of the immediate manager and the employees’ motivation to participate on enterprise social media both in daily knowledge sharing activities and in creating and discussing change solutions. Key words: Internal social media...... is based on a quantitative study in a global Danish company with approximately 18,000 employees worldwide. The company has a strategic focus on implementing social collaboration platforms to create a global working culture. An online survey was conducted globally and a total of 1.046 employees replied (n=1...

  9. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mehmet Ali Akinlar

    2013-01-01

    Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.

  10. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  11. Non-perturbative analytical solutions of the space- and time-fractional Burgers equations

    International Nuclear Information System (INIS)

    Momani, Shaher

    2006-01-01

    Non-perturbative analytical solutions for the generalized Burgers equation with time- and space-fractional derivatives of order α and β, 0 < α, β ≤ 1, are derived using Adomian decomposition method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed

  12. Analytical techniques for characterization of raw materials in cell culture media

    Directory of Open Access Journals (Sweden)

    Sharma Chandana

    2011-11-01

    Full Text Available Abstract Raw materials are a critical part of any cell culture medium; therefore, it is of utmost importance to understand and characterize them for high-quality product. The raw material characterization (RMC program at SAFC focuses on individual screening of raw materials both analytically and biologically. The goal of the program is to develop the best-in-class knowledge base of the raw materials used in SAFC’s media formulations and their impact on performance of products.

  13. Spherical indentation of a freestanding circular membrane revisited: Analytical solutions and experiments

    International Nuclear Information System (INIS)

    Jin, Congrui; Davoodabadi, Ali; Li, Jianlin; Wang, Yanli; Singler, Timothy

    2017-01-01

    Because of the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl–Hecky membrane indented by a frictionless spherical indenter. In this study, experiments of spherical indentation has been performed, and the exact analytical solution presented in this article is compared against experimental data from existing literature as well as our own experimental results.

  14. Decision Exploration Lab : A Visual Analytics Solution for Decision Management

    NARCIS (Netherlands)

    Broeksema, Bertjan; Baudel, Thomas; Telea, Alex; Crisafulli, Paolo

    2013-01-01

    We present a visual analytics solution designed to address prevalent issues in the area of Operational Decision Management (ODM). In ODM, which has its roots in Artificial Intelligence (Expert Systems) and Management Science, it is increasingly important to align business decisions with business

  15. An improved analytic solution for analysis of particle trajectories in fibrous, two-dimensional filters

    International Nuclear Information System (INIS)

    Marshall, H.; Sahraoui, M.; Kaviany, M.

    1994-01-01

    The Kuwabara solution for creeping fluid flow through periodic arrangement of cylinders is widely used in analytic and numerical studies of fibrous filters. Numerical solutions have shown that the Kuwabara solution has systematic errors, and when used for the particle trajectories in filters it results in some error in the predicted filter efficiency. The numerical solutions, although accurate, preclude further analytic treatments, and are not as compact and convenient to use as the Kuwabara solution. By reexamining the outer boundary conditions of the Kuwabara solution, a correction term to the Kuwabara solution has been derived to obtain an extended solution that is more accurate and improves prediction of the filter efficiency. By comparison with the numerical solutions, it is shown that the Kuwabara solution is the high porosity asymptote, and that the extended solution has an improved porosity dependence. A rectification is explained that can make particle collection less efficient for periodic, in-line arrangements of fibers with particle diffusion or body force. This rectification also results in the alignment of particles with inertia (i.e., high Stokes number particles)

  16. Closed form analytic solutions describing glow discharge plasma

    International Nuclear Information System (INIS)

    Pai, S.T.; Guo, X.M.; Zhou, T.D.

    1996-01-01

    On the basis of an analytic model developed previously [S. T. Pai, J. Appl. Phys. 71, 5820 (1992)], an improved version of the model for the description of dc glow discharge plasma was successfully developed. A set of closed form solutions was obtained from the governing equations. The two-dimensional, analytic solutions are functional and completely satisfy the governing equations, the actual boundary conditions, and Maxwell equations. They can be readily used to carry out numerical calculations without the necessity of employing any assumed boundary conditions. Results obtained from the model reveal that as the discharge gap spacing or pressure increases the maximum value in the electron density distribution moves toward the cathode. At a sufficiently large value of gap spacing, the positive column phenomenon begins to appear in the discharge region. The model has the capability of treating the positive column and negative glow as a continuous system without the necessity of studying them separately. The model also predicts a sharp rise of the positive ion density near the cathode and field reversal in the anode region. Variation of the electrode radius produces little effect on the axial spatial distribution of physical quantities studied. copyright 1996 American Institute of Physics

  17. Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Palacios, Sergio L.

    2004-01-01

    We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

  18. Numerical and analytical solutions for problems relevant for quantum computers

    International Nuclear Information System (INIS)

    Spoerl, Andreas

    2008-01-01

    Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)

  19. Baseline configuration for GNSS attitude determination with an analytical least-squares solution

    International Nuclear Information System (INIS)

    Chang, Guobin; Wang, Qianxin; Xu, Tianhe

    2016-01-01

    The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance–covariance matrix. (paper)

  20. Analytical solutions for ozone generation by point to plane corona discharge

    International Nuclear Information System (INIS)

    Bestman, A.R.

    1990-12-01

    A recent mathematical model developed for ozone production is tackled analytically by asymptotic approximation. The results obtained are compared with existing numerical solutions. The comparison shows good agreement. (author). 3 refs, 1 fig

  1. Hydraulic modeling of riverbank filtration systems with curved boundaries using analytic elements and series solutions

    Science.gov (United States)

    Bakker, Mark

    2010-08-01

    A new analytic solution approach is presented for the modeling of steady flow to pumping wells near rivers in strip aquifers; all boundaries of the river and strip aquifer may be curved. The river penetrates the aquifer only partially and has a leaky stream bed. The water level in the river may vary spatially. Flow in the aquifer below the river is semi-confined while flow in the aquifer adjacent to the river is confined or unconfined and may be subject to areal recharge. Analytic solutions are obtained through superposition of analytic elements and Fourier series. Boundary conditions are specified at collocation points along the boundaries. The number of collocation points is larger than the number of coefficients in the Fourier series and a solution is obtained in the least squares sense. The solution is analytic while boundary conditions are met approximately. Very accurate solutions are obtained when enough terms are used in the series. Several examples are presented for domains with straight and curved boundaries, including a well pumping near a meandering river with a varying water level. The area of the river bottom where water infiltrates into the aquifer is delineated and the fraction of river water in the well water is computed for several cases.

  2. An approximate and an analytical solution to the carousel-pendulum problem

    Energy Technology Data Exchange (ETDEWEB)

    Vial, Alexandre [Pole Physique, Mecanique, Materiaux et Nanotechnologies, Universite de technologie de Troyes, 12, rue Marie Curie BP-2060, F-10010 Troyes Cedex (France)], E-mail: alexandre.vial@utt.fr

    2009-09-15

    We show that an improved solution to the carousel-pendulum problem can be easily obtained through a first-order Taylor expansion, and its accuracy is determined after the obtention of an unusable analytical exact solution, advantageously replaced by a numerical one. It is shown that the accuracy is unexpectedly high, even when the ratio length of the pendulum to carousel radius approaches unity. (letters and comments)

  3. Analytical approximate solutions for a general class of nonlinear delay differential equations.

    Science.gov (United States)

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

    We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

  4. The Analytic Solution of Schroedinger Equation with Potential Function Superposed by Six Terms with Positive-power and Inverse-power Potentials

    International Nuclear Information System (INIS)

    Hu Xianquan; Luo Guang; Cui Lipeng; Niu Lianbin; Li Fangyu

    2009-01-01

    The analytic solution of the radial Schroedinger equation is studied by using the tight coupling condition of several positive-power and inverse-power potential functions in this article. Furthermore, the precisely analytic solutions and the conditions that decide the existence of analytic solution have been searched when the potential of the radial Schroedinger equation is V(r) = α 1 r 8 + α 2 r 3 + α 3 r 2 + β 3 r -1 + β 2 r -3 + β 1 r -4 . Generally speaking, there is only an approximate solution, but not analytic solution for Schroedinger equation with several potentials' superposition. However, the conditions that decide the existence of analytic solution have been found and the analytic solution and its energy level structure are obtained for the Schroedinger equation with the potential which is motioned above in this paper. According to the single-value, finite and continuous standard of wave function in a quantum system, the authors firstly solve the asymptotic solution through the radial coordinate r → and r → 0; secondly, they make the asymptotic solutions combining with the series solutions nearby the neighborhood of irregular singularities; and then they compare the power series coefficients, deduce a series of analytic solutions of the stationary state wave function and corresponding energy level structure by tight coupling among the coefficients of potential functions for the radial Schroedinger equation; and lastly, they discuss the solutions and make conclusions. (general)

  5. Solution-based analysis of multiple analytes by a sensor array: toward the development of an electronic tongue

    Science.gov (United States)

    Savoy, Steven M.; Lavigne, John J.; Yoo, J. S.; Wright, John; Rodriguez, Marc; Goodey, Adrian; McDoniel, Bridget; McDevitt, John T.; Anslyn, Eric V.; Shear, Jason B.; Ellington, Andrew D.; Neikirk, Dean P.

    1998-12-01

    A micromachined sensor array has been developed for the rapid characterization of multi-component mixtures in aqueous media. The sensor functions in a manner analogous to that of the mammalian tongue, using an array composed of individually immobilized polystyrene-polyethylene glycol composite microspheres selectively arranged in micromachined etch cavities localized o n silicon wafers. Sensing occurs via colorimetric or fluorometric changes to indicator molecules that are covalently bound to amine termination sites on the polymeric microspheres. The hybrid micromachined structure has been interfaced directly to a charged-coupled-device that is used for the simultaneous acquisition of the optical data from the individually addressable `taste bud' elements. With the miniature sensor array, acquisition of data streams composed of red, green, and blue color patterns distinctive for the analytes in the solution are rapidly acquired. The unique combination of carefully chosen reporter molecules with water permeable microspheres allows for the simultaneous detection and quantification of a variety of analytes. The fabrication of the sensor structures and the initial colorimetric and fluorescent responses for pH, Ca+2, Ce+3, and sugar are reported. Interface to microfluidic components should also be possible, producing a complete sampling/sensing system.

  6. On the nonlinear dynamics of trolling-mode AFM: Analytical solution using multiple time scales method

    Science.gov (United States)

    Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

    2018-06-01

    Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.

  7. Analytical solution to convection-radiation of a continuously moving fin with temperature-dependent thermal conductivity

    Directory of Open Access Journals (Sweden)

    Moradi Amir

    2013-01-01

    Full Text Available In this article, the simultaneous convection-radiation heat transfer of a moving fin of variable thermal conductivity is studied. The differential transformation method (DTM is applied for an analytic solution for heat transfer in fin with two different profiles. Fin profiles are rectangular and exponential. The accuracy of analytic solution is validated by comparing it with the numerical solution that is obtained by fourth-order Runge-Kutta method. The analytical and numerical results are shown for different values of the embedding parameters. DTM results show that series converge rapidly with high accuracy. The results indicate that the fin tip temperature increases when ambient temperature increases. Conversely, the fin tip temperature decreases with an increase in the Peclet number, convection-conduction and radiation-conduction parameters. It is shown that the fin tip temperature of the exponential profile is higher than the rectangular one. The results indicate that the numerical data and analytical method are in a good agreement with each other.

  8. Semi-analytical solution to arbitrarily shaped beam scattering

    Science.gov (United States)

    Wang, Wenjie; Zhang, Huayong; Sun, Yufa

    2017-07-01

    Based on the field expansions in terms of appropriate spherical vector wave functions and the method of moments scheme, an exact semi-analytical solution to the scattering of an arbitrarily shaped beam is given. For incidence of a Gaussian beam, zero-order Bessel beam and Hertzian electric dipole radiation, numerical results of the normalized differential scattering cross section are presented to a spheroid and a circular cylinder of finite length, and the scattering properties are analyzed concisely.

  9. Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

    International Nuclear Information System (INIS)

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-01-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  10. A Physically Based Analytical Model to Describe Effective Excess Charge for Streaming Potential Generation in Water Saturated Porous Media

    Science.gov (United States)

    Guarracino, L.; Jougnot, D.

    2018-01-01

    Among the different contributions generating self-potential, the streaming potential is of particular interest in hydrogeology for its sensitivity to water flow. Estimating water flux in porous media using streaming potential data relies on our capacity to understand, model, and upscale the electrokinetic coupling at the mineral-solution interface. Different approaches have been proposed to predict streaming potential generation in porous media. One of these approaches is the flux averaging which is based on determining the excess charge which is effectively dragged in the medium by water flow. In this study, we develop a physically based analytical model to predict the effective excess charge in saturated porous media using a flux-averaging approach in a bundle of capillary tubes with a fractal pore size distribution. The proposed model allows the determination of the effective excess charge as a function of pore water ionic concentration and hydrogeological parameters like porosity, permeability, and tortuosity. The new model has been successfully tested against different set of experimental data from the literature. One of the main findings of this study is the mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by several researchers. The proposed model also highlights the link to other lithological properties, and it is able to reproduce the evolution of effective excess charge with electrolyte concentrations.

  11. Solution of the isotopic depletion equation using decomposition method and analytical solution

    Energy Technology Data Exchange (ETDEWEB)

    Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: fprata@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear

    2011-07-01

    In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)

  12. Solution of the isotopic depletion equation using decomposition method and analytical solution

    International Nuclear Information System (INIS)

    Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S.

    2011-01-01

    In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)

  13. Analytical solutions for the study of immersed unanchored structures under seismic loading

    International Nuclear Information System (INIS)

    Mege, Romain

    2011-01-01

    In the nuclear energy industry, most of the major components are anchored to the civil works using numerous types of supports devices. These anchorages are big issues of the nuclear plant design: the implantation of the components has to be fixed definitely, stress concentration in the surroundings of the anchorage, and for immersed structure, possible loss of the impermeability. Thereby, under certain safety regulations, some structures lay directly on the ground. This is the case for in air or underwater structure, such as fuel storage racks. This solution gives more flexibility in the use of the components and a decrease of the stress. However, one has to evaluate precisely the behavior of this sliding structure, and in particular, the cumulated sliding displacement during a seismic event in order to prevent any impact with other components. During a seismic event, the unanchored structure can slide, rotate and tilt. The aim of this paper is to present analytical solutions to estimate the sliding amplitudes of different simplified systems which represent a given dynamic behavior. These simplified models are: a sliding mass and a complex sliding structure defined by its eigenmodes. Each simplified system corresponds to a different set of assumptions made on the flexibility of the structure. Two analytical solutions are presented in this article: single sliding mass and a vertical sliding beam. In each model, the fluid-structure interaction between the immersed body and the pool is modeled as hydrodynamic masses. The sliding is represented by Coulomb friction. The seismic loading can be any 3D seismic accelerogram. The analytical solutions are obtained considering the different phases of the movement and the continuity between each phase. The results are then compared to the values computed with the commercial Finite Element package ANSYS TM . The analytical curves show a good fit of the computational results. (author)

  14. The foam drainage equation for drainage dynamics in unsaturated porous media

    Science.gov (United States)

    Lehmann, P.; Hoogland, F.; Assouline, S.; Or, D.

    2017-07-01

    Similarity in liquid-phase configuration and drainage dynamics of wet foam and gravity drainage from unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation—SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. The study provides new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions. Two novel analytical solutions for saturation profile evolution were derived and tested in good agreement with a numerical solution of the SFDE. The study and the proposed solutions rectify the original formulation of foam drainage dynamics of Or and Assouline (2013). The new framework broadens the scope of methods available for quantifying unsaturated flow in porous media, where the intrinsic conductivity and geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.

  15. Social media analytics dashboard for academics and the decision-making process: A systematic literature review

    DEFF Research Database (Denmark)

    Christensen, Line Lisberg; Khalid, Md. Saifuddin

    2018-01-01

    uncovered 11 texts of relevance to the topic, along with five pre-determined texts. In order to create a legible overview of the literature, a qualitative content analysis was conducted, coded with 21 themes, and merged into three categories: (1) Bibliometrics, social media analytics and alternative metrics...

  16. Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

    Science.gov (United States)

    Khan, Farman U; Qamar, Shamsul

    2017-05-01

    A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  17. Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

    Science.gov (United States)

    Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

    2002-01-01

    Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

  18. An analytical model for solute transport through a GCL-based two-layered liner considering biodegradation

    Energy Technology Data Exchange (ETDEWEB)

    Guan, C. [Institute of Hydrology and Water Resources Engineering, Zhejiang University, Hangzhou 310058 (China); Xie, H.J., E-mail: xiehaijian@zju.edu.cn [Institute of Hydrology and Water Resources Engineering, Zhejiang University, Hangzhou 310058 (China); MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058 (China); Wang, Y.Z.; Chen, Y.M.; Jiang, Y.S.; Tang, X.W. [MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058 (China)

    2014-01-01

    An analytical model for solute advection and dispersion in a two-layered liner consisting of a geosynthetic clay liner (GCL) and a soil liner (SL) considering the effect of biodegradation was proposed. The analytical solution was derived by Laplace transformation and was validated over a range of parameters using the finite-layer method based software Pollute v7.0. Results show that if the half-life of the solute in GCL is larger than 1 year, the degradation in GCL can be neglected for solute transport in GCL/SL. When the half-life of GCL is less than 1 year, neglecting the effect of degradation in GCL on solute migration will result in a large difference of relative base concentration of GCL/SL (e.g., 32% for the case with half-life of 0.01 year). The 100-year solute base concentration can be reduced by a factor of 2.2 when the hydraulic conductivity of the SL was reduced by an order of magnitude. The 100-year base concentration was reduced by a factor of 155 when the half life of the contaminant in the SL was reduced by an order of magnitude. The effect of degradation is more important in approving the groundwater protection level than the hydraulic conductivity. The analytical solution can be used for experimental data fitting, verification of complicated numerical models and preliminary design of landfill liner systems. - Highlights: •Degradation of contaminants was considered in modeling solute transport in GCL/SL. •Analytical solutions were derived for assessment of GCL/SL with degradation. •Degradation in GCL can be ignored as half-life is larger than 1 year. •Base concentration is more sensitive to half-life of SL than to permeability of SL.

  19. An analytical model for solute transport through a GCL-based two-layered liner considering biodegradation

    International Nuclear Information System (INIS)

    Guan, C.; Xie, H.J.; Wang, Y.Z.; Chen, Y.M.; Jiang, Y.S.; Tang, X.W.

    2014-01-01

    An analytical model for solute advection and dispersion in a two-layered liner consisting of a geosynthetic clay liner (GCL) and a soil liner (SL) considering the effect of biodegradation was proposed. The analytical solution was derived by Laplace transformation and was validated over a range of parameters using the finite-layer method based software Pollute v7.0. Results show that if the half-life of the solute in GCL is larger than 1 year, the degradation in GCL can be neglected for solute transport in GCL/SL. When the half-life of GCL is less than 1 year, neglecting the effect of degradation in GCL on solute migration will result in a large difference of relative base concentration of GCL/SL (e.g., 32% for the case with half-life of 0.01 year). The 100-year solute base concentration can be reduced by a factor of 2.2 when the hydraulic conductivity of the SL was reduced by an order of magnitude. The 100-year base concentration was reduced by a factor of 155 when the half life of the contaminant in the SL was reduced by an order of magnitude. The effect of degradation is more important in approving the groundwater protection level than the hydraulic conductivity. The analytical solution can be used for experimental data fitting, verification of complicated numerical models and preliminary design of landfill liner systems. - Highlights: •Degradation of contaminants was considered in modeling solute transport in GCL/SL. •Analytical solutions were derived for assessment of GCL/SL with degradation. •Degradation in GCL can be ignored as half-life is larger than 1 year. •Base concentration is more sensitive to half-life of SL than to permeability of SL

  20. Auxiliary fields as a tool for computing analytical solutions of the Schroedinger equation

    International Nuclear Information System (INIS)

    Silvestre-Brac, Bernard; Semay, Claude; Buisseret, Fabien

    2008-01-01

    We propose a new method to obtain approximate solutions for the Schroedinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows to find in many cases, analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which greatly improves the corresponding formulae that can be found in the literature

  1. Auxiliary fields as a tool for computing analytical solutions of the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Silvestre-Brac, Bernard [LPSC Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France); Semay, Claude; Buisseret, Fabien [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium)], E-mail: silvestre@lpsc.in2p3.fr, E-mail: claude.semay@umh.ac.be, E-mail: fabien.buisseret@umh.ac.be

    2008-07-11

    We propose a new method to obtain approximate solutions for the Schroedinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows to find in many cases, analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which greatly improves the corresponding formulae that can be found in the literature.

  2. Finite medium Green's function solutions to nuclide transport in porous media

    International Nuclear Information System (INIS)

    Oston, S.G.

    1979-01-01

    Current analytical techniques for predicting the transport of nuclides in porous materials center on the Green's function approach - i.e., determining the response characteristics of a geologic pathway to an impulse function input. To data, the analyses all have set the boundary conditions needed to solve the 1-D transport equation as though each pathway were infinite in length. The purpose of this work is to critically examine the effect that this infinite pathway assumption has on Green's function models of nuclide transport in porous media. The work described herein has directly attacked the more difficult problem of obtaining suitable Green's functions for finite pathways whose dimensions, in fact, may not be much greater than the diffusion length. Two different finite media Green's functions describing the nuclide mass flux have been determined, depending on whether the pathway is terminated by a high or a low flow resistance at the outlet end. Pulse shapes and peak amplitudes have been computed for each Green's function over a wide range of geohydrologic parameters. These results have been compared to both infinite and semi-infinite medium solutions. It was found that predicted pulse shapes are quite sensitive to selection of a Green's function model for short pathways only. For long pathways all models tend toward a symmetric Gaussian flux-time history at the outlet. Thus, the results of our previous waste transport studies using the infinite pathway assumption are still generally valid because they always included at least one long pathway. It was also found that finite medium models offer some unique computational advantages for evaluating nuclide transport in a series of connecting pathways

  3. Exact solutions of the Navier-Stokes equations generalized for flow in porous media

    Science.gov (United States)

    Daly, Edoardo; Basser, Hossein; Rudman, Murray

    2018-05-01

    Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

  4. A Content Analytic Technique for Measuring the Sexiness of Women's Business Attire in Media Presentations.

    Science.gov (United States)

    White, Sylvia E.

    1995-01-01

    Describes development of an objective content analytic category scheme for measuring the sexiness of women's business attire in media presentations. Finds women's business attire in television soap operas significantly more provocative than real-world attire. Finds a significant positive correlation between the degree of sexiness as measured by…

  5. Analytic study of nonperturbative solutions in open string field theory

    International Nuclear Information System (INIS)

    Bars, I.; Kishimoto, I.; Matsuo, Y.

    2003-01-01

    We propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the spectrum of two identical half strings which are independent from each other. The second one, which we call midpoint correction, shifts the half string spectrum to that of the standard open string. We show that the nonlinear equation of motion of string field theory is exactly solvable at zeroth order in the midpoint correction. An infinite number of solutions are classified in terms of projection operators. Among them, there exists only one stable solution which is identical to the standard butterfly state. We include the effect of the midpoint correction around each exact zeroth order solution as a perturbation expansion which can be formally summed to the complete exact solution

  6. Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

    Energy Technology Data Exchange (ETDEWEB)

    Messaris, Gerasimos A. T., E-mail: messaris@upatras.gr [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece); School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Hadjinicolaou, Maria [School of Science and Technology, Hellenic Open University, 11 Sahtouri Street, GR 262 22 Patras (Greece); Karahalios, George T. [Department of Physics, Division of Theoretical Physics, University of Patras, GR 265 04 Rion (Greece)

    2016-08-15

    The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses

  7. Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

    International Nuclear Information System (INIS)

    Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

    2016-01-01

    The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses

  8. Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

    Science.gov (United States)

    Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.

    2016-08-01

    The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions

  9. On analytic solutions of (1+3)D relativistic ideal hydrodynamic equations

    International Nuclear Information System (INIS)

    Lin Shu; Liao Jinfeng

    2010-01-01

    In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble embedding, for which a single ordinary differential equation for the remaining velocity field can be derived. Using this equation, all solutions with transverse 2D Hubble embedding and power law ansatz for the remaining longitudinal velocity field will be found. Going beyond the power law ansatz, we further find a few solutions with transverse 2D Hubble embedding and nontrivial longitudinal velocity field. Finally we investigate general scaling flows with each component of the velocity fields scaling independently, for which we also find all possible solutions.

  10. Multiscale modelling of dual-porosity porous media; a computational pore-scale study for flow and solute transport

    Science.gov (United States)

    de Vries, Enno T.; Raoof, Amir; van Genuchten, Martinus Th.

    2017-07-01

    Many environmental and agricultural applications involve the transport of water and dissolved constituents through aggregated soil profiles, or porous media that are structured, fractured or macroporous in other ways. During the past several decades, various process-based macroscopic models have been used to simulate contaminant transport in such media. Many of these models consider advective-dispersive transport through relatively large inter-aggregate pore domains, while exchange with the smaller intra-aggregate pores is assumed to be controlled by diffusion. Exchange of solute between the two domains is often represented using a first-order mass transfer coefficient, which is commonly obtained by fitting to observed data. This study aims to understand and quantify the solute exchange term by applying a dual-porosity pore-scale network model to relatively large domains, and analysing the pore-scale results in terms of the classical dual-porosity (mobile-immobile) transport formulation. We examined the effects of key parameters (notably aggregate porosity and aggregate permeability) on the main dual-porosity model parameters, i.e., the mobile water fraction (ϕm) and the mass transfer coefficient (α). Results were obtained for a wide range of aggregate porosities (between 0.082 and 0.700). The effect of aggregate permeability was explored by varying pore throat sizes within the aggregates. Solute breakthrough curves (BTCs) obtained with the pore-scale network model at several locations along the domain were analysed using analytical solutions of the dual-porosity model to obtain estimates of ϕm and α. An increase in aggregate porosity was found to decrease ϕm and increase α, leading to considerable tailing in the BTCs. Changes in the aggregate pore throat size affected the relative flow velocity between the intra- and inter-aggregate domains. Higher flow velocities within the aggregates caused a change in the transport regime from diffusion dominated to more

  11. Colloid transport in dual-permeability media

    Science.gov (United States)

    Leij, Feike J.; Bradford, Scott A.

    2013-07-01

    It has been widely reported that colloids can travel faster and over longer distances in natural structured porous media than in uniform structureless media used in laboratory studies. The presence of preferential pathways for colloids in the subsurface environment is of concern because of the increased risks for disease caused by microorganisms and colloid-associated contaminants. This study presents a model for colloid transport in dual-permeability media that includes reversible and irreversible retention of colloids and first-order exchange between the aqueous phases of the two regions. The model may also be used to describe transport of other reactive solutes in dual-permeability media. Analytical solutions for colloid concentrations in aqueous and solid phases were obtained using Laplace transformation and matrix decomposition. The solutions proved convenient to assess the effect of model parameters on the colloid distribution. The analytical model was used to describe effluent concentrations for a bromide tracer and 3.2- or 1-μm-colloids that were observed after transport through a composite 10-cm long porous medium made up of a cylindrical lens or core of sand and a surrounding matrix with sand of a different grain size. The tracer data were described very well and realistic estimates were obtained for the pore-water velocity in the two flow domains. An accurate description was also achieved for most colloid breakthrough curves. Dispersivity and retention parameters were typically greater for the larger 3.2-μm-colloids while both reversible and irreversible retention rates tended to be higher for the finer sands than the coarser sand. The relatively small sample size and the complex flow pattern in the composite medium made it difficult to reach definitive conclusions regarding transport parameters for colloid transport.

  12. Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation

    International Nuclear Information System (INIS)

    Durand, B.; Durand, L.

    1983-01-01

    We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly

  13. Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

    Science.gov (United States)

    Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan

    2008-09-01

    We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier-Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.

  14. Transport of radionuclides in stochastic media. Pt. 1: The quasi-asymptotic approximation

    International Nuclear Information System (INIS)

    Devooght, J.; Smidts, O.F.

    1996-01-01

    A three-dimensional quasi-asymptotic approximate equation is developed for the transport of radionuclides in a stochastic velocity field. This approximation is derived from an integro-differential equation of transport in stochastic media, commonly encountered in hydrogeology. The quasi-asymptotic equation turns out to be a generalised Telegrapher's equation as found by Williams in the particular context of fractured media. We obtain the Telegrapher's equation without specifying the causes responsible for the random velocity field. Our model may thus be applied in porous media as well as in fractured media. We give the developments leading to the analytical solution of the three-dimensional Telegrapher's equation for constant parameters. This solution is then visualised for a source in the form of a square wave. (Author)

  15. Analytical Solution of a Generalized Hirota-Satsuma Equation

    Science.gov (United States)

    Kassem, M.; Mabrouk, S.; Abd-el-Malek, M.

    A modified version of generalized Hirota-Satsuma is here solved using a two parameter group transformation method. This problem in three dimensions was reduced by Estevez [1] to a two dimensional one through a Lie transformation method and left unsolved. In the present paper, through application of symmetry transformation the Lax pair has been reduced to a system of ordinary equations. Three transformations cases are investigated. The obtained analytical solutions are plotted and show a profile proper to deflagration processes, well described by Degasperis-Procesi equation.

  16. Developing semi-analytical solution for multiple-zone transient storage model with spatially non-uniform storage

    Science.gov (United States)

    Deng, Baoqing; Si, Yinbing; Wang, Jia

    2017-12-01

    Transient storages may vary along the stream due to stream hydraulic conditions and the characteristics of storage. Analytical solutions of transient storage models in literature didn't cover the spatially non-uniform storage. A novel integral transform strategy is presented that simultaneously performs integral transforms to the concentrations in the stream and in storage zones by using the single set of eigenfunctions derived from the advection-diffusion equation of the stream. The semi-analytical solution of the multiple-zone transient storage model with the spatially non-uniform storage is obtained by applying the generalized integral transform technique to all partial differential equations in the multiple-zone transient storage model. The derived semi-analytical solution is validated against the field data in literature. Good agreement between the computed data and the field data is obtained. Some illustrative examples are formulated to demonstrate the applications of the present solution. It is shown that solute transport can be greatly affected by the variation of mass exchange coefficient and the ratio of cross-sectional areas. When the ratio of cross-sectional areas is big or the mass exchange coefficient is small, more reaches are recommended to calibrate the parameter.

  17. Analytic Closed-Form Solution of a Mixed Layer Model for Stratocumulus Clouds

    Science.gov (United States)

    Akyurek, Bengu Ozge

    Stratocumulus clouds play an important role in climate cooling and are hard to predict using global climate and weather forecast models. Thus, previous studies in the literature use observations and numerical simulation tools, such as large-eddy simulation (LES), to solve the governing equations for the evolution of stratocumulus clouds. In contrast to the previous works, this work provides an analytic closed-form solution to the cloud thickness evolution of stratocumulus clouds in a mixed-layer model framework. With a focus on application over coastal lands, the diurnal cycle of cloud thickness and whether or not clouds dissipate are of particular interest. An analytic solution enables the sensitivity analysis of implicitly interdependent variables and extrema analysis of cloud variables that are hard to achieve using numerical solutions. In this work, the sensitivity of inversion height, cloud-base height, and cloud thickness with respect to initial and boundary conditions, such as Bowen ratio, subsidence, surface temperature, and initial inversion height, are studied. A critical initial cloud thickness value that can be dissipated pre- and post-sunrise is provided. Furthermore, an extrema analysis is provided to obtain the minima and maxima of the inversion height and cloud thickness within 24 h. The proposed solution is validated against LES results under the same initial and boundary conditions. Then, the proposed analytic framework is extended to incorporate multiple vertical columns that are coupled by advection through wind flow. This enables a bridge between the micro-scale and the mesoscale relations. The effect of advection on cloud evolution is studied and a sensitivity analysis is provided.

  18. Analytical Solution for Optimum Design of Furrow Irrigation Systems

    Science.gov (United States)

    Kiwan, M. E.

    1996-05-01

    An analytical solution for the optimum design of furrow irrigation systems is derived. The non-linear calculus optimization method is used to formulate a general form for designing the optimum system elements under circumstances of maximizing the water application efficiency of the system during irrigation. Different system bases and constraints are considered in the solution. A full irrigation water depth is considered to be achieved at the tail of the furrow line. The solution is based on neglecting the recession and depletion times after off-irrigation. This assumption is valid in the case of open-end (free gradient) furrow systems rather than closed-end (closed dike) systems. Illustrative examples for different systems are presented and the results are compared with the output obtained using an iterative numerical solution method. The final derived solution is expressed as a function of the furrow length ratio (the furrow length to the water travelling distance). The function of water travelling developed by Reddy et al. is considered for reaching the optimum solution. As practical results from the study, the optimum furrow elements for free gradient systems can be estimated to achieve the maximum application efficiency, i.e. furrow length, water inflow rate and cutoff irrigation time.

  19. Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields

    International Nuclear Information System (INIS)

    Baxter, Mathew; Van Gorder, Robert A

    2013-01-01

    We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)

  20. Power Users and Patchworking – an Analytical Approach to Critical Studies of Young People’s Learning with Digital Media

    DEFF Research Database (Denmark)

    Ryberg, Thomas; Dirckinck-Holmfeld, Lone

    2008-01-01

    This paper sets out to problematize generational categories such as ‘Power Users’ or ‘New Millennium Learners’ by discussing these in the light of recent research on youth and ICT. We then suggest analytic and conceptual pathways to engage in more critical and empirically founded studies of young...... people’s learning in technology and media-rich settings. Based on a study of a group of young ‘Power Users’ it is argued, that conceptualising and analysing learning as a process of patchworking can enhance our knowledge of young people’s learning in such settings. We argue that the analytical approach...... gives us ways of critically investigating young people’s learning in technology and media-rich settings, and study if these are processes of critical, reflexive enquiry where resources are creatively re-appropriated. With departure in an analytical example the paper presents the proposed metaphor...

  1. Muonium hyperfine structure : An analytical solution to perturbative calculations

    International Nuclear Information System (INIS)

    Wotzasek, C.J.; Gregorio, M.A.; Reinecke, S.

    1982-01-01

    The purely coulombian contribution to the terms of order E sub(F) (α 2 m sub(e)/m sub(μ))ln α - 1 of the hyperfine splitting of muonium is computed. Results agree with those of other authors. The goal of the work was twofold: first, to confirm that contribution; second, and perhaps more important, to check the analytic solution of the relativistic coulombian problem of the Bethe-Salpeter equation with instantaneous kernel. (Author) [pt

  2. Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube

    International Nuclear Information System (INIS)

    Eraslan, Ahmet N.; Akis, Tolga

    2006-01-01

    Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states are investigated. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected significantly by the material nonhomogeneity. Different modes of plasticization may take place unlike the homogeneous case. It is also shown mathematically that the nonhomogeneous elastoplastic solution presented here reduces to that of a homogeneous one by appropriate choice of the material parameters

  3. Explicit analytical solution of a pendulum with periodically varying length

    International Nuclear Information System (INIS)

    Yang Tianzhi; Fang Bo; Li Song; Huang Wenhu

    2010-01-01

    A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper, we use the homotopy analysis method to explore the approximate solution to this system. The method can easily self-adjust and control the convergence region. By applying the method to the governing equation of the pendulum, we obtain the approximation solution in a closed form. It is shown by the numerical method that the homotopy analysis method supplies a more accurate analytical solution for predicting the long-term behaviour of the pendulum. We believe that this system may be a good example for undergraduate and graduate students for better understanding of nonlinear oscillations.

  4. Application of an analytical method for solution of thermal hydraulic conservation equations

    Energy Technology Data Exchange (ETDEWEB)

    Fakory, M.R. [Simulation, Systems & Services Technologies Company (S3 Technologies), Columbia, MD (United States)

    1995-09-01

    An analytical method has been developed and applied for solution of two-phase flow conservation equations. The test results for application of the model for simulation of BWR transients are presented and compared with the results obtained from application of the explicit method for integration of conservation equations. The test results show that with application of the analytical method for integration of conservation equations, the Courant limitation associated with explicit Euler method of integration was eliminated. The results obtained from application of the analytical method (with large time steps) agreed well with the results obtained from application of explicit method of integration (with time steps smaller than the size imposed by Courant limitation). The results demonstrate that application of the analytical approach significantly improves the numerical stability and computational efficiency.

  5. Comparison between numeric and approximate analytic solutions for the prediction of soil metal uptake by roots. Example of cadmium.

    Science.gov (United States)

    Schneider, André; Lin, Zhongbing; Sterckeman, Thibault; Nguyen, Christophe

    2018-04-01

    The dissociation of metal complexes in the soil solution can increase the availability of metals for root uptake. When it is accounted for in models of bioavailability of soil metals, the number of partial differential equations (PDEs) increases and the computation time to numerically solve these equations may be problematic when a large number of simulations are required, for example for sensitivity analyses or when considering root architecture. This work presents analytical solutions for the set of PDEs describing the bioavailability of soil metals including the kinetics of complexation for three scenarios where the metal complex in solution was fully inert, fully labile, or partially labile. The analytical solutions are only valid i) at steady-state when the PDEs become ordinary differential equations, the transient phase being not covered, ii) when diffusion is the major mechanism of transport and therefore, when convection is negligible, iii) when there is no between-root competition. The formulation of the analytical solutions is for cylindrical geometry but the solutions rely on the spread of the depletion profile around the root, which was modelled assuming a planar geometry. The analytical solutions were evaluated by comparison with the corresponding PDEs for cadmium in the case of the French agricultural soils. Provided that convection was much lower than diffusion (Péclet's number<0.02), the cumulative uptakes calculated from the analytic solutions were in very good agreement with those calculated from the PDEs, even in the case of a partially labile complex. The analytic solutions can be used instead of the PDEs to predict root uptake of metals. The analytic solutions were also used to build an indicator of the contribution of a complex to the uptake of the metal by roots, which can be helpful to predict the effect of soluble organic matter on the bioavailability of soil metals. Copyright © 2017 Elsevier B.V. All rights reserved.

  6. Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

    KAUST Repository

    Mazaré , Pierre Emmanuel; Dehwah, Ahmad H.; Claudel, Christian G.; Bayen, Alexandre M.

    2011-01-01

    In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.

  7. Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

    KAUST Repository

    Mazaré, Pierre Emmanuel

    2011-12-01

    In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.

  8. Analytical methods for predicting contaminant transport

    International Nuclear Information System (INIS)

    Pigford, T.H.

    1989-09-01

    This paper summarizes some of the previous and recent work at the University of California on analytical solutions for predicting contaminate transport in porous and fractured geologic media. Emphasis is given here to the theories for predicting near-field transport, needed to derive the time-dependent source term for predicting far-field transport and overall repository performance. New theories summarized include solubility-limited release rate with flow backfill in rock, near-field transport of radioactive decay chains, interactive transport of colloid and solute, transport of carbon-14 as carbon dioxide in unsaturated rock, and flow of gases out of and a waste container through cracks and penetrations. 28 refs., 4 figs

  9. Radionuclide transport through heteogeneous media

    International Nuclear Information System (INIS)

    Hadermann, J.

    1980-01-01

    One-dimensional radionuclide migration for conevective water transport with sorption and longitudinal dispersion is investigated. A semianalytic solution for layered media with piecewise constant parametes can be written when taking into account mass conservation and approximate flux conservation at interlayer boundaries. The solution is analytic in the first layer and allows for a recursive calculation in the following layers. Scaling laws for the relevant parameters can be formulated. Numerical examples exhibit the importance of at least a single highly sorbing layer. Small values of dispersivity may not lead to a conservative estimate of conservation at the geological column's end

  10. Analytical solution for vacuum preloading considering the nonlinear distribution of horizontal permeability within the smear zone.

    Directory of Open Access Journals (Sweden)

    Jie Peng

    Full Text Available The vacuum preloading is an effective method which is widely used in ground treatment. In consolidation analysis, the soil around prefabricated vertical drain (PVD is traditionally divided into smear zone and undisturbed zone, both with constant permeability. In reality, the permeability of soil changes continuously within the smear zone. In this study, the horizontal permeability coefficient of soil within the smear zone is described by an exponential function of radial distance. A solution for vacuum preloading consolidation considers the nonlinear distribution of horizontal permeability within the smear zone is presented and compared with previous analytical results as well as a numerical solution, the results show that the presented solution correlates well with the numerical solution, and is more precise than previous analytical solution.

  11. New Analytic Solution to the Lane-Emden Equation of Index 2

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2012-01-01

    Full Text Available We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986 which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.

  12. Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator

    Directory of Open Access Journals (Sweden)

    Takibayev N.Zh.

    2010-04-01

    Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two fixed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei fixed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.

  13. Transport of titanium dioxide nanoparticles in saturated porous media under various solution chemistry conditions

    International Nuclear Information System (INIS)

    Wang Yu; Gao Bin; Morales, Verónica L.; Tian Yuan; Wu Lei; Gao Jie; Bai Wei; Yang Liuyan

    2012-01-01

    Because of its wide applications, nanosized titanium dioxide may become a potential environmental risk to soil and groundwater system. It is therefore important to improve current understanding of the environmental fate and transport of titanium oxides nanoparticles (TONPs). In this work, the effect of solution chemistry (i.e., pH, ionic strength, and natural organic matter (NOM) concentration) on the deposition and transport of TONPs in saturated porous media was examined in detail. Laboratory columns packed with acid-cleaned quartz sand were used in the experiment as porous media. Transport experiments were conducted with various chemistry combinations, including four ionic strengths, three pH levels, and two NOM concentrations. The results showed that TONP mobility increased with increasing solution pH, but decreased with increasing solution ionic strength. It is also found that the presence of NOM in the system enhanced the mobility of TONPs in the saturated porous media. The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory was used to justify the mobility trends observed in the experimental data. Predictions from the theory agreed excellently with the experimental data.

  14. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

    OpenAIRE

    Xiao-Li Ding; Juan J. Nieto

    2018-01-01

    In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

  15. Does Implementation of Big Data Analytics Improve Firms’ Market Value? Investors’ Reaction in Stock Market

    Directory of Open Access Journals (Sweden)

    Hansol Lee

    2017-06-01

    Full Text Available Recently, due to the development of social media, multimedia, and the Internet of Things (IoT, various types of data have increased. As the existing data analytics tools cannot cover this huge volume of data, big data analytics becomes one of the emerging technologies for business today. Considering that big data analytics is an up-to-date term, in the present study, we investigated the impact of implementing big data analytics in the short-term perspective. We used an event study methodology to investigate the changes in stock price caused by announcements on big data analytics solution investment. A total of 54 investment announcements of firms publicly traded in NASDAQ and NYSE from 2010 to 2015 were collected. Our results empirically demonstrate that announcement of firms’ investment on big data solution leads to positive stock market reactions. In addition, we also found that investments on small vendors’ solution with industry-oriented functions tend to result in higher abnormal returns than those on big vendors’ solution with general functions. Finally, our results also suggest that stock market investors highly evaluate big data analytics investments of big firms as compared to those of small firms.

  16. An analytical solution for two-dimensional vacuum preloading combined with electro-osmosis consolidation using EKG electrodes

    Science.gov (United States)

    Qiu, Chenchen; Li, Yande

    2017-01-01

    China is a country with vast territory, but economic development and population growth have reduced the usable land resources in recent years. Therefore, reclamation by pumping and filling is carried out in eastern coastal regions of China in order to meet the needs of urbanization. However, large areas of reclaimed land need rapid drainage consolidation treatment. Based on past researches on how to improve the treatment efficiency of soft clay using vacuum preloading combined with electro-osmosis, a two-dimensional drainage plane model was proposed according to the Terzaghi and Esrig consolidation theory. However, the analytical solution using two-dimensional plane model was never involved. Current analytical solutions can’t have a thorough theoretical analysis of practical engineering and give relevant guidance. Considering the smearing effect and the rectangle arrangement pattern, an analytical solution is derived to describe the behavior of pore-water and the consolidation process by using EKG (electro-kinetic geo synthetics) materials. The functions of EKG materials include drainage, electric conduction and corrosion resistance. Comparison with test results is carried out to verify the analytical solution. It is found that the measured value is larger than the applied vacuum degree because of the stacking effect of the vacuum preloading and electro-osmosis. The trends of the mean measured value and the mean analytical value processes are comparable. Therefore, the consolidation model can accurately assess the change in pore-water pressure and the consolidation process during vacuum preloading combined with electro-osmosis. PMID:28771496

  17. An analytical solution for two-dimensional vacuum preloading combined with electro-osmosis consolidation using EKG electrodes.

    Directory of Open Access Journals (Sweden)

    Yang Shen

    Full Text Available China is a country with vast territory, but economic development and population growth have reduced the usable land resources in recent years. Therefore, reclamation by pumping and filling is carried out in eastern coastal regions of China in order to meet the needs of urbanization. However, large areas of reclaimed land need rapid drainage consolidation treatment. Based on past researches on how to improve the treatment efficiency of soft clay using vacuum preloading combined with electro-osmosis, a two-dimensional drainage plane model was proposed according to the Terzaghi and Esrig consolidation theory. However, the analytical solution using two-dimensional plane model was never involved. Current analytical solutions can't have a thorough theoretical analysis of practical engineering and give relevant guidance. Considering the smearing effect and the rectangle arrangement pattern, an analytical solution is derived to describe the behavior of pore-water and the consolidation process by using EKG (electro-kinetic geo synthetics materials. The functions of EKG materials include drainage, electric conduction and corrosion resistance. Comparison with test results is carried out to verify the analytical solution. It is found that the measured value is larger than the applied vacuum degree because of the stacking effect of the vacuum preloading and electro-osmosis. The trends of the mean measured value and the mean analytical value processes are comparable. Therefore, the consolidation model can accurately assess the change in pore-water pressure and the consolidation process during vacuum preloading combined with electro-osmosis.

  18. Hyporheic less-mobile porosity and solute transport in porous media

    Science.gov (United States)

    MahmoodPoorDehkordy, F.; Briggs, M. A.; Day-Lewis, F. D.; Scruggs, C.; Singha, K.; Zarnetske, J. P.; Lane, J. W., Jr.; Bagtzoglou, A. C.

    2017-12-01

    Solute transport and reactive processes are strongly influenced by hydrodynamic exchange with the hyporheic zone. Contaminant transport and redox zonation in the hyporheic zone and near-stream aquifer can be impacted by the exchange between mobile and less-mobile porosity zones in heterogeneous porous media. Less-mobile porosity zones can be created by fine materials with tight pore throats (e.g. clay, organics) and in larger, well-connected pores down gradient of flow obstructions (e.g. sand behind cobbles). Whereas fluid sampling is primarily responsive to the more-mobile domain, tracking solute tracer dynamics by geoelectrical methods provides direct information about both more- and less-mobile zones. During tracer injection through porous media of varied pore connectivity, a lag between fluid and bulk electrical conductivity is observed, creating a hysteresis loop when plotted in conductivity space. Thus, the combination of simultaneous fluid and bulk electrical conductivity measurements enables a much improved quantification of less-mobile solute dynamics compared to traditional fluid-only sampling approaches. We have demonstrated the less-mobile porosity exchange in laboratory-scale column experiments verified by simulation models. The experimental approach has also been applied to streambed sediments in column and reach-scale field experiments and verified using numerical simulation. Properties of the resultant hysteresis loops can be used to estimate exchange parameters of less-mobile porosity. Our integrated approach combining field experiments, laboratory experiments, and numerical modeling provides new insights into the effect of less-mobile porosity on solute transport in the hyporheic zone.

  19. On Analytical Solutions of f(R) Modified Gravity Theories in FLRW Cosmologies

    Science.gov (United States)

    Domazet, Silvije; Radovanović, Voja; Simonović, Marko; Štefančić, Hrvoje

    2013-02-01

    A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R), which leads to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.

  20. An analytic solution of the static problem of inclined risers conveying fluid

    KAUST Repository

    Alfosail, Feras; Nayfeh, Ali H.; Younis, Mohammad I.

    2016-01-01

    We use the method of matched asymptotic expansion to develop an analytic solution to the static problem of clamped–clamped inclined risers conveying fluid. The inclined riser is modeled as an Euler–Bernoulli beam taking into account its self

  1. Analytical solution of the toroidal constant tension solenoid

    International Nuclear Information System (INIS)

    Gralnick, S.L.; Tenney, F.H.

    1975-01-01

    The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 percent

  2. Diffusion Dominant Solute Transport Modelling in Fractured Media Under Deep Geological Environment - 12211

    Energy Technology Data Exchange (ETDEWEB)

    Kwong, S. [National Nuclear Laboratory (United Kingdom); Jivkov, A.P. [Research Centre for Radwaste and Decommissioning and Modelling and Simulation Centre, University of Manchester (United Kingdom)

    2012-07-01

    Deep geologic disposal of high activity and long-lived radioactive waste is gaining increasing support in many countries, where suitable low permeability geological formation in combination with engineered barriers are used to provide long term waste contaminant and minimise the impacts to the environment and risk to the biosphere. This modelling study examines the solute transport in fractured media under low flow velocities that are relevant to a deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes. The effects of water velocity in the fracture, matrix porosity and diffusion on solute transport are investigated and discussed. Some illustrative modelled results are presented to demonstrate the use of the model to examine the effects of media degradation on solute transport, under the influences of hydrogeological (diffusion dominant) and microbially mediated chemical processes. The challenges facing the prediction of long term degradation such as cracks evolution, interaction and coalescence are highlighted. The potential of a novel microstructure informed modelling approach to account for these effects is discussed, particularly with respect to investigating multiple phenomena impact on material performance. The GRM code is used to examine the effects of media degradation for a geological waste disposal package, under the combined hydrogeological (diffusion dominant) and chemical effects in low groundwater flow conditions that are typical of deep geological disposal systems. An illustrative reactive transport modelling application demonstrates the use of the code to examine the interplay of kinetic controlled biogeochemical reactive processes with advective and diffusive transport, under the influence of media degradation. The initial model results are encouraging which show the

  3. Analytical model for advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

    Science.gov (United States)

    Chen, Jui-Sheng; Li, Loretta Y.; Lai, Keng-Hsin; Liang, Ching-Ping

    2017-11-01

    A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.

  4. The Unintended Consequences of Social Media in Healthcare: New Problems and New Solutions.

    Science.gov (United States)

    Hors-Fraile, S; Atique, S; Mayer, M A; Denecke, K; Merolli, M; Househ, M

    2016-11-10

    Social media is increasingly being used in conjunction with health information technology (health IT). The objective of this paper is to identify some of the undesirable outcomes that arise from this integration and to suggest solutions to these problems. After a discussion with experts to elicit the topics that should be included in the survey, we performed a narrative review based on recent literature and interviewed multidisciplinary experts from different areas. In each case, we identified and analyzed the unintended effects of social media in health IT. Each analyzed topic provided a different set of unintended consequences. Most relevant consequences include lack of privacy with ethical and legal issues, patient confusion in disease management, poor information accuracy in crowdsourcing, unclear responsibilities, misleading and biased information in the prevention and detection of epidemics, and demotivation in gamified health solutions with social components. Using social media in healthcare offers several benefits, but it is not exempt of potential problems, and not all of these problems have clear solutions. We recommend careful design of digital systems in order to minimize patient's feelings of demotivation and frustration and we recommend following specific guidelines that should be created by all stakeholders in the healthcare ecosystem.

  5. 1-D DC Resistivity Modeling and Interpretation in Anisotropic Media Using Particle Swarm Optimization

    Science.gov (United States)

    Pekşen, Ertan; Yas, Türker; Kıyak, Alper

    2014-09-01

    We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.

  6. Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

    Science.gov (United States)

    Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

    2014-12-01

    Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

  7. Analytical Solution of Unsteady Gravity Flows of A Power-Law Fluid ...

    African Journals Online (AJOL)

    We present an analytical study of unsteady non-linear rheological effects of a power-law fluid under gravity. The fluid flows through a porous medium. The governing equations are derived and similarity solutions are determined. The results show the existence of traveling waves. It is assumed that the viscosity is temperature ...

  8. Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

    International Nuclear Information System (INIS)

    Darmani, G.; Setayeshi, S.; Ramezanpour, H.

    2012-01-01

    In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

  9. Analytic structure of solutions to multiconfiguration equations

    Energy Technology Data Exchange (ETDEWEB)

    Fournais, Soeren [Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, DK-8000 Arhus C (Denmark); Hoffmann-Ostenhof, Maria [Fakultaet fuer Mathematik, Universitaet Wien, Nordbergstrasse 15, A-1090 Vienna (Austria); Hoffmann-Ostenhof, Thomas [Institut fuer Theoretische Chemie, Waehringerstrasse 17, Universitaet Wien, A-1090 Vienna (Austria); Soerensen, Thomas Oestergaard [Department of Mathematics, Imperial College London, Huxley Building, 180 Queen' s Gate, London SW7 2AZ (United Kingdom)], E-mail: fournais@imf.au.dk, E-mail: Maria.Hoffmann-Ostenhof@univie.ac.at, E-mail: thoffman@esi.ac.at, E-mail: t.sorensen@imperial.ac.uk

    2009-08-07

    We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree-Fock) of Coulomb systems. We prove the following: let {l_brace}{psi}{sub 1}, ..., {psi}{sub M}{r_brace} be any solution to the rank-M multiconfiguration equations for a molecule with L fixed nuclei at R{sub 1},...,R{sub L} element of R{sup 3}. Then, for any j in {l_brace}1, ..., M{r_brace}, k in {l_brace}1, ..., L{r_brace}, there exists a neighborhood U{sub j,k} subset or equal R{sup 3} of R{sub k}, and functions {psi}{sup (1)}{sub j,k}, {psi}{sup (2)}{sub j,k}, real analytic in U{sub j,k}, such that {phi}{sub j}(x)={phi}{sub j,k}{sup (1)}(x)+|x-R{sub k}|{phi}{sub j,k}{sup (2)}(x), x element of U{sub j,k}. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo-Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schroedinger operator of atoms and molecules near two-particle coalescence points.

  10. Analytic self-similar solutions of the Oberbeck–Boussinesq equations

    International Nuclear Information System (INIS)

    Barna, I.F.; Mátyás, L.

    2015-01-01

    In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtonian–Navier–Stokes — with Boussinesq approximation — and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field shows a strongly damped single periodic oscillation which can mimic the appearance of Rayleigh–Bénard convection cells. Finally, it is discussed how our result may be related to nonlinear or chaotic dynamical regimes

  11. Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

    International Nuclear Information System (INIS)

    Basak, K C; Ray, P C; Bera, R K

    2009-01-01

    The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

  12. Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

    International Nuclear Information System (INIS)

    Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.

    2009-01-01

    The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

  13. Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

    Energy Technology Data Exchange (ETDEWEB)

    Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)

    2009-09-15

    The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

  14. The influence of transverse diffusion/dispersion on the migration of radionuclides in porous media

    International Nuclear Information System (INIS)

    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. Consequently, radionuclide transport through the geosphere is of crucial importance, because the geological medium acts as the last barrier to the biosphere. The influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere is dealt with. Migration in porous media only is considered which is the standard approach of most existing transport models. The present study shows that it is only for homogeneous-isotropic media that the three-dimensional time-dependent transport equation can be solved analytically - provided that only simple source geometries and leach processes are taken into account. For heterogeneous layered media only the two-dimensional quasi-stationary transport equation can be solved; the only time dependent process which can be handled is simple radioactive decay excluding extended decay chains. The study shows moreover that only for an idealized three-layer geology can analytical solutions be found. In particular the solutions for multi-layered media cannot be derived from single-layer solutions; each problem with special source and boundary conditions has to be solved directly. The numerical results from the present study show a relatively strong influence of the transverse dispersion effect in the case of homogeneous-isotropic media. (Auth.)

  15. Solution of stochastic media transport problems using a numerical quadrature-based method

    International Nuclear Information System (INIS)

    Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.

    2013-01-01

    We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)

  16. Exact solution of a model for diffusion particles and longitudinal dispersion in packed beds

    International Nuclear Information System (INIS)

    Rasmuson, A.; Neretnieks, I.

    1979-08-01

    An analytical solution of a model for diffusion in particles and longitudinal despersion in porous media is derived. The solution is obtained by the method of Laplace transform. The result is expressed as an infinite integral of five deminsionless quanitities. The extension for a decaying species is given. (authors)

  17. Approximate analytical solutions of Klein-Gordon equation with Hulthen potentials for nonzero angular momentum

    International Nuclear Information System (INIS)

    Chen Changyuan; Sun Dongsheng; Lu Falin

    2007-01-01

    Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of bound states are attained for different l. The analytical energy equation and the unnormalized radial wave functions expressed in terms of hypergeometric polynomials are given

  18. Time-domain analytic Solutions of two-wire transmission line excited by a plane-wave field

    Institute of Scientific and Technical Information of China (English)

    Ni Gu-Yan; Yan Li; Yuan Nai-Chang

    2008-01-01

    This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain.By the frequency-domain Baum-Liu-Tesche(BLT)equation,the time-domain analytic solutions are obtained and expressed in an infinite geometric series.Moreover,it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval.In other word.the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval.The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform,and the agreement is excellent.

  19. New integrable models and analytical solutions in f (R ) cosmology with an ideal gas

    Science.gov (United States)

    Papagiannopoulos, G.; Basilakos, Spyros; Barrow, John D.; Paliathanasis, Andronikos

    2018-01-01

    In the context of f (R ) gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R ) theories for which new analytical solutions are given and closed-form solutions are provided.

  20. Real analytic solutions for marginal deformations in open superstring field theory

    International Nuclear Information System (INIS)

    Okawa, Yuji

    2007-01-01

    We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction

  1. Real analytic solutions for marginal deformations in open superstring field theory

    International Nuclear Information System (INIS)

    Okawa, Y.

    2007-04-01

    We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction. (orig.)

  2. Traveltime approximations for inhomogeneous HTI media

    KAUST Repository

    Alkhalifah, Tariq Ali

    2011-01-01

    Traveltimes information is convenient for parameter estimation especially if the medium is described by an anisotropic set of parameters. This is especially true if we could relate traveltimes analytically to these medium parameters, which is generally hard to do in inhomogeneous media. As a result, I develop traveltimes approximations for horizontaly transversely isotropic (HTI) media as simplified and even linear functions of the anisotropic parameters. This is accomplished by perturbing the solution of the HTI eikonal equation with respect to η and the azimuthal symmetry direction (usually used to describe the fracture direction) from a generally inhomogeneous elliptically anisotropic background medium. The resulting approximations can provide accurate analytical description of the traveltime in a homogenous background compared to other published moveout equations out there. These equations will allow us to readily extend the inhomogenous background elliptical anisotropic model to an HTI with a variable, but smoothly varying, η and horizontal symmetry direction values. © 2011 Society of Exploration Geophysicists.

  3. Microchannel electrokinetics of charged analytes in buffered solutions near floating electrodes

    DEFF Research Database (Denmark)

    Andersen, Mathias Bækbo; Wolfcale, Trevor; Gregersen, Misha Marie

    to accurately predict such behavior in these flow regimes. Experimentally, using conventional fluorescence microscopy, we investigated the concentration gradient (as well as the associated electroosmosis, induced-charge electro-osmosis, and electrophoresis) of the charged analyte near the floating electrode......We present both experimental and numerical studies of nonlinear electrokinetic flow of buffered solutions seeded with dilute analytes in a straight microchannel (0.6 μm high, 250 μm wide, and 9000 μm long) with a 0.15 μm high 60 μm wide electrode situated at the bottom center of the channel...... as a function of analyte (1 to 10 μM fluorescein and bodipy) and buffer (1 to 10 mM borate and posphate) concentrations and an externally applied voltage drop (50 to 100 V) along the channel. We have implemented a nonlinear continuum kinetics model of the system involving the electric potential, the buffer flow...

  4. The suite of analytical benchmarks for neutral particle transport in infinite isotropically scattering media

    International Nuclear Information System (INIS)

    Kornreich, D.E.; Ganapol, B.D.

    1997-01-01

    The linear Boltzmann equation for the transport of neutral particles is investigated with the objective of generating benchmark-quality evaluations of solutions for homogeneous infinite media. In all cases, the problems are stationary, of one energy group, and the scattering is isotropic. The solutions are generally obtained through the use of Fourier transform methods with the numerical inversions constructed from standard numerical techniques such as Gauss-Legendre quadrature, summation of infinite series, and convergence acceleration. Consideration of the suite of benchmarks in infinite homogeneous media begins with the standard one-dimensional problems: an isotropic point source, an isotropic planar source, and an isotropic infinite line source. The physical and mathematical relationships between these source configurations are investigated. The progression of complexity then leads to multidimensional problems with source configurations that also emit particles isotropically: the finite line source, the disk source, and the rectangular source. The scalar flux from the finite isotropic line and disk sources will have a two-dimensional spatial variation, whereas a finite rectangular source will have a three-dimensional variation in the scalar flux. Next, sources emitting particles anisotropically are considered. The most basic such source is the point beam giving rise to the Green's function, which is physically the most fundamental transport problem, yet may be constructed from the isotropic point source solution. Finally, the anisotropic plane and anisotropically emitting infinite line sources are considered. Thus, a firm theoretical and numerical base is established for the most fundamental neutral particle benchmarks in infinite homogeneous media

  5. Analytical solution and simplified analysis of coupled parent-daughter steady-state transport with multirate mass transfer

    Science.gov (United States)

    R. Haggerty

    2013-01-01

    In this technical note, a steady-state analytical solution of concentrations of a parent solute reacting to a daughter solute, both of which are undergoing transport and multirate mass transfer, is presented. Although the governing equations are complicated, the resulting solution can be expressed in simple terms. A function of the ratio of concentrations, In (daughter...

  6. Power Optimization of Wireless Media Systems With Space-Time Block Codes

    OpenAIRE

    Yousefi'zadeh, Homayoun; Jafarkhani, Hamid; Moshfeghi, Mehran

    2004-01-01

    We present analytical and numerical solutions to the problem of power control in wireless media systems with multiple antennas. We formulate a set of optimization problems aimed at minimizing total power consumption of wireless media systems subject to a given level of QoS and an available bit rate. Our formulation takes in to consideration the power consumption related to source coding, channel coding, and transmission of multiple-transmit antennas. In our study, we consider Gauss-Markov and...

  7. On the Analytical Solution of Non-Orthogonal Stagnation Point Flow towards a Stretching Sheet

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Bagheri, G. H.; Barari, Amin

    2011-01-01

    An analytical solution for non-orthogonal stagnation point for the steady flow of a viscous and incompressible fluid is presented. The governing nonlinear partial differential equations for the flow field are reduced to ordinary differential equations by using similarity transformations existed...... in the literature and are solved analytically by means of the Homotopy Analysis Method (HAM). The comparison of results from this paper and those published in the literature confirms the precise accuracy of the HAM. The resulting analytical equation from HAM is valid for entire physical domain and effective...

  8. Analytical solution for the mode conversion equations with steep exponential density profiles

    International Nuclear Information System (INIS)

    Alava, M.J.; Heikkinen, J.A.

    1992-01-01

    A general analytical solution for the converted power from the fast magnetosonic wave to an ion Bernstein wave in a magnetized plasma with an exponential steeply increasing density profile is given in the closed form. The solution covers both the conversion at the lower-hybrid resonance and the conversion through the density gradient for small parallel wave numbers. As an application, the conversion coefficients at the scrape-off layer plasma are estimated in the context of ion cyclotron heating of a tokamak plasma

  9. Analytical solution of Mori's equation with secant hyperbolic memory

    International Nuclear Information System (INIS)

    Tankeshwar, K.; Pathak, K.N.

    1993-07-01

    The equation of motion of the auto-correlation function has been solved analytically using a secant-hyperbolic form of the memory function. The analytical results obtained for the long time expansion together with the short time expansion provide a good description over the whole time domain as judged by their comparison with the numerical solution of Mori's equation of motion. We also find that the time evolution of the auto-correlation function is determined by a single parameter τ which is related to the frequency sum rules up to the fourth order. The auto-correlation function has been found to show simple decaying or oscillatory behaviour depending on whether the parameter τ is greater than or less than some critical values. Similarities as well as differences in time evolution of the auto-correlation have been discussed for exponential, secant-hyperbolic and Gaussian approaches of the memory function. (author). 16 refs, 5 figs

  10. An analytic solution for the enrichment of uranium hexafluoride in long countercurrent centrifuges

    International Nuclear Information System (INIS)

    Raetz, E.

    1977-01-01

    The paper describes an analytic solution for the enrichment and the separative power of long countercurrent centrifuges. Equations to derive optimal operation parameters like feed and feed input height are derived and solved. (orig.) [de

  11. Exact analytical solutions of continuity equation for electron beams precipitating in Coulomb collisions

    Energy Technology Data Exchange (ETDEWEB)

    Dobranskis, R. R.; Zharkova, V. V., E-mail: valentina.zharkova@northumbria.ac.uk [Department of Mathematics and Information Sciences, University of Northumbria, Newcastle upon Tyne NE1 2XP (United Kingdom)

    2014-06-10

    The original continuity equation (CE) used for the interpretation of the power law energy spectra of beam electrons in flares was written and solved for an electron beam flux while ignoring an additional free term with an electron density. In order to remedy this omission, the original CE for electron flux, considering beam's energy losses in Coulomb collisions, was first differentiated by the two independent variables: depth and energy leading to partial differential equation for an electron beam density instead of flux with the additional free term. The analytical solution of this partial differential continuity equation (PDCE) is obtained by using the method of characteristics. This solution is further used to derive analytical expressions for mean electron spectra for Coulomb collisions and to carry out numeric calculations of hard X-ray (HXR) photon spectra for beams with different parameters. The solutions revealed a significant departure of electron densities at lower energies from the original results derived from the CE for the flux obtained for Coulomb collisions. This departure is caused by the additional exponential term that appeared in the updated solutions for electron differential density leading to its faster decrease at lower energies (below 100 keV) with every precipitation depth similar to the results obtained with numerical Fokker-Planck solutions. The effects of these updated solutions for electron densities on mean electron spectra and HXR photon spectra are also discussed.

  12. Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

    Science.gov (United States)

    Garnier, Alain; Gaillet, Bruno

    2015-12-01

    Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.

  13. Analysis of radioactive waste contamination in soils: solution via symbolic manipulation

    International Nuclear Information System (INIS)

    Cotta, R.M.; Mikhailov, M.D.; Ruperti, N.J. Jr.

    1998-01-01

    A demonstration is made of the automatic symbolic-numerical solution of the one-dimensional linearized Burgers equation with linear decay, which models the migration of radionuclides in porous media, by using the generalized integral transform technique and the Mathematica software system. An example is considered to allow for comparisons between the proposed hybrid numerical-analytical solution and the exact solution. Different filtering strategies are also reviewed in terms of the effects on convergence rates. (author)

  14. An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

    International Nuclear Information System (INIS)

    Milazzo, A; Orlando, C; Alaimo, A

    2009-01-01

    Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution

  15. Analytical solutions for tsunami runup on a plane beach

    DEFF Research Database (Denmark)

    Madsen, Per A.; Schäffer, Hemming Andreas

    2010-01-01

    wavetrains generated by monopole and dipole disturbances in the deep ocean. The evolution of these wavetrains, while travelling a considerable distance over a constant depth, is influenced by weak dispersion and is governed by the linear Korteweg-De Vries (KdV) equation. This process is described......) of the wave, which is not realistic for geophysical tsunamis. To resolve this problem, we first derive analytical solutions to the nonlinear shallow-water (NSW) equations for the runup/rundown of single waves, where the duration and the wave height can be specified separately. The formulation is then extended...

  16. Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field

    International Nuclear Information System (INIS)

    Ni Guyan; Yan Li; Yuan Naichang

    2008-01-01

    This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum–Liu–Tesche (BLT) equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent. (the physics of elementary particles and fields)

  17. Analytical solution for Joule-Thomson cooling during CO2 geo-sequestration in depleted oil and gas reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Mathias, S.A.; Gluyas, J.G.; Oldenburg, C.M.; Tsang, C.-F.

    2010-05-21

    Mathematical tools are needed to screen out sites where Joule-Thomson cooling is a prohibitive factor for CO{sub 2} geo-sequestration and to design approaches to mitigate the effect. In this paper, a simple analytical solution is developed by invoking steady-state flow and constant thermophysical properties. The analytical solution allows fast evaluation of spatiotemporal temperature fields, resulting from constant-rate CO{sub 2} injection. The applicability of the analytical solution is demonstrated by comparison with non-isothermal simulation results from the reservoir simulator TOUGH2. Analysis confirms that for an injection rate of 3 kg s{sup -1} (0.1 MT yr{sup -1}) into moderately warm (>40 C) and permeable formations (>10{sup -14} m{sup 2} (10 mD)), JTC is unlikely to be a problem for initial reservoir pressures as low as 2 MPa (290 psi).

  18. Analytical reconstruction schemes for coarse-mesh spectral nodal solution of slab-geometry SN transport problems

    International Nuclear Information System (INIS)

    Barros, R. C.; Filho, H. A.; Platt, G. M.; Oliveira, F. B. S.; Militao, D. S.

    2009-01-01

    Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two analytical reconstruction schemes for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (S N ) transport model in slab geometry. The first scheme we describe is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the spatial grid set up on the slab. The second scheme is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction schemes, as described in this paper. (authors)

  19. New Analytical Solution of the Equilibrium Ampere's Law Using the Walker's Method: a Didactic Example

    Science.gov (United States)

    Sousa, A. N. Laurindo; Ojeda-González, A.; Prestes, A.; Klausner, V.; Caritá, L. A.

    2018-02-01

    This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere's law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker's generating function in details without omitting any step. The Walker's generating function g( ζ) is written in a new way as the tangent of an unspecified function K( ζ). In this trend, the general solution of the GS equation is expressed as exp(- 2Ψ) = 4| K '( ζ)|2/cos2[ K( ζ) - K( ζ ∗)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris's solution as a test, in this case K( ζ) = arctan(exp( i ζ)). In summary, one of the article purposes is to present a review of the Harris's solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g( ζ) = tan( K( ζ)). We also present a new analytical solution to the equilibrium Ampere's law using g( ζ) = cosh( b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.

  20. Progress in electrical impedance imaging of binary media: 1: Analytical and numerical methods

    International Nuclear Information System (INIS)

    Ovacik, Levent; Lin Jentai; Jones, Owen C.

    1998-01-01

    This is the first of two papers summarizing the use of electrical impedance excitation/measurement for producing cross sectional images of the distribution of insulating media imbedded in conducting media. This computed tomographic approach finds the distribution of electrical properties of an electric field which minimizes in the least squares sense the difference between measured and computed boundary response to excitation. In this paper we briefly review the basic analytical methods developed for this system. We then extend these methods to three dimensions, add a method for preconditioning voltages for error correction, describe methods for optimizing the resolution of a target by providing optimal excitation patterns and then describe the overall numerical sensitivity. The second paper then demonstrates the ability of this system to image multiple, separate, differently-sized two-dimensional or three-dimensional targets with demonstrated linear sensitivity of over 30:1 with maximum possible linear sensitivity of one part in 1300 based on our ability to distinguish variations from a homogeneous background. (author)

  1. Analytical Radiation Transport Benchmarks for The Next Century

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2005-01-01

    Verification of large-scale computational algorithms used in nuclear engineering and radiological applications is an essential element of reliable code performance. For this reason, the development of a suite of multidimensional semi-analytical benchmarks has been undertaken to provide independent verification of proper operation of codes dealing with the transport of neutral particles. The benchmarks considered cover several one-dimensional, multidimensional, monoenergetic and multigroup, fixed source and critical transport scenarios. The first approach, called the Green's Function. In slab geometry, the Green's function is incorporated into a set of integral equations for the boundary fluxes. Through a numerical Fourier transform inversion and subsequent matrix inversion for the boundary fluxes, a semi-analytical benchmark emerges. Multidimensional solutions in a variety of infinite media are also based on the slab Green's function. In a second approach, a new converged SN method is developed. In this method, the SN solution is ''minded'' to bring out hidden high quality solutions. For this case multigroup fixed source and criticality transport problems are considered. Remarkably accurate solutions can be obtained with this new method called the Multigroup Converged SN (MGCSN) method as will be demonstrated

  2. Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

    Science.gov (United States)

    Wu, Yang; Kelly, Damien P.

    2014-12-01

    The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

  3. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

    Directory of Open Access Journals (Sweden)

    Xiao-Li Ding

    2018-01-01

    Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

  4. Analytical Solutions of a Model for Brownian Motion in the Double Well Potential

    International Nuclear Information System (INIS)

    Liu Ai-Jie; Zheng Lian-Cun; Zhang Xin-Xin; Ma Lian-Xi

    2015-01-01

    In this paper, the analytical solutions of Schrödinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker—Planck equation known as the Klein—Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schrödinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function. (general)

  5. Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

    Science.gov (United States)

    Saengow, C.; Giacomin, A. J.

    2017-12-01

    The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

  6. Closed-form analytical solutions incorporating pumping and tidal effects in various coastal aquifer systems

    Science.gov (United States)

    Wang, Chaoyue; Li, Hailong; Wan, Li; Wang, Xusheng; Jiang, Xiaowei

    2014-07-01

    Pumping wells are common in coastal aquifers affected by tides. Here we present analytical solutions of groundwater table or head variations during a constant rate pumping from a single, fully-penetrating well in coastal aquifer systems comprising an unconfined aquifer, a confined aquifer and semi-permeable layer between them. The unconfined aquifer terminates at the coastline (or river bank) and the other two layers extend under tidal water (sea or tidal river) for a certain distance L. Analytical solutions are derived for 11 reasonable combinations of different situations of the L-value (zero, finite, and infinite), of the middle layer's permeability (semi-permeable and impermeable), of the boundary condition at the aquifer's submarine terminal (Dirichlet describing direct connection with seawater and no-flow describing the existence of an impermeable capping), and of the tidal water body (sea and tidal river). Solutions are discussed with application examples in fitting field observations and parameter estimations.

  7. Analytic solutions for neutrino momenta in decay of top quarks

    Energy Technology Data Exchange (ETDEWEB)

    Betchart, Burton A., E-mail: bbetchar@pas.rochester.edu; Demina, Regina, E-mail: regina@pas.rochester.edu; Harel, Amnon, E-mail: amnon.harel@cern.ch

    2014-02-01

    We employ a geometric approach to analytically solve equations of constraint on the decay of top quarks involving leptons. The neutrino momentum is found as a function of the 4-vectors of the associated bottom quark and charged lepton, the masses of the top quark and W boson, and a single parameter, which constrains it to an ellipse. We show how the measured imbalance of momenta in the event reduces the solutions for neutrino momenta to a discrete set, in the cases of one or two top quarks decaying to leptons. The algorithms can be implemented concisely with common linear algebra routines. -- Highlights: • Neutrino momentum from top quark decay is constrained to an ellipse. • We find analytically the best neutrino momenta given the momentum imbalance. • A reference implementation of the algorithms is included.

  8. Big data analytics as a service infrastructure: challenges, desired properties and solutions

    International Nuclear Information System (INIS)

    Martín-Márquez, Manuel

    2015-01-01

    CERN's accelerator complex generates a very large amount of data. A large volumen of heterogeneous data is constantly generated from control equipment and monitoring agents. These data must be stored and analysed. Over the decades, CERN's researching and engineering teams have applied different approaches, techniques and technologies for this purpose. This situation has minimised the necessary collaboration and, more relevantly, the cross data analytics over different domains. These two factors are essential to unlock hidden insights and correlations between the underlying processes, which enable better and more efficient daily-based accelerator operations and more informed decisions. The proposed Big Data Analytics as a Service Infrastructure aims to: (1) integrate the existing developments; (2) centralise and standardise the complex data analytics needs for CERN's research and engineering community; (3) deliver real-time, batch data analytics and information discovery capabilities; and (4) provide transparent access and Extract, Transform and Load (ETL), mechanisms to the various and mission-critical existing data repositories. This paper presents the desired objectives and properties resulting from the analysis of CERN's data analytics requirements; the main challenges: technological, collaborative and educational and; potential solutions. (paper)

  9. Analytic rotating black-hole solutions in N-dimensional f(T) gravity

    Energy Technology Data Exchange (ETDEWEB)

    Nashed, G.G.L. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Cairo (Egypt); Ain Shams University, Faculty of Science, Mathematics Department, Cairo (Egypt); Egyptian Relativity Group (ERG), Cairo (Egypt); El Hanafy, W. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Cairo (Egypt); Egyptian Relativity Group (ERG), Cairo (Egypt)

    2017-02-15

    A non-diagonal vielbein ansatz is applied to the N-dimension field equations of f(T) gravity. An analytical vacuum solution is derived for the quadratic polynomial f(T)=T+εT{sup 2} and an inverse relation between the coupling constant ε and the cosmological constant Λ. Since the induced metric has off-diagonal components, it cannot be removed by a mere coordinate transformation, the solution has a rotating parameter. The curvature and torsion scalars invariants are calculated to study the singularities and horizons of the solution. In contrast to general relativity, the Cauchy horizon differs from the horizon which shows the effect of the higher order torsion. The general expression of the energy-momentum vector of f(T) gravity is used to calculate the energy of the system. Finally, we have shown that this kind of solution satisfies the first law of thermodynamics in the framework of f(T) gravitational theories. (orig.)

  10. Big Data Analytics Solutions: The Implementation Challenges in the Financial Services Industry

    Science.gov (United States)

    Ojo, Michael O.

    2016-01-01

    The challenges of Big Data (BD) and Big Data Analytics (BDA) have attracted disproportionately less attention than the overwhelmingly espoused benefits and game-changing promises. While many studies have examined BD challenges across multiple industry verticals, very few have focused on the challenges of implementing BDA solutions. Fewer of these…

  11. An analytical solution of the one-dimensional neutron diffusion kinetic equation in cartesian geometry

    International Nuclear Information System (INIS)

    Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.

    2009-01-01

    In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)

  12. Analytical solutions of heat transfer for laminar flow in rectangular channels

    Directory of Open Access Journals (Sweden)

    Rybiński Witold

    2014-12-01

    Full Text Available The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type. The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.

  13. Verification of T2VOC using an analytical solution for VOC transport in vadose zone

    Energy Technology Data Exchange (ETDEWEB)

    Shan, C. [Lawrence Berkeley Laboratory, Berkeley, CA (United States)

    1995-03-01

    T2VOC represents an adaption of the STMVOC to the TOUGH2 environment. In may contaminated sites, transport of volatile organic chemicals (VOC) is a serious problem which can be simulated by T2VOC. To demonstrate the accuracy and robustness of the code, we chose a practical problem of VOC transport as the test case, conducted T2VOC simulations, and compared the results of T2VOC with those of an analytical solution. The agreements between T2VOC and the analytical solutions are excellent. In addition, the numerical results of T2VOC are less sensitive to grid size and time step to a certain extent.

  14. Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

    International Nuclear Information System (INIS)

    Coelho, Pedro J.

    2014-01-01

    Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

  15. Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

    Science.gov (United States)

    Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

    2015-12-01

    Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

  16. Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdi Rashidi

    2008-01-01

    Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

  17. Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

    Science.gov (United States)

    Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

    2014-01-01

    Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

  18. Text Stream Trend Analysis using Multiscale Visual Analytics with Applications to Social Media Systems

    Energy Technology Data Exchange (ETDEWEB)

    Steed, Chad A [ORNL; Beaver, Justin M [ORNL; BogenII, Paul L. [Google Inc.; Drouhard, Margaret MEG G [ORNL; Pyle, Joshua M [ORNL

    2015-01-01

    In this paper, we introduce a new visual analytics system, called Matisse, that allows exploration of global trends in textual information streams with specific application to social media platforms. Despite the potential for real-time situational awareness using these services, interactive analysis of such semi-structured textual information is a challenge due to the high-throughput and high-velocity properties. Matisse addresses these challenges through the following contributions: (1) robust stream data management, (2) automated sen- timent/emotion analytics, (3) inferential temporal, geospatial, and term-frequency visualizations, and (4) a flexible drill-down interaction scheme that progresses from macroscale to microscale views. In addition to describing these contributions, our work-in-progress paper concludes with a practical case study focused on the analysis of Twitter 1% sample stream information captured during the week of the Boston Marathon bombings.

  19. Analytical solution of the thermo-mechanical stresses in a multilayered composite pressure vessel considering the influence of the closed ends

    International Nuclear Information System (INIS)

    Zhang, Q.; Wang, Z.W.; Tang, C.Y.; Hu, D.P.; Liu, P.Q.; Xia, L.Z.

    2012-01-01

    Limited work has been reported on determining the thermo-mechanical stresses in a multilayered composite pressure vessel when the influence of its closed ends is considered. In this study, an analytical solution was derived for determining the stress distribution of a multilayered composite pressure vessel subjected to an internal fluid pressure and a thermal load, based on thermo-elasticity theory. In the solution, a pseudo extrusion pressure was proposed to emulate the effect of the closed ends of the pressure vessel. To validate the analytical solution, the stress distribution of the pressure vessel was also computed using finite element (FE) method. It was found that the analytical results were in good agreement with the computational ones, and the effect of thermal load on the stress distribution was discussed in detail. The proposed analytical solution provides an exact means to design multilayered composite pressure vessels. Highlights: ► The thermal-mechanical stress was derived for a multilayered pressure vessel. ► A new pseudo extrusion pressure was proposed to emulate the effect of closed ends. ► The analytical results are in good agreement with the computational ones using FEM. ► The solution provides an exact way to design the multilayered pressure vessel.

  20. Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

    Science.gov (United States)

    Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

    2012-10-01

    We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.

  1. Capacity of the circular plate condenser: analytical solutions for large gaps between the plates

    International Nuclear Information System (INIS)

    Rao, T V

    2005-01-01

    A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to O(τ -(2N+1) ) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to O(τ -9 ). Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the O(τ -9 ) approximation predicts the capacity extremely well for any τ ≥ 2 and an O(τ -3 ) approximation gives, for all practical purposes, results of adequate accuracy for τ ≥ 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to O(τ -6 ) for τ ≥ 2

  2. Well test analysis in fractured media

    Energy Technology Data Exchange (ETDEWEB)

    Karasaki, K.

    1986-04-01

    In this study the behavior of fracture systems under well test conditions and methods for analyzing well test data from fractured media are investigated. Several analytical models are developed to be used for analyzing well test data from fractured media. Numerical tools that may be used to simulate fluid flow in fractured media are also presented. Three types of composite models for constant flux tests are investigated. Several slug test models with different geometric conditions that may be present in fractured media are also investigated. A finite element model that can simulate transient fluid flow in fracture networks is used to study the behavior of various two-dimensional fracture systems under well test conditions. A mesh generator that can be used to model mass and heat flow in a fractured-porous media is presented. This model develops an explicit solution in the porous matrix as well as in the discrete fractures. Because the model does not require the assumptions of the conventional double porosity approach, it may be used to simulate cases where double porosity models fail.

  3. Media Education and Media Criticism in the Educational Process in Russia

    Science.gov (United States)

    Fedorov, Alexander; Levitskaya, Anastasia

    2017-01-01

    Media criticism and media education have a lot in common. For example, both media education and media criticism attach great importance to the development of analytical thinking of the audience. Indeed, one of the most important tasks of media education is precisely to teach the audience not only to analyze media texts of any types, but also to…

  4. Diffusion Dominant Solute Transport Modelling In Deep Repository Under The Effect of Emplacement Media Degradation - 13285

    International Nuclear Information System (INIS)

    Kwong, S.; Jivkov, A.P.

    2013-01-01

    Deep geologic disposal of high activity and long-lived radioactive waste is being actively considered and pursued in many countries, where low permeability geological formations are used to provide long term waste contaminant with minimum impact to the environment and risk to the biosphere. A multi-barrier approach that makes use of both engineered and natural barriers (i.e. geological formations) is often used to further enhance the containment performance of the repository. As the deep repository system subjects to a variety of thermo-hydro-chemo-mechanical (THCM) effects over its long 'operational' lifespan (e.g. 0.1 to 1.0 million years, the integrity of the barrier system will decrease over time (e.g. fracturing in rock or clay)). This is broadly referred as media degradation in the present study. This modelling study examines the effects of media degradation on diffusion dominant solute transport in fractured media that are typical of deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes, while the effects of degradation is studied using a pore network model that considers the media diffusivity and network changes. Model results are presented to demonstrate the use of a 3D pore-network model, using a novel architecture, to calculate macroscopic properties of the medium such as diffusivity, subject to pore space changes as the media degrade. Results from a reactive transport model of a representative geological waste disposal package are also presented to demonstrate the effect of media property change on the solute migration behaviour, illustrating the complex interplay between kinetic biogeochemical processes and diffusion dominant transport. The initial modelling results demonstrate the feasibility of a coupled modelling approach (using pore-network model and reactive

  5. Analytical solutions for evaluating the thermal performances of wet air cooling coils under both unit and non-unit Lewis Factors

    International Nuclear Information System (INIS)

    Xia Liang; Chan, M.Y.; Deng, S.M.; Xu, X.G.

    2010-01-01

    Analytical solutions for evaluating the thermal performances of both chilled water wet cooling coils and direct expansion (DX) wet cooling coils, respectively, under both unit and non-unit Lewis Factors are developed and reported in this paper. The analytical solution was validated by comparing its predictions with those from numerically solving the fundamental governing equations of heat and mass transfer taking place in a wet cooling coil. With the analytical solutions, the distributions of air temperature and humidity ratio along air flow direction in a wet cooling coil can be predicted, and the differences in the thermal performances of the cooling coils under both unit and non-unit Lewis Factors can be identified. The analytical solutions, on one hand, can be a low-cost replacement to numerically solving the fundamental heat and mass transfer governing equations, and on the other hand, is able to deal with evaluating thermal performance for wet air cooling coils operated under both unit and non-unit Lewis Factors.

  6. Analytical solutions for tomato peeling with combined heat flux and convective boundary conditions

    Science.gov (United States)

    Cuccurullo, G.; Giordano, L.; Metallo, A.

    2017-11-01

    Peeling of tomatoes by radiative heating is a valid alternative to steam or lye, which are expensive and pollutant methods. Suitable energy densities are required in order to realize short time operations, thus involving only a thin layer under the tomato surface. This paper aims to predict the temperature field in rotating tomatoes exposed to the source irradiation. Therefore, a 1D unsteady analytical model is presented, which involves a semi-infinite slab subjected to time dependent heating while convective heat transfer takes place on the exposed surface. In order to account for the tomato rotation, the heat source is described as the positive half-wave of a sinusoidal function. The problem being linear, the solution is derived following the Laplace Transform Method. In addition, an easy-to-handle solution for the problem at hand is presented, which assumes a differentiable function for approximating the source while neglecting convective cooling, the latter contribution turning out to be negligible for the context at hand. A satisfying agreement between the two analytical solutions is found, therefore, an easy procedure for a proper design of the dry heating system can be set up avoiding the use of numerical simulations.

  7. Approximate analytical solutions in the analysis of elastic structures of complex geometry

    Science.gov (United States)

    Goloskokov, Dmitriy P.; Matrosov, Alexander V.

    2018-05-01

    A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

  8. Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions

    International Nuclear Information System (INIS)

    Kriventsev, Vladimir

    2000-09-01

    Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed

  9. Analytical solution for beam with time-dependent boundary conditions versus response spectrum

    International Nuclear Information System (INIS)

    Gou, P.F.; Panahi, K.K.

    2001-01-01

    This paper studies the responses of a uniform simple beam for which the supports are subjected to time-dependent conditions. Analytical solution in terms of series was presented for two cases: (1) Two supports of a simple beam are subjected to a harmonic motion, and (2) One of the two supports is stationary while the other is subjected to a harmonic motion. The results of the analytical solution were investigated and compared with the results of conventional response spectrum method using the beam finite element model. One of the applications of the results presented in this paper can be used to assess the adequacy and accuracy of the engineering approaches such as response spectra methods. It has been found that, when the excitation frequency equals the fundamental frequency of the beam, the results from response spectrum method are in good agreement with the exact calculation. The effects of initial conditions on the responses are also examined. It seems that the non-zero initial velocity has pronounced effects on the displacement time histories but it has no effect on the maximum accelerations. (author)

  10. Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.

    2011-01-01

    In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...

  11. Applications of Analytical Self-Similar Solutions of Reynolds-Averaged Models for Instability-Induced Turbulent Mixing

    Science.gov (United States)

    Hartland, Tucker; Schilling, Oleg

    2017-11-01

    Analytical self-similar solutions to several families of single- and two-scale, eddy viscosity and Reynolds stress turbulence models are presented for Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instability-induced turbulent mixing. The use of algebraic relationships between model coefficients and physical observables (e.g., experimental growth rates) following from the self-similar solutions to calibrate a member of a given family of turbulence models is shown. It is demonstrated numerically that the algebraic relations accurately predict the value and variation of physical outputs of a Reynolds-averaged simulation in flow regimes that are consistent with the simplifying assumptions used to derive the solutions. The use of experimental and numerical simulation data on Reynolds stress anisotropy ratios to calibrate a Reynolds stress model is briefly illustrated. The implications of the analytical solutions for future Reynolds-averaged modeling of hydrodynamic instability-induced mixing are briefly discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  12. An analytical solution describing the shape of a yield stress material subjected to an overpressure

    DEFF Research Database (Denmark)

    Hovad, Emil; Spangenberg, Jon; Larsen, P.

    2016-01-01

    as well as the spread length and height of the material when deformed in a box due to gravity. In the present work, the analytical solution is extended with the addition of an overpressure that acts over the entire body of the material. This extension enables finding the shape of a yield stress material......Many fluids and granular materials are able to withstand a limited shear stress without flowing. These materials are known as yields stress materials. Previously, an analytical solution was presented to quantify the yield stress for such materials. The yields stress is obtained based on the density...... with known density and yield stress when for instance deformed under water or subjected to a forced air pressure....

  13. Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments

    Science.gov (United States)

    Majdalani, Samer; Guinot, Vincent; Delenne, Carole; Gebran, Hicham

    2018-06-01

    This paper is devoted to theoretical and experimental investigations of solute dispersion in heterogeneous porous media. Dispersion in heterogenous porous media has been reported to be scale-dependent, a likely indication that the proposed dispersion models are incompletely formulated. A high quality experimental data set of breakthrough curves in periodic model heterogeneous porous media is presented. In contrast with most previously published experiments, the present experiments involve numerous replicates. This allows the statistical variability of experimental data to be accounted for. Several models are benchmarked against the data set: the Fickian-based advection-dispersion, mobile-immobile, multirate, multiple region advection dispersion models, and a newly proposed transport model based on pure advection. A salient property of the latter model is that its solutions exhibit a ballistic behaviour for small times, while tending to the Fickian behaviour for large time scales. Model performance is assessed using a novel objective function accounting for the statistical variability of the experimental data set, while putting equal emphasis on both small and large time scale behaviours. Besides being as accurate as the other models, the new purely advective model has the advantages that (i) it does not exhibit the undesirable effects associated with the usual Fickian operator (namely the infinite solute front propagation speed), and (ii) it allows dispersive transport to be simulated on every heterogeneity scale using scale-independent parameters.

  14. Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

    Science.gov (United States)

    Wu, Yang; Kelly, Damien P

    2014-12-12

    The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally

  15. Effects of Unsaturated Zones on Baseflow Recession: Analytical Solution and Application

    Science.gov (United States)

    Zhan, H.; Liang, X.; Zhang, Y. K.

    2017-12-01

    Unsaturated flow is an important process in baseflow recessions and its effect is rarely investigated. A mathematical model for a coupled unsaturated-saturated flow in a horizontally unconfined aquifer with time-dependent infiltrations is presented. Semi-analytical solutions for hydraulic heads and discharges are derived using Laplace transform and Cosine transform. The solutions are compared with solutions of the linearized Boussinesq equation (LB solution) and the linearized Laplace equation (LL solution), respectively. The result indicates that a larger dimensionless constitutive exponent κD of the unsaturated zone leads to a smaller discharge during the infiltration period and a larger discharge after the infiltration. The lateral discharge of the unsaturated zone is significant when κD≤1, and becomes negligible when κD≥100. For late times, the power index b of the recession curve-dQ/dt aQb, is 1 and independent of κD, where Q is the baseflow and a is a constant lumped aquifer parameter. For early times, b is approximately equal to 3 but it approaches infinity when t→1. The present solution is applied to synthetic and field cases. The present solution matched the synthetic data better than both the LL and LB solutions, with a minimum relative error of 16% for estimate of hydraulic conductivity. The present solution was applied to the observed streamflow discharge in Iowa, and the estimated values of the aquifer parameters were reasonable.

  16. Effect of water content on dispersion of transferred solute in unsaturated porous media

    Energy Technology Data Exchange (ETDEWEB)

    Latrille, C. [CEA Saclay, DEN/DANS/DPC/SECR/L3MR, 91191 Gif sur Yvette (France)

    2013-07-01

    Estimating contaminant migration in the context of waste disposal and/or environmental remediation of polluted soils requires a complete understanding of the underlying transport processes. In unsaturated porous media, water content impacts directly on porous solute transfer. Depending on the spatial distribution of water content, the flow pathway is more complex than in water saturated media. Dispersivity is consequently dependent on water content. Non-reactive tracer experiments performed using unsaturated sand columns confirm the dependence of dispersivity with pore velocity; moreover, a power law relationship between dispersivity and water content is evidenced. (authors)

  17. Solution of Media Risk and Social Responsibility Governance of Social Media

    Directory of Open Access Journals (Sweden)

    Zhang Yuan

    2017-01-01

    Full Text Available The rapid development of media technology makes the modern society become a “social media” or even “over social media”, the rise of social media makes it beyond the tool attribute, and become an important force in the reconstruction of contemporary society, the risk of concomitant. The anomie and breach of Social media regularly staged, weakened its positive social function, forcing us to think about the social responsibility of social media,which are reflections on the lack of responsibility, but also positive response of resolving the media risk and ask for moral strength.

  18. Solved problems in classical mechanics analytical and numerical solutions with comments

    CERN Document Server

    de Lange, O L

    2010-01-01

    Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

  19. assessment of concentration of air pollutants using analytical and numerical solution of the atmospheric diffusion equation

    International Nuclear Information System (INIS)

    Esmail, S.F.H.

    2011-01-01

    The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.

  20. Comparison of analytical transport and stochastic solutions for neutron slowing down in an infinite medium

    International Nuclear Information System (INIS)

    Jahshan, S.N.; Wemple, C.A.; Ganapol, B.D.

    1993-01-01

    A comparison of the numerical solutions of the transport equation describing the steady neutron slowing down in an infinite medium with constant cross sections is made with stochastic solutions obtained from tracking successive neutron histories in the same medium. The transport equation solution is obtained using a numerical Laplace transform inversion algorithm. The basis for the algorithm is an evaluation of the Bromwich integral without analytical continuation. Neither the transport nor the stochastic solution is limited in the number of scattering species allowed. The medium may contain an absorption component as well. (orig.)

  1. An analytical multigroup benchmark for (n, γ) and (n, n', γ) verification of diffusion theory algorithms

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2011-01-01

    Highlights: → Coupled neutron and gamma transport is considered in the multigroup diffusion approximation. → The model accommodates fission, up- and down-scattering and common neutron-gamma interactions. → The exact solution to the diffusion equation in a heterogeneous media of any number of regions is found. → The solution is shown to parallel the one-group case in a homogeneous medium. → The discussion concludes with a heterogeneous, 2 fuel-plate 93.2% enriched reactor fuel benchmark demonstration. - Abstract: The angular flux for the 'rod model' describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.

  2. Media-fill simulation tests in manual and robotic aseptic preparation of injection solutions in syringes.

    Science.gov (United States)

    Krämer, Irene; Federici, Matteo; Kaiser, Vanessa; Thiesen, Judith

    2016-04-01

    The purpose of this study was to evaluate the contamination rate of media-fill products either prepared automated with a robotic system (APOTECAchemo™) or prepared manually at cytotoxic workbenches in the same cleanroom environment and by experienced operators. Media fills were completed by microbiological environmental control in the critical zones and used to validate the cleaning and disinfection procedures of the robotic system. The aseptic preparation of patient individual ready-to-use injection solutions was simulated by using double concentrated tryptic soy broth as growth medium, water for injection and plastic syringes as primary packaging materials. Media fills were either prepared automated (500 units) in the robot or manually (500 units) in cytotoxic workbenches in the same cleanroom over a period of 18 working days. The test solutions were incubated at room temperature (22℃) over 4 weeks. Products were visually inspected for turbidity after a 2-week and 4-week period. Following incubation, growth promotion tests were performed with Staphylococcus epidermidis. During the media-fill procedures, passive air monitoring was performed with settle plates and surface monitoring with contact plates on predefined locations as well as fingerprints. The plates got incubated for 5-7 days at room temperature, followed by 2-3 days at 30-35℃ and the colony forming units (cfu) counted after both periods. The robot was cleaned and disinfected according to the established standard operating procedure on two working days prior to the media-fill session, while on six other working days only six critical components were sanitized at the end of the media-fill sessions. Every day UV irradiation was operated for 4 h after finishing work. None of the 1000 media-fill products prepared in the two different settings showed turbidity after the incubation period thereby indicating no contamination with microorganisms. All products remained uniform, clear, and light

  3. Analytical Solutions of Fractional Walter’s B Fluid with Applications

    Directory of Open Access Journals (Sweden)

    Qasem Al-Mdallal

    2018-01-01

    Full Text Available Fractional Walter’s Liquid Model-B has been used in this work to study the combined analysis of heat and mass transfer together with magnetohydrodynamic (MHD flow over a vertically oscillating plate embedded in a porous medium. A newly defined approach of Caputo-Fabrizio fractional derivative (CFFD has been used in the mathematical formulation of the problem. By employing the dimensional analysis, the dimensional governing partial differential equations have been transformed into dimensionless form. The problem is solved analytically and solutions of mass concentration, temperature distribution, and velocity field are obtained in the presence and absence of porous and magnetic field impacts. The general solutions are expressed in the format of generalized Mittag-Leffler function MΩ2,Ω3Ω1χ and Fox-H function Hp,q+11,p satisfying imposed conditions on the problem. These solutions have combined effects of heat and mass transfer; this is due to free convections differences between mass concentration and temperature distribution. Graphical illustration is depicted in order to bring out the effects of various physical parameters on flow. From investigated general solutions, the well-known previously published results in the literature have been recovered. Graphs are plotted and discussed for rheological parameters.

  4. Approximate and analytical solutions for solute transport from an injection well into a single fracture

    International Nuclear Information System (INIS)

    Chen, C.S.; Yates, S.R.

    1989-01-01

    In dealing with problems related to land-based nuclear waste management, a number of analytical and approximate solutions were developed to quantify radionuclide transport through fractures contained in the porous formation. It has been reported that by treating the radioactive decay constant as the appropriate first-order rate constant, these solutions can also be used to study injection problems of a similar nature subject to first-order chemical or biological reactions. The fracture is idealized by a pair of parallel, smooth plates separated by an aperture of constant thickness. Groundwater was assumed to be immobile in the underlying and overlying porous formations due to their low permeabilities. However, the injected radionuclides were able to move from the fracture into the porous matrix by molecular diffusion (the matrix diffusion) due to possible concentration gradients across the interface between the fracture and the porous matrix. Calculation of the transient solutions is not straightforward, and the paper documents a contained Fortran program, which computes the Stehfest inversion, the Airy functions, and gives the concentration distributions in the fracture as well as in the porous matrix for both transient and steady-state cases

  5. ANALYTICAL SOLUTIONS OF SINGULAR ISOTHERMAL QUADRUPOLE LENS

    International Nuclear Information System (INIS)

    Chu Zhe; Lin, W. P.; Yang Xiaofeng

    2013-01-01

    Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.

  6. Analytical solution and numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe

    Science.gov (United States)

    Cai, Haibing; Xu, Liuxun; Yang, Yugui; Li, Longqi

    2018-05-01

    Artificial liquid nitrogen freezing technology is widely used in urban underground engineering due to its technical advantages, such as simple freezing system, high freezing speed, low freezing temperature, high strength of frozen soil, and absence of pollution. However, technical difficulties such as undefined range of liquid nitrogen freezing and thickness of frozen wall gradually emerge during the application process. Thus, the analytical solution of the freezing-temperature field of a single pipe is established considering the freezing temperature of soil and the constant temperature of freezing pipe wall. This solution is then applied in a liquid nitrogen freezing project. Calculation results show that the radius of freezing front of liquid nitrogen is proportional to the square root of freezing time. The radius of the freezing front also decreases with decreased the freezing temperature, and the temperature gradient of soil decreases with increased distance from the freezing pipe. The radius of cooling zone in the unfrozen area is approximately four times the radius of the freezing front. Meanwhile, the numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe is conducted using the Abaqus finite-element program. Results show that the numerical simulation of soil temperature distribution law well agrees with the analytical solution, further verifies the reliability of the established analytical solution of the liquid nitrogen freezing-temperature field of a single pipe.

  7. Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series

    Directory of Open Access Journals (Sweden)

    Xiang-Chao Shi

    2014-01-01

    Full Text Available Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.

  8. Novel analytical methods for characterising binding media and protective coatings in artworks

    International Nuclear Information System (INIS)

    Domenech-Carbo, Maria Teresa

    2008-01-01

    Since the first reported analytical studies and technical examinations of art and archaeological objects conducted in the late 18th century, analytical techniques and methods applied to the study of artworks have constantly grown. Among the materials composing the art object, organic compounds used as binding media or protective coatings have attracted the attention of the conservation profession given their noticeable ability for undergoing morphological and chemical changes on ageing. Thus, the aim of this paper is to review the most recent advances in the identification and determination of organic compounds present in art and art conservation materials. Immunofluorescence techniques have been proposed in recent decades as an alternative to the classical and simpler microchemical tests. Besides, a variety of instrumental techniques have also been improved in an attempt to enhance the sensitivity, repeatability and accuracy of the analytical results. Spectroscopic techniques, such as UV-vis, FTIR and Raman spectroscopy, have been coupled with light microscopes for these purposes. Synchrotron radiation FTIR microspectroscopy has also been successfully applied to the analysis of artworks. Mass spectrometry has also been increasingly used as a detector system coupled with a chromatographic device. Chromatographic methods have also improved in recent years. Paper and thin layer chromatographic techniques have been progressively replaced with gas chromatography (GC), pyrolysis-GC, high performance liquid chromatography and capillary electrophoresis. More complex proteomics hyphenated techniques, such as nano-liquid chromatography-nano-electrospray ionisation/collision quadrupole time-of-flight tandem mass spectrometry, have been recently applied to the identification and determination of proteinaceous binders. Microbeam analytical techniques have also been incorporated into the list of advanced instrumental techniques for art conservation purposes. Finally, a number

  9. Novel analytical methods for characterising binding media and protective coatings in artworks

    Energy Technology Data Exchange (ETDEWEB)

    Domenech-Carbo, Maria Teresa [Institut de Restauracio del Patrimoni, Universitat Politecnica de Valencia, Cami de Vera s/n, 46022 Valencia (Spain)], E-mail: tdomenec@crbc.upv.es

    2008-07-28

    Since the first reported analytical studies and technical examinations of art and archaeological objects conducted in the late 18th century, analytical techniques and methods applied to the study of artworks have constantly grown. Among the materials composing the art object, organic compounds used as binding media or protective coatings have attracted the attention of the conservation profession given their noticeable ability for undergoing morphological and chemical changes on ageing. Thus, the aim of this paper is to review the most recent advances in the identification and determination of organic compounds present in art and art conservation materials. Immunofluorescence techniques have been proposed in recent decades as an alternative to the classical and simpler microchemical tests. Besides, a variety of instrumental techniques have also been improved in an attempt to enhance the sensitivity, repeatability and accuracy of the analytical results. Spectroscopic techniques, such as UV-vis, FTIR and Raman spectroscopy, have been coupled with light microscopes for these purposes. Synchrotron radiation FTIR microspectroscopy has also been successfully applied to the analysis of artworks. Mass spectrometry has also been increasingly used as a detector system coupled with a chromatographic device. Chromatographic methods have also improved in recent years. Paper and thin layer chromatographic techniques have been progressively replaced with gas chromatography (GC), pyrolysis-GC, high performance liquid chromatography and capillary electrophoresis. More complex proteomics hyphenated techniques, such as nano-liquid chromatography-nano-electrospray ionisation/collision quadrupole time-of-flight tandem mass spectrometry, have been recently applied to the identification and determination of proteinaceous binders. Microbeam analytical techniques have also been incorporated into the list of advanced instrumental techniques for art conservation purposes. Finally, a number

  10. An approximate analytical solution for describing surface runoff and sediment transport over hillslope

    Science.gov (United States)

    Tao, Wanghai; Wang, Quanjiu; Lin, Henry

    2018-03-01

    Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

  11. Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

    Science.gov (United States)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2012-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.

  12. Analytic solution of field distribution and demagnetization function of ideal hollow cylindrical field source

    Science.gov (United States)

    Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min

    2017-09-01

    The Halbach type hollow cylindrical permanent magnet array (HCPMA) is a volume compact and energy conserved field source, which have attracted intense interests in many practical applications. Here, using the complex variable integration method based on the Biot-Savart Law (including current distributions inside the body and on the surfaces of magnet), we derive analytical field solutions to an ideal multipole HCPMA in entire space including the interior of magnet. The analytic field expression inside the array material is used to construct an analytic demagnetization function, with which we can explain the origin of demagnetization phenomena in HCPMA by taking into account an ideal magnetic hysteresis loop with finite coercivity. These analytical field expressions and demagnetization functions provide deeper insight into the nature of such permanent magnet array systems and offer guidance in designing optimized array system.

  13. A physically-based analytical model to describe effective excess charge for streaming potential generation in saturated porous media

    Science.gov (United States)

    Jougnot, D.; Guarracino, L.

    2016-12-01

    The self-potential (SP) method is considered by most researchers the only geophysical method that is directly sensitive to groundwater flow. One source of SP signals, the so-called streaming potential, results from the presence of an electrical double layer at the mineral-pore water interface. When water flows through the pore space, it gives rise to a streaming current and a resulting measurable electrical voltage. Different approaches have been proposed to predict streaming potentials in porous media. One approach is based on the excess charge which is effectively dragged in the medium by the water flow. Following a recent theoretical framework, we developed a physically-based analytical model to predict the effective excess charge in saturated porous media. In this study, the porous media is described by a bundle of capillary tubes with a fractal pore-size distribution. First, an analytical relationship is derived to determine the effective excess charge for a single capillary tube as a function of the pore water salinity. Then, this relationship is used to obtain both exact and approximated expressions for the effective excess charge at the Representative Elementary Volume (REV) scale. The resulting analytical relationship allows the determination of the effective excess charge as a function of pore water salinity, fractal dimension and hydraulic parameters like porosity and permeability, which are also obtained at the REV scale. This new model has been successfully tested against data from the literature of different sources. One of the main finding of this study is that it provides a mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by various researchers. The proposed petrophysical relationship also contributes to understand the role of porosity and water salinity on effective excess charge and will help to push further the use of streaming potential to monitor groundwater flow.

  14. Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

    KAUST Repository

    Younis, Mohammad I.

    2014-08-17

    We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

  15. Acid in perchloroethylene scrubber solutions used in HTGR fuel preparation processes. Analytical chemistry studies

    International Nuclear Information System (INIS)

    Lee, D.A.

    1979-02-01

    Acids and corrosion products in used perchloroethylene scrubber solutions collected from HTGR fuel preparation processes have been analyzed by several analytical methods to determine the source and possible remedy of the corrosion caused by these solutions. Hydrochloric acid was found to be concentrated on the carbon particles suspended in perchloroethylene. Filtration of carbon from the scrubber solutions removed the acid corrosion source in the process equipment. Corrosion products chemisorbed on the carbon particles were identified. Filtered perchloroethylene from used scrubber solutions contained practically no acid. It is recommended that carbon particles be separated from the scrubber solutions immediately after the scrubbing process to remove the source of acid and that an inhibitor be used to prevent the hydrolysis of perchloroethylene and the formation of acids

  16. Analytical solution for the normal emission portion of the averaged Yarkovsky-O'Keefe-Radzvieskii-Paddack coefficient for a single facet

    Science.gov (United States)

    Albuja, Antonella A.; Scheeres, Daniel J.

    2015-02-01

    The Yarkovsky-O'Keefe-Radzvieskii-Paddack (YORP) effect has been well studied for asteroids. This paper develops an analytic solution to find the normal emission YORP component for a single facet. The solution presented here does not account for self-shadowing or self-heating. The YORP coefficient for all facets can be summed together to find the total coefficient of the asteroid. The normal emission component of YORP has been shown to be the most important for asteroids and it directly affects the rate of change of the asteroid's spin period. The analytical solution found is a sole function of the facet's geometry and the obliquity of the asteroid. This solution is universal for any facet and its orientation. The behaviour of the coefficient is analysed with this analytical solution. The closed-form solution is used to find the total YORP coefficient for the asteroids Apollo and 1998 ML14 whose shape models are composed of different numbers of facets. The results are then compared to published results and those obtained through numerical quadrature for validation.

  17. Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

    Science.gov (United States)

    Xie, Dexuan; Volkmer, Hans W.; Ying, Jinyong

    2016-04-01

    The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

  18. Solution of Media Risk and Social Responsibility Governance of Social Media

    OpenAIRE

    Zhang Yuan; Li Ming-De; Zhang Hong-Bang

    2017-01-01

    The rapid development of media technology makes the modern society become a “social media” or even “over social media”, the rise of social media makes it beyond the tool attribute, and become an important force in the reconstruction of contemporary society, the risk of concomitant. The anomie and breach of Social media regularly staged, weakened its positive social function, forcing us to think about the social responsibility of social media,which are reflections on the lack of responsibility...

  19. Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

    KAUST Repository

    Icardi, Matteo; Boccardo, Gianluca; Marchisio, Daniele L.; Tosco, Tiziana; Sethi, Rajandrea

    2014-01-01

    In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed

  20. Analytical solution for the transient response of a fluid/saturated porous medium halfspace system subjected to an impulsive line source

    Science.gov (United States)

    Shan, Zhendong; Ling, Daosheng; Jing, Liping; Li, Yongqiang

    2018-05-01

    In this paper, transient wave propagation is investigated within a fluid/saturated porous medium halfspace system with a planar interface that is subjected to a cylindrical P-wave line source. Assuming the permeability coefficient is sufficiently large, analytical solutions for the transient response of the fluid/saturated porous medium halfspace system are developed. Moreover, the analytical solutions are presented in simple closed forms wherein each term represents a transient physical wave, especially the expressions for head waves. The methodology utilised to determine where the head wave can emerge within the system is also given. The wave fields within the fluid and porous medium are first defined considering the behaviour of two compressional waves and one tangential wave in the saturated porous medium and one compressional wave in the fluid. Substituting these wave fields into the interface continuity conditions, the analytical solutions in the Laplace domain are then derived. To transform the solutions into the time domain, a suitable distortion of the contour is provided to change the integration path of the solution, after which the analytical solutions in the Laplace domain are transformed into the time domain by employing Cagniard's method. Numerical examples are provided to illustrate some interesting features of the fluid/saturated porous medium halfspace system. In particular, the interface wave and head waves that propagate along the interface between the fluid and saturated porous medium can be observed.

  1. Physics of continuous media problems and solutions in electromagnetism, fluid mechanics and MHD

    CERN Document Server

    Vekstein, Grigory

    2013-01-01

    This book presents an excellent and exemplary collection of up-to-date exercises and their solutions on continuous media, covering a wide range of topics from electro-, magnetohydro- and fluid dynamics, and from the theory of elasticity. The author is an international expert with many years of research and teaching experience in the field. Each chapter begins with a comprehensive summary of definitions and the mathematical description of the physical laws necessary to understand and solve the series of problems that follow. The problems and exercises are a gradual built up in each of the topics and they introduce the reader step by step into the principles of the subject. The solutions are well explained and detailed with additional readings when necessary. This exercise book is written in a true scholarly manner that allows the reader to understand the basic principles and physical laws of continuous media. This problem-solving book is highly recommended to graduate and postgraduate students, postdoctoral re...

  2. Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material

    OpenAIRE

    Dalarsson, Mariana; Tassin, Philippe

    2012-01-01

    We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results o...

  3. Analysis of radioactive waste contamination in soils. Part IV: solution via symbolic manipulation

    International Nuclear Information System (INIS)

    Cotta, R.M.; Mikhailov, M.D.; Ruperti Junior, N.J.

    1997-01-01

    The goal of this paper is to demonstrate the automatic symbolic-numerical solution of the one-dimensional linearized Burgers equation with linear decay, which models the migration of radionuclides in porous media, by using the generalized integral transform technique and the Mathematic system. An example is considered to allow for comparison between the proposed hybrid numerical-analytical solution and the exact solution. Different filtering strategies are also investigated, in terms of the effects on convergence rates. (author)

  4. Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: Analytical and semi-analytical solutions

    Science.gov (United States)

    Ferrás, L. L.; Afonso, A. M.; Alves, M. A.; Nóbrega, J. M.; Pinho, F. T.

    2016-09-01

    In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye-Hückel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the distance between the microfluidic device walls is at least one order of magnitude larger than the electric double-layer thickness. To describe the complex fluid rheology, several viscoelastic differential constitutive models were used, namely, the simplified Phan-Thien-Tanner model with linear, quadratic or exponential kernel for the stress coefficient function, the Johnson-Segalman model, and the Giesekus model. The results obtained illustrate the effects of the Weissenberg number, the Johnson-Segalman slip parameter, the Giesekus mobility parameter, and the relative strengths of the electro-osmotic and pressure gradient-driven forcings on the dynamics of these viscoelastic flows.

  5. The effect of injection of high K+ solution into scala media.

    Science.gov (United States)

    Fukazawa, T; Ohmura, M; Yagi, N

    1987-01-01

    Thirty guinea pig ears were studied to investigate the effect of endolymphatic hydrops on the cochlea. High K+ solution was injected into the scala media, and cochlear microphonics (CM) and endocochlear potential (EP) were observed before, during and after the injection. The CM amplitude decreased rapidly after injection, ending in a depressed plateau value. By contrast, EP remained almost unchanged. By changing the composition of the solution it was suggested that the effect of the injection was mechanical one, rather than biochemical. In three ears, spontaneous recovery of CM was observed during a relatively long interval after the injection. The meaning of these findings for the hearing loss in Meniere's disease is discussed.

  6. Analytical Solutions for the Surface States of Bi1-xSbx (0 ≤ x ≲ 0.1)

    Science.gov (United States)

    Fuseya, Yuki; Fukuyama, Hidetoshi

    2018-04-01

    Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are two types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, and (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [https://doi.org/10.1103/PhysRevB.52.1566" xlink:type="simple">Phys. Rev. B 52, 1566 (1995)] for Bi1-xSbx (0 ≤ x ≤ 0.1). A perfect correspondence between the analytic and numerical solutions is obtained around the \\bar{M} point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a "thick" films ( ≲ 200 bilayers ≃ 80 nm) of pure bismuth. Consequently, in such a film of Bi1-xSbx, there is no apparent change in the SSs through the band inversion at x ≃ 0.04, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi1-xSbx (0 ≤ x ≲ 0.1) are discussed.

  7. ANALYTICAL SOLUTION OF THE K-TH ORDER AUTONOMOUS ORDINARY DIFFERENTIAL EQUATION

    Directory of Open Access Journals (Sweden)

    Ronald Orozco López

    2017-04-01

    Full Text Available The main objective of this paper is to find the analytical solution of the autonomous equation y(k = f (y and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.

  8. Analytical solutions for recession analyses of sloping aquifers - applicability on relict rock glaciers in alpine catchments

    Science.gov (United States)

    Pauritsch, Marcus; Birk, Steffen; Hergarten, Stefan; Kellerer-Pirklbauer, Andreas; Winkler, Gerfried

    2014-05-01

    Rock glaciers as aquifer systems in alpine catchments may strongly influence the hydrological characteristics of these catchments. Thus, they have a high impact on the ecosystem and potential natural hazards such as for example debris flow. Therefore, knowledge of the hydrodynamic processes, internal structure and properties of these aquifers is important for resource management and risk assessment. The investigation of such aquifers often turns out to be expensive and technically complicated because of their strongly limited accessibility. Analytical solutions of discharge recession provide a quick and easy way to estimate aquifer parameters. However, due to simplifying assumptions the validity of the interpretation is often questionable. In this study we compared results of an analytical solution of discharge recessions with results based on a numerical model. This was done in order to analyse the range of uncertainties and the applicability of the analytical method in alpine catchment areas. The research area is a 0.76 km² large catchment in the Seckauer Tauern Range, Austria. The dominant aquifer in this catchment is a rock glacier, namely the Schöneben Rock Glacier. This relict rock glacier (i.e. containing no permafrost at present) covers an area of 0.11 km² and is drained by one spring at the rock glacier front. The rock glacier consists predominantly of gneissic sediments (mainly coarse-grained, blocky at the surface) and extends from 1720 to 1905 m a.s.l.. Discharge of the rock glacier spring is automatically measured since 2002. Electric conductivity and water temperature is monitored since 2008. An automatic weather station was installed in 2011 in the central part of the catchment. Additionally data of geophysical surveys (refraction seismic and ground penetrating radar) have been used to analyse the base slope and inner structure of the rock glacier. The measured data are incorporated into a numerical model implemented in MODFLOW. The numerical

  9. An Analytical Solution for Yaw Maneuver Optimization on the International Space Station and Other Orbiting Space Vehicles

    Science.gov (United States)

    Dobrinskaya, Tatiana

    2015-01-01

    This paper suggests a new method for optimizing yaw maneuvers on the International Space Station (ISS). Yaw rotations are the most common large maneuvers on the ISS often used for docking and undocking operations, as well as for other activities. When maneuver optimization is used, large maneuvers, which were performed on thrusters, could be performed either using control moment gyroscopes (CMG), or with significantly reduced thruster firings. Maneuver optimization helps to save expensive propellant and reduce structural loads - an important factor for the ISS service life. In addition, optimized maneuvers reduce contamination of the critical elements of the vehicle structure, such as solar arrays. This paper presents an analytical solution for optimizing yaw attitude maneuvers. Equations describing pitch and roll motion needed to counteract the major torques during a yaw maneuver are obtained. A yaw rate profile is proposed. Also the paper describes the physical basis of the suggested optimization approach. In the obtained optimized case, the torques are significantly reduced. This torque reduction was compared to the existing optimization method which utilizes the computational solution. It was shown that the attitude profiles and the torque reduction have a good match for these two methods of optimization. The simulations using the ISS flight software showed similar propellant consumption for both methods. The analytical solution proposed in this paper has major benefits with respect to computational approach. In contrast to the current computational solution, which only can be calculated on the ground, the analytical solution does not require extensive computational resources, and can be implemented in the onboard software, thus, making the maneuver execution automatic. The automatic maneuver significantly simplifies the operations and, if necessary, allows to perform a maneuver without communication with the ground. It also reduces the probability of command

  10. Non-dissipative kinetic simulation and analytical solution of three-mode equations of ion temperature gradient instability

    International Nuclear Information System (INIS)

    Watanabe, T.-H.; Sugama, H.; Sato, T.

    1999-12-01

    A non-dissipative drift kinetic simulation scheme, which rigorously satisfies the time-reversibility, is applied to the three-mode coupling problem of the ion temperature gradient (ITG) instability. It is found from the simulation that the three-mode ITG system repeats growth and decay with a period which shows a logarithmic divergence for infinitesimal initial perturbations. Accordingly, time average of the mode amplitude vanishes, as the initial amplitude approaches to zero. An exact solution is analytically given for a class of initial conditions. An excellent agreement is confirmed between the analytical solution and numerical results. The results obtained here provide a useful reference for basic benchmarking of theories and simulation of the ITG modes. (author)

  11. An analytical solution to the heat transfer problem in thick-walled hunt flow

    International Nuclear Information System (INIS)

    Bluck, Michael J; Wolfendale, Michael J

    2017-01-01

    Highlights: • Convective heat transfer in Hunt type flow of a liquid metal in a rectangular duct. • Analytical solution to the H1 constant peripheral temperature in a rectangular duct. • New H1 result demonstrating the enhancement of heat transfer due to flow distortion by the applied magnetic field. • Analytical solution to the H2 constant peripheral heat flux in a rectangular duct. • New H2 result demonstrating the reduction of heat transfer due to flow distortion by the applied magnetic field. • Results are important for validation of CFD in magnetohydrodynamics and for implementation of systems code approaches. - Abstract: The flow of a liquid metal in a rectangular duct, subject to a strong transverse magnetic field is of interest in a number of applications. An important application of such flows is in the context of coolants in fusion reactors, where heat is transferred to a lead-lithium eutectic. It is vital, therefore, that the heat transfer mechanisms are understood. Forced convection heat transfer is strongly dependent on the flow profile. In the hydrodynamic case, Nusselt numbers and the like, have long been well characterised in duct geometries. In the case of liquid metals in strong magnetic fields (magnetohydrodynamics), the flow profiles are very different and one can expect a concomitant effect on convective heat transfer. For fully developed laminar flows, the magnetohydrodynamic problem can be characterised in terms of two coupled partial differential equations. The problem of heat transfer for perfectly electrically insulating boundaries (Shercliff case) has been studied previously (Bluck et al., 2015). In this paper, we demonstrate corresponding analytical solutions for the case of conducting hartmann walls of arbitrary thickness. The flow is very different from the Shercliff case, exhibiting jets near the side walls and core flow suppression which have profound effects on heat transfer.

  12. Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam

    Science.gov (United States)

    Spatially-resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of infinitely small size light beam. The method is, however, prone to error in m...

  13. Analytical solutions to the electromagnetic field in a cylindrical shell excited by external axial current

    International Nuclear Information System (INIS)

    Jing, Wu; Chun-Yan, Xiao

    2010-01-01

    The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained. (classical areas of phenomenology)

  14. Comment on 'analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation'

    International Nuclear Information System (INIS)

    Lucha, W.; Schoeberl, F.F.

    1994-01-01

    We demonstrate that the analytic solution for the set of energy eigenvalues of the semi-relativistic Coulomb problem reported by B. and L. Durand is in clear conflict with an upper bound on the ground-state energy level derived by some straightforward variational procedure. (authors)

  15. The Potential of an Alliance of Media Literacy Education and Media Criticism in Russia

    Science.gov (United States)

    Levitskaya, Anastasia

    2015-01-01

    Media criticism and media literacy education have much in common. For example, media literacy education and media criticism attaches great importance to the development of analytical thinking audience. Indeed, one of the most important tasks of media literacy education is precisely to teach the audience not only to analyze media texts of any kinds…

  16. Seismic Wave Propagation in Layered Viscoelastic Media

    Science.gov (United States)

    Borcherdt, R. D.

    2008-12-01

    Advances in the general theory of wave propagation in layered viscoelastic media reveal new insights regarding seismic waves in the Earth. For example, the theory predicts: 1) P and S waves are predominantly inhomogeneous in a layered anelastic Earth with seismic travel times, particle-motion orbits, energy speeds, Q, and amplitude characteristics that vary with angle of incidence and hence, travel path through the layers, 2) two types of shear waves exist, one with linear and the other with elliptical particle motions each with different absorption coefficients, and 3) surface waves with amplitude and particle motion characteristics not predicted by elasticity, such as Rayleigh-Type waves with tilted elliptical particle motion orbits and Love-Type waves with superimposed sinusoidal amplitude dependencies that decay exponentially with depth. The general theory provides closed-form analytic solutions for body waves, reflection-refraction problems, response of multiple layers, and surface wave problems valid for any material with a viscoelastic response, including the infinite number of models, derivable from various configurations of springs and dashpots, such as elastic, Voight, Maxwell, and Standard Linear. The theory provides solutions independent of the amount of intrinsic absorption and explicit analytic expressions for physical characteristics of body waves in low-loss media such as the deep Earth. The results explain laboratory and seismic observations, such as travel-time and wide-angle reflection amplitude anomalies, not explained by elasticity or one dimensional Q models. They have important implications for some forward modeling and inverse problems. Theoretical advances and corresponding numerical results as recently compiled (Borcherdt, 2008, Viscoelastic Waves in Layered Media, Cambridge University Press) will be reviewed.

  17. Analysis of radioactive waste contamination in soils. Part IV: solution via symbolic manipulation

    Energy Technology Data Exchange (ETDEWEB)

    Cotta, R.M.; Mikhailov, M.D. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Lab. de Transmissao e Tecnologia do Calor; Ruperti Junior, N.J. [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil). Coordenacao de Rejeitos Radioativos

    1997-12-31

    The goal of this paper is to demonstrate the automatic symbolic-numerical solution of the one-dimensional linearized Burgers equation with linear decay, which models the migration of radionuclides in porous media, by using the generalized integral transform technique and the Mathematic system. An example is considered to allow for comparison between the proposed hybrid numerical-analytical solution and the exact solution. Different filtering strategies are also investigated, in terms of the effects on convergence rates. (author) 6 refs., 7 figs., 7 tabs.

  18. Existence and Uniqueness of Solutions to the Stochastic Porous Media Equations of Saturated Flows

    International Nuclear Information System (INIS)

    Ciotir, Ioana

    2010-01-01

    This paper proves the existence and uniqueness of nonnegative solutions for the stochastic porous media equations with multiplicative noise, infinite jump and discontinuous diffusivity function relevant in description of saturation processes in underground water infiltration in a bounded domain of R 3 .

  19. Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

    International Nuclear Information System (INIS)

    Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong

    2008-01-01

    Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through

  20. The method of lines solution of discrete ordinates method for non-grey media

    International Nuclear Information System (INIS)

    Cayan, Fatma Nihan; Selcuk, Nevin

    2007-01-01

    A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach

  1. The ''2T'' ion-electron semi-analytic shock solution for code-comparison with xRAGE: A report for FY16

    International Nuclear Information System (INIS)

    Ferguson, Jim Michael

    2016-01-01

    This report documents an effort to generate the semi-analytic '2T' ion-electron shock solution developed in the paper by Masser, Wohlbier, and Lowrie, and the initial attempts to understand how to use this solution as a code-verification tool for one of LANL's ASC codes, xRAGE. Most of the work so far has gone into generating the semi-analytic solution. Considerable effort will go into understanding how to write the xRAGE input deck that both matches the boundary conditions imposed by the solution, and also what physics models must be implemented within the semi-analytic solution itself to match the model assumptions inherit within xRAGE. Therefore, most of this report focuses on deriving the equations for the semi-analytic 1D-planar time-independent '2T' ion-electron shock solution, and is written in a style that is intended to provide clear guidance for anyone writing their own solver.

  2. Social media management and media environment

    Directory of Open Access Journals (Sweden)

    Šiđanin Iva

    2012-01-01

    Full Text Available The paper deals with the system of services that social media management can offer to a variety of users. As social media systems are emerging, social media management can strengthen teams in social media and help to manage numerous social channels and distribution of social information from one place. Social media management is a system of procedures that are used to manage the flow of information in the environment of social media. This involves connecting with social media like Facebook, Twitter, LinkedIn, Plaxo, Ecademy, YouTube and many others, then the aggregation and management of social data. Social media management services are analysed through various fields, such as managing multiple social media profiles, mail scheduling and filtering, reporting and analytics. Social media management enables managing personal business through social media, which contributes to a significant reduction in expenditures. The paper also discusses the importance of social media management in marketing activities and various forms of social promotion, which allow companies to easily reach their customers.

  3. Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

    Directory of Open Access Journals (Sweden)

    De-Gang Wang

    2012-01-01

    Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

  4. Two-particle correlations in the one-dimensional Hubbard model: a ground-state analytical solution

    CERN Document Server

    Vallejo, E; Espinosa, J E

    2003-01-01

    A solution to the extended Hubbard Hamiltonian for the case of two-particles in an infinite one-dimensional lattice is presented, using a real-space mapping method and the Green function technique. This Hamiltonian considers the on-site (U) and the nearest-neighbor (V) interactions. The method is based on mapping the correlated many-body problem onto an equivalent site-impurity tight-binding one in a higher dimensional space. In this new space we obtained the analytical solution for the ground state binding energy. Results are in agreement with the numerical solution obtained previously [1], and with those obtained in the reciprocal space [2]. (Author)

  5. An Exact Analytical Solution to Exponentially Tapered Piezoelectric Energy Harvester

    Directory of Open Access Journals (Sweden)

    H. Salmani

    2015-01-01

    Full Text Available It has been proven that tapering the piezoelectric beam through its length optimizes the power extracted from vibration based energy harvesting. This phenomenon has been investigated by some researchers using semianalytical, finite element and experimental methods. In this paper, an exact analytical solution is presented to calculate the power generated from vibration of exponentially tapered unimorph and bimorph with series and parallel connections. The mass normalized mode shapes of the exponentially tapered piezoelectric beam with tip mass are implemented to transfer the proposed electromechanical coupled equations into modal coordinates. The steady states harmonic solution results are verified both numerically and experimentally. Results show that there exist values for tapering parameter and electric resistance in a way that the output power per mass of the energy harvester will be maximized. Moreover it is concluded that the electric resistance must be higher than a specified value for gaining more power by tapering the beam.

  6. Recursive analytical solution describing artificial satellite motion perturbed by an arbitrary number of zonal terms

    Science.gov (United States)

    Mueller, A. C.

    1977-01-01

    An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.

  7. A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media.

    Science.gov (United States)

    de Barros, F P J; Fiori, A; Boso, F; Bellin, A

    2015-01-01

    Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data. Copyright © 2015 Elsevier B.V. All rights reserved.

  8. Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films

    Science.gov (United States)

    Perazzo, Carlos Alberto; Mac Intyre, J. R.; Gomba, J. M.

    2017-12-01

    By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.

  9. Myelography iodinated contrast media. I. Unraveling the atropisomerism properties in solution.

    Science.gov (United States)

    Fontanive, Luca; D'Amelio, Nicola; Cesàro, Attilio; Gamini, Amelia; Tavagnacco, Letizia; Paolantoni, Marco; Brady, John W; Maiocchi, Alessandro; Uggeri, Fulvio

    2015-06-01

    The present work reports a thorough conformational analysis of iodinated contrast media: iomeprol, iopamidol (the world's most utilized contrast agent), and iopromide. Its main aim is the understanding of the complex structural features of these atropisomeric molecules, characterized by the presence of many conformers with hindered rotations, and of the role of atropisomerism in the physicochemical properties of their aqueous solutions. The problem was tackled by using an extensive analysis of (13)C NMR data on the solutions of whole molecules and of simple precursors in addition to FT-IR investigation and molecular simulations. This analysis demonstrated that out of the many possible atropisomers, only a few are significantly populated, and their relative population is provided. The conformational analysis also indicated that the presence of a sterically hindered amidic bond, allowing a significant population of cis forms (E in iopromide and exo in iomeprol), may be the basis for an increased thermodynamic solubility of concentrated solutions of iomeprol.

  10. Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: the Lagrangian approach.

    Science.gov (United States)

    Soltanian, Mohamad Reza; Ritzi, Robert W; Dai, Zhenxue; Huang, Chao Cheng

    2015-03-01

    Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion. Copyright © 2014 Elsevier Ltd. All rights reserved.

  11. Measurement of Actinides in Molybdenum-99 Solution Analytical Procedure

    International Nuclear Information System (INIS)

    Soderquist, Chuck Z.; Weaver, Jamie L.

    2015-01-01

    This document is a companion report to a previous report, PNNL 24519, Measurement of Actinides in Molybdenum-99 Solution, A Brief Review of the Literature, August 2015. In this companion report, we report a fast, accurate, newly developed analytical method for measurement of trace alpha-emitting actinide elements in commercial high-activity molybdenum-99 solution. Molybdenum-99 is widely used to produce 99m Tc for medical imaging. Because it is used as a radiopharmaceutical, its purity must be proven to be extremely high, particularly for the alpha emitting actinides. The sample of 99 Mo solution is measured into a vessel (such as a polyethylene centrifuge tube) and acidified with dilute nitric acid. A gadolinium carrier is added (50 µg). Tracers and spikes are added as necessary. Then the solution is made strongly basic with ammonium hydroxide, which causes the gadolinium carrier to precipitate as hydrous Gd(OH) 3 . The precipitate of Gd(OH) 3 carries all of the actinide elements. The suspension of gadolinium hydroxide is then passed through a membrane filter to make a counting mount suitable for direct alpha spectrometry. The high-activity 99 Mo and 99m Tc pass through the membrane filter and are separated from the alpha emitters. The gadolinium hydroxide, carrying any trace actinide elements that might be present in the sample, forms a thin, uniform cake on the surface of the membrane filter. The filter cake is first washed with dilute ammonium hydroxide to push the last traces of molybdate through, then with water. The filter is then mounted on a stainless steel counting disk. Finally, the alpha emitting actinide elements are measured by alpha spectrometry.

  12. Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.

  13. Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

    Energy Technology Data Exchange (ETDEWEB)

    Paster, Amir, E-mail: paster@tau.ac.il [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978 (Israel); Bolster, Diogo [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); Benson, David A. [Hydrologic Science and Engineering, Colorado School of Mines, Golden, CO, 80401 (United States)

    2014-04-15

    We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.

  14. Numerically calibrated model for propagation of a relativistic unmagnetized jet in dense media

    Science.gov (United States)

    Harrison, Richard; Gottlieb, Ore; Nakar, Ehud

    2018-03-01

    Relativistic jets reside in high-energy astrophysical systems of all scales. Their interaction with the surrounding media is critical as it determines the jet evolution, observable signature, and feedback on the environment. During its motion the interaction of the jet with the ambient media inflates a highly pressurized cocoon, which under certain conditions collimates the jet and strongly affects its propagation. Recently, Bromberg et al. (2011b) derived a general simplified (semi)analytic solution for the evolution of the jet and the cocoon in case of an unmagnetized jet that propagates in a medium with a range of density profiles. In this work we use a large suite of 2D and 3D relativistic hydrodynamic simulations in order to test the validity and accuracy of this model. We discuss the similarities and differences between the analytic model and numerical simulations and also, to some extent, between 2D and 3D simulations. Our main finding is that although the analytic model is highly simplified, it properly predicts the evolution of the main ingredients of the jet-cocoon system, including its temporal evolution and the transition between various regimes (e.g., collimated to uncollimated). The analytic solution predicts a jet head velocity that is faster by a factor of about 3 compared to the simulations, as long as the head velocity is Newtonian. We use the results of the simulations to calibrate the analytic model which significantly increases its accuracy. We provide an applet that calculates semi-analytically the propagation of a jet in an arbitrary density profile defined by the user at http://www.astro.tau.ac.il/ ore/propagation.html.

  15. Numerically calibrated model for propagation of a relativistic unmagnetized jet in dense media

    Science.gov (United States)

    Harrison, Richard; Gottlieb, Ore; Nakar, Ehud

    2018-06-01

    Relativistic jets reside in high-energy astrophysical systems of all scales. Their interaction with the surrounding media is critical as it determines the jet evolution, observable signature, and feedback on the environment. During its motion, the interaction of the jet with the ambient media inflates a highly pressurized cocoon, which under certain conditions collimates the jet and strongly affects its propagation. Recently, Bromberg et al. derived a general simplified (semi-)analytic solution for the evolution of the jet and the cocoon in case of an unmagnetized jet that propagates in a medium with a range of density profiles. In this work we use a large suite of 2D and 3D relativistic hydrodynamic simulations in order to test the validity and accuracy of this model. We discuss the similarities and differences between the analytic model and numerical simulations and also, to some extent, between 2D and 3D simulations. Our main finding is that although the analytic model is highly simplified, it properly predicts the evolution of the main ingredients of the jet-cocoon system, including its temporal evolution and the transition between various regimes (e.g. collimated to uncollimated). The analytic solution predicts a jet head velocity that is faster by a factor of about 3 compared to the simulations, as long as the head velocity is Newtonian. We use the results of the simulations to calibrate the analytic model which significantly increases its accuracy. We provide an applet that calculates semi-analytically the propagation of a jet in an arbitrary density profile defined by the user at http://www.astro.tau.ac.il/˜ore/propagation.html.

  16. Porous media: Analysis, reconstruction and percolation

    DEFF Research Database (Denmark)

    Rogon, Thomas Alexander

    1995-01-01

    functions of Gaussian fields and spatial autocorrelation functions of binary fields. An enhanced approach which embodies semi-analytical solutions for the conversions has been made. The scope and limitations of the method have been analysed in terms of realizability of different model correlation functions...... stereological methods. The measured sample autocorrelations are modeled by analytical correlation functions. A method for simulating porous networks from their porosity and spatial correlation originally developed by Joshi (14) is presented. This method is based on a conversion between spatial autocorrelation...... in binary fields. Percolation threshold of reconstructed porous media has been determined for different discretizations of a selected model correlation function. Also critical exponents such as the correlation length exponent v, the strength of the infinite network and the mean size of finite clusters have...

  17. Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material.

    Science.gov (United States)

    Dalarsson, Mariana; Tassin, Philippe

    2009-04-13

    We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.

  18. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2014-01-01

    Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

  19. A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

    Science.gov (United States)

    Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

  20. Solubility limited radionuclide transport through geologic media

    International Nuclear Information System (INIS)

    Muraoka, Susumu; Iwamoto, Fumio; Pigford, T.H.

    1980-11-01

    Prior analyses for the migration of radionuclides neglect solubility limits of resolved radionuclide in geologic media. But actually some of the actinides may appear in chemical forms of very low solubility. In the present report we have proposed the migration model with no decay parents in which concentration of radionuclide is limited in concentration of solubility in ground water. In addition, the analytical solutions of the space-time-dependent concentration are presented in the case of step release, band release and exponential release. (author)

  1. An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method

    International Nuclear Information System (INIS)

    Yabushita, Kazuki; Yamashita, Mariko; Tsuboi, Kazuhiro

    2007-01-01

    We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 x 10 3 ∼ 2 x 10 5 (for instance, a sphere) for practical situations, such as throwing a ball. It has been considered that the equations of motion of this case are unsolvable for a general projectile angle, although some solutions have been obtained for a small projectile angle using perturbation techniques. To obtain a general analytic solution, we apply Liao's homotopy analysis method to this problem. The homotopy analysis method, which is different from a perturbation technique, can be applied to a problem which does not include small parameters. We apply the homotopy analysis method for not only governing differential equations, but also an algebraic equation of a velocity vector to extend the radius of convergence. Ultimately, we obtain the analytic solution to this problem and investigate the validation of the solution

  2. Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method

    Directory of Open Access Journals (Sweden)

    S. Das

    2013-12-01

    Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.

  3. Analysis and Computation of Acoustic and Elastic Wave Equations in Random Media

    KAUST Repository

    Motamed, Mohammad

    2014-01-06

    We propose stochastic collocation methods for solving the second order acoustic and elastic wave equations in heterogeneous random media and subject to deterministic boundary and initial conditions [1, 4]. We assume that the medium consists of non-overlapping sub-domains with smooth interfaces. In each sub-domain, the materials coefficients are smooth and given or approximated by a finite number of random variable. One important example is wave propagation in multi-layered media with smooth interfaces. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems [2, 3], the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence is only algebraic. A fast spectral rate of convergence is still possible for some quantities of interest and for the wave solutions with particular types of data. We also show that the semi-discrete solution is analytic with respect to the random variables with the radius of analyticity proportional to the grid/mesh size h. We therefore obtain an exponential rate of convergence which deteriorates as the quantity h p gets smaller, with p representing the polynomial degree in the stochastic space. We have shown that analytical results and numerical examples are consistent and that the stochastic collocation method may be a valid alternative to the more traditional Monte Carlo method. Here we focus on the stochastic acoustic wave equation. Similar results are obtained for stochastic elastic equations.

  4. 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)

  5. Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

    Science.gov (United States)

    Chen, Shanzhen; Jiang, Xiaoyun

    2012-08-01

    In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

  6. Numerical modelling of coupled fluid, heat, and solute transport in deformable fractured rock

    International Nuclear Information System (INIS)

    Chan, T.; Reid, J.A.K.

    1987-01-01

    This paper reports on a three-dimensional (3D) finite-element code, MOTIF (model of transport in fractured/porous media), developed to model the coupled processes of groundwater flow, heat transport, brine transport, and one-species radionuclide transport in geological media. Three types of elements are available: a 3D continuum element, a planar fracture element that can be oriented in any arbitrary direction in 3D space or pipe flow in 3D space, and a line element for simulating fracture flow in 2D space or pipe flow in 3D space. As a quality-assurance measure, the MOTIF code was verified by comparison of its results with analytical solutions and other published numerical solutions

  7. The General Analytic Solution of a Functional Equation of Addition Type

    OpenAIRE

    Braden, H. W.; Buchstaber, V. M.

    1995-01-01

    The general analytic solution to the functional equation $$ \\phi_1(x+y)= { { \\biggl|\\matrix{\\phi_2(x)&\\phi_2(y)\\cr\\phi_3(x)&\\phi_3(y)\\cr}\\biggr|} \\over { \\biggl|\\matrix{\\phi_4(x)&\\phi_4(y)\\cr\\phi_5(x)&\\phi_5(y)\\cr}\\biggr|} } $$ is characterised. Up to the action of the symmetry group, this is described in terms of Weierstrass elliptic functions. We illustrate our theory by applying it to the classical addition theorems of the Jacobi elliptic functions and the functional equations $$ \\phi_1(x+...

  8. Water, gas and solute movement through argillaceous media

    International Nuclear Information System (INIS)

    Horseman, S.T.; Higgo, J.J.W.; Alexander, J.; Harrington, J.F.

    1996-01-01

    This report was commissioned by a consortium of companies and organisations with a common concern: the capacity of clay-rich media to act as barriers to the movement of radionuclides. Since the migration of such contaminants occurs primarily in aqueous solutions, considerable emphasis is placed on the motion of groundwater in the subsurface environment and on the advective and diffusive transport of solutes within this water. This report examines clay systems at a very wide range of scales, from the molecular-scale interactions between water molecules and clay surfaces, through to large-scale processes such as the movement of fluids in sedimentary basins. Its goal is to study the links between the colloidal interactions between clay mineral particles, the mechanical responses of the system and the movement of fluids. The Darcy's or Fick's laws were adopted as a basis for the phenomenological mass transfer calculations, and a very idealized porous medium having clearly identifiable characteristics and properties was considered to replace the inordinately complex and highly-variable geologic medium. It is also assumed that geological processes, other than transport processes, either cease to operate over the time-scale of interest or can have no secondary effect on mass transport. (J.S.). 737 refs., 25 figs., 4 tabs., 2 appends

  9. On the analytic solution of the steady flow of a fourth grade fluid

    International Nuclear Information System (INIS)

    Sajid, M.; Hayat, T.; Asghar, S.

    2006-01-01

    The steady flow of a fourth grade fluid is a problem belonging to non-Newtonian fluid mechanics and deserves to be more widely studied than it has been to date. In the non-linear regime the literature is scarce. We develop a formulation suitable for solution of hydrodynamic equation containing non-linear rheological effects of fourth grade fluids. The homotopy analysis method (HAM) is used to investigate the flow of a fourth grade fluid past a porous plate. Explicit analytic solution is given. The non-linear effects on the velocity distribution is shown and discussed. Comparison of the present analysis is also made with the existing results in the literature

  10. Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Pankaj, E-mail: psharma@rtu.ac.in; Parashar, Sandeep Kumar, E-mail: parashar2@yahoo.com [Mechanical Engineering Department, Rajasthan Technical University, Kota (India)

    2016-05-06

    The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

  11. Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution

    OpenAIRE

    Farjas, Jordi; Roura, Pere

    2008-01-01

    Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding n...

  12. Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

    International Nuclear Information System (INIS)

    Theodorakis, Stavros

    2003-01-01

    We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions

  13. Geological entropy and solute transport in heterogeneous porous media

    Science.gov (United States)

    Bianchi, Marco; Pedretti, Daniele

    2017-06-01

    We propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer, which we fully characterize with two measurable parameters: the variance of the log K values (σY2), and a new indicator (HR) that integrates multiple properties of the K field into a global measure of spatial disorder or geological entropy. From the results of a detailed numerical experiment considering solute transport in K fields representing realistic distributions of hydrofacies in alluvial aquifers, we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane. The analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder (i.e., HR increasing), while highly skewed distributions are observed in more orderly structures (i.e., HR decreasing) or at higher σY2. We found that simple closed-form empirical expressions of the bivariate dependency of skewness on HR and σY2 can be used to predict the emergence of non-Fickian transport in K fields considering a range of structures and heterogeneity levels, some of which based on documented real aquifers. The accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the K field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media.

  14. Consolidating Social Media Strategies

    DEFF Research Database (Denmark)

    Gyimóthy, Szilvia; Munar, Ana Maria; Larson, Mia

    2014-01-01

    This study revisits and integrates the insights of recent studies on emergent social media strategies deployed by destination and event management organisations. In a comparative analysis Munar (2012) identified four generic approaches pursued by national tourism boards in the Nordic region, while...... Gyimóthy & Larson (2014) portrayed three digital value co-creation strategies deployed by festival social media. Both frameworks provided novel analytical typologies which identified a series of categories (mimetic, analytic, immersion, advertising and insourcing, crowdsourcing and community consolidation......). This paper discusses the complementary nature of these conceptual proposals and advances an integrated conceptual framework of social media strategies. Based on the empirical findings of a case study that revisits evolving digital and social media strategies of European DMOs this paper maps the dynamics...

  15. Measurement of Actinides in Molybdenum-99 Solution Analytical Procedure

    Energy Technology Data Exchange (ETDEWEB)

    Soderquist, Chuck Z. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Weaver, Jamie L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

    2015-11-01

    This document is a companion report to a previous report, PNNL 24519, Measurement of Actinides in Molybdenum-99 Solution, A Brief Review of the Literature, August 2015. In this companion report, we report a fast, accurate, newly developed analytical method for measurement of trace alpha-emitting actinide elements in commercial high-activity molybdenum-99 solution. Molybdenum-99 is widely used to produce 99mTc for medical imaging. Because it is used as a radiopharmaceutical, its purity must be proven to be extremely high, particularly for the alpha emitting actinides. The sample of 99Mo solution is measured into a vessel (such as a polyethylene centrifuge tube) and acidified with dilute nitric acid. A gadolinium carrier is added (50 µg). Tracers and spikes are added as necessary. Then the solution is made strongly basic with ammonium hydroxide, which causes the gadolinium carrier to precipitate as hydrous Gd(OH)3. The precipitate of Gd(OH)3 carries all of the actinide elements. The suspension of gadolinium hydroxide is then passed through a membrane filter to make a counting mount suitable for direct alpha spectrometry. The high-activity 99Mo and 99mTc pass through the membrane filter and are separated from the alpha emitters. The gadolinium hydroxide, carrying any trace actinide elements that might be present in the sample, forms a thin, uniform cake on the surface of the membrane filter. The filter cake is first washed with dilute ammonium hydroxide to push the last traces of molybdate through, then with water. The filter is then mounted on a stainless steel counting disk. Finally, the alpha emitting actinide elements are measured by alpha spectrometry.

  16. An analytical approach to the solution of in-itself strong focusing beam

    International Nuclear Information System (INIS)

    Paulin, A.; Ticar, I.; Zoric, T.; Znidarsic, K.; Bezic, N.

    1981-01-01

    The aim of this paper is a description of the problem, how to represent the high current, high current density charged particle beam with straightforward analytical expressions. The principal difficulties in the solution of differential equation for stationary, axial and radial distribution of charged particles in the high current, high current density beam are mentioned. In all the derivations, an accomplished space charge effects compensation with suitable combined beam of oppositely charged particles is assumed. (author)

  17. Social Sensor Analytics: Making Sense of Network Models in Social Media

    Energy Technology Data Exchange (ETDEWEB)

    Dowling, Chase P.; Harrison, Joshua J.; Sathanur, Arun V.; Sego, Landon H.; Corley, Courtney D.

    2015-07-27

    Social networks can be thought of as noisy sensor networks mapping real world information to the web. Owing to the extensive body of literature in sensor network analysis, this work sought to apply several novel and traditional methods in sensor network analysis for the purposes of efficiently interrogating social media data streams from raw data. We carefully revisit our definition of a social media signal from previous work both in terms of time-varying features within the data and the networked nature of the medium. Further, we detail our analysis of global patterns in Twitter over the months of November 2013 and June 2014, detect and categorize events, and illustrate how these analyses can be used to inform graph-based models of Twitter, namely using a recent network influence model called PhySense: similar to PageRank but tuned to behavioral analysis by leveraging a sociologically inspired probabilistic model. We ultimately identify forms of information dissemination via analysis of time series and dynamic graph spectra and corroborate these findings through manual investigation of the data as a requisite step in modeling the diffusion process with PhySense. We hope to sufficiently characterize global behavior in a medium such as Twitter as a means of learning global model parameters one may use to predict or simulate behavior on a large scale. We have made our time series and dynamic graph analytical code available via a GitHub repository https://github.com/cpatdowling/salsa and our data are available upon request.

  18. Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

    Directory of Open Access Journals (Sweden)

    Te-Wen Tu

    2015-01-01

    Full Text Available An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

  19. A semi-analytical solution for viscothermal wave propagation in narrow gaps with arbitrary boundary conditions.

    NARCIS (Netherlands)

    Wijnant, Ysbrand H.; Spiering, R.M.E.J.; Blijderveen, M.; de Boer, Andries

    2006-01-01

    Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap

  20. Analytical general solutions for static wormholes in f(R,T) gravity

    Science.gov (United States)

    Moraes, P. H. R. S.; Correa, R. A. C.; Lobato, R. V.

    2017-07-01

    Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f(R,T) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T-dependence in f(R,T) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f(R,T) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.

  1. Analytical general solutions for static wormholes in f ( R , T ) gravity

    Energy Technology Data Exchange (ETDEWEB)

    Moraes, P.H.R.S.; Correa, R.A.C.; Lobato, R.V., E-mail: moraes.phrs@gmail.com, E-mail: fis04132@gmail.com, E-mail: ronaldo.lobato@icranet.org [ITA-Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP (Brazil)

    2017-07-01

    Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f ( R , T ) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T -dependence in f ( R , T ) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f ( R , T ) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.

  2. A semi-analytical solution for slug tests in an unconfined aquifer considering unsaturated flow

    Science.gov (United States)

    Sun, Hongbing

    2016-01-01

    A semi-analytical solution considering the vertical unsaturated flow is developed for groundwater flow in response to a slug test in an unconfined aquifer in Laplace space. The new solution incorporates the effects of partial penetrating, anisotropy, vertical unsaturated flow, and a moving water table boundary. Compared to the Kansas Geological Survey (KGS) model, the new solution can significantly improve the fittings of the modeled to the measured hydraulic heads at the late stage of slug tests in an unconfined aquifer, particularly when the slug well has a partially submerged screen and moisture drainage above the water table is significant. The radial hydraulic conductivities estimated with the new solution are comparable to those from the KGS, Bouwer and Rice, and Hvorslev methods. In addition, the new solution also can be used to examine the vertical conductivity, specific storage, specific yield, and the moisture retention parameters in an unconfined aquifer based on slug test data.

  3. Modeling of the anode side of a direct methanol fuel cell with analytical solutions

    International Nuclear Information System (INIS)

    Mosquera, Martin A.; Lizcano-Valbuena, William H.

    2009-01-01

    In this work, analytical solutions were derived (for any methanol oxidation reaction order) for the profiles of methanol concentration and proton current density, by assuming diffusion mass transport mechanism, Tafel kinetics, and fast proton transport in the anodic catalyst layer of a direct methanol fuel cell. An expression for the Thiele modulus that allows to express the anodic overpotential as a function of the cell current and kinetic and mass transfer parameters was obtained. For high cell current densities, it was found that the Thiele modulus (φ 2 ) varies quadratically with cell current density; yielding a simple correlation between anodic overpotential and cell current density. Analytical solutions were derived for the profiles of both local methanol concentration in the catalyst layer and local anodic current density in the catalyst layer. Under the assumptions of the model presented here, in general, the local methanol concentration in the catalyst layer cannot be expressed as an explicit function of the position in the layer. In spite of this, the equations presented here for the anodic overpotential allow the derivation of new semi-empirical equations

  4. An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

    Directory of Open Access Journals (Sweden)

    Ryoichi Chiba

    2018-01-01

    Full Text Available An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of n layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at n-1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

  5. Analytical and numerical investigation of double diffusion in thermally anisotropy multilayer porous medium

    Energy Technology Data Exchange (ETDEWEB)

    Bennacer, R. [Neuville sur Oise, LEEVAM 5 mail Gay Lussac, Cergy-Pontoise Cedex (France); Mohamad, A.A. [CEERE University of Calgary, Department of Mechanical and Manufacturing Engineering, Calgary, Alberta (Canada); Ganaoui, M.El [Faculte des Sciences et Techniques de Limoges, Limoges (France)

    2005-02-01

    Double-diffusive natural convection within a multilayer anisotropic porous medium is studied numerically and analytically. The domain composed of two horizontal porous layers is subjected to a uniform horizontal heat flux and a vertical mass flux, where only the lower one is thermally anisotropic. Darcy model with classical Boussinesq approximation is used in formulating the mathematical model. The effect of thermal anisotropy and the relative width of the two layers on the flow and transfers is illustrated with characterising the transitions from the diffusive to the convective solution. Results were well compared with respect to a developed analytical approach, based on a parallel flow approximation for thermally anisotropic multilayer media. (orig.)

  6. The analytical solution to the problem on the temperature field in a structural element of rectangular profile for third kind boundary conditions

    International Nuclear Information System (INIS)

    Kulich, N.V.; Nemtsev, V.A.

    1986-01-01

    The analytical solution to the problem on the stationary temperature field in an infinite structural element of rectangular profile characteristic of the conjugation points of a vessel and a tube sheet of a heat exchanger (or of a finned surface) at the third-kind boundary conditions has been obtained by the methods of the complex variable function theory. With the help of the obtained analytical dependences the calculations of the given element of the design and the comparison with the known data have been conducted. The proposed analytical solution can be effectively used in calculations of temperature fields in finned surfaces and structural elements of the power equipment of the considered profile and the method is applied for solution of the like problems

  7. The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

    Science.gov (United States)

    Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

    2018-04-01

    We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

  8. An Equal-Strain Analytical Solution for the Radial Consolidation of Unsaturated Soils by Vertical Drains considering Drain Resistance

    Directory of Open Access Journals (Sweden)

    Feng Zhou

    2018-01-01

    Full Text Available Developing an analytical solution for the consolidation of unsaturated soils remains a challenging task due to the complexity of coupled governing equations for air and water phases. This paper presents an equal-strain model for the radial consolidation of unsaturated soils by vertical drains, and the effect of drain resistance is also considered. Simplified governing equations are established, and an analytical solution to calculate the excess pore-air and pore-water pressures is derived by using the methods of matrix analysis and eigenfunction expansion. The average degrees of consolidation for air and water phases and the ground surface settlement are also given. The solutions of the equal-strain model are verified by comparing the proposed free-strain model with the equal-strain model, and reasonably good agreement is obtained. Moreover, parametric studies regarding the drain resistance effect are graphically presented.

  9. Simplified semi-analytical model for mass transport simulation in unsaturated zone

    International Nuclear Information System (INIS)

    Sa, Bernadete L. Vieira de; Hiromoto, Goro

    2001-01-01

    This paper describes a simple model to determine the flux of radionuclides released from a concrete vault repository and its implementation through the development of a computer program. The radionuclide leach rate from waste is calculated using a model based on simple first order kinetics and the transport through porous media bellow the waste is determined using a semi-analytical solution of the mass transport equation. Results obtained in the IAEA intercomparison program are also related in this communication. (author)

  10. Analytical-numerical solution for the trajectory of seismic rays in media with vertical heterogeneity

    International Nuclear Information System (INIS)

    Imhof, Armando Luis; Calvo, Carlos Adolfo; Moyano, Amalia; Sanchez, Manuel

    2015-01-01

    A determined curve path is followed by the propagation of seismic waves generated in emitters and detected in receivers by the principle of minimum time of Fermat. An ordinary differential equation is derived from the application of the calculation of variations. Due to the compaction of the terrain, the speed usually increases with depth. The experimental laws for each soil have led to this variation leading to a numerical resolution. The adjustment of experimental speed data by an exponential function; the analytical integration of the differential equation and the numerical determination of the integration constants are studied. A geophysical method such as up-hole or down-hole has determined the experimental data. Its main application is centered in the validation of numerical models of curved trajectories. Then time of first arrivals through tomographic algorithms for detection and modeling of anomalies in the first 12 m depth. (author) [es

  11. U.S. News Media Coverage of Pharmaceutical Pollution in the Aquatic Environment: A Content Analysis of the Problems and Solutions Presented by Actors.

    Science.gov (United States)

    Blair, Benjamin; Zimny-Schmitt, Daniel; Rudd, Murray A

    2017-08-01

    Pharmaceutical pollution in the aquatic environment is an issue of concern that has attracted attention by the news media. Understanding the factors that contribute to media framing of pharmaceutical pollution may lead to a better understanding of the management and governance of this issue, including why these pollutants are generally unregulated at this time. This study conducted a content analysis of 405 newspaper articles (81 had substantive information on the topic) from 2007 to 2014, using the search terms "water" and "pharmaceuticals" in the Chicago Tribune, Denver Post, Los Angeles Times, New York Daily News, New York Times, USA Today, Wall Street Journal, and Washington Post. We sought to analyze the factors that contributed to the news media presentation of pharmaceutical pollution in the United States, including the presentation of the risks/safety and solutions by various actors. We found that the primary issues in the news media were uncertainty regarding public health and harm to the environment. The primary solutions recommended within the news media were implementing additional water treatment technologies, taking unused pharmaceuticals to predetermined sites for disposal (take-back programs), and trash disposal of unused pharmaceuticals. Water utilities and scientists presented improved water treatment technology, government actors presented take-back programs, and pharmaceutical representatives, while sparsely involved in the news media, presented trash disposal as their primary solutions. To advance the understanding of the management of pharmaceutical pollution, this article offers further insight into the debate and potential solutions within the news media presentation of this complex scientific topic.

  12. U.S. News Media Coverage of Pharmaceutical Pollution in the Aquatic Environment: A Content Analysis of the Problems and Solutions Presented by Actors

    Science.gov (United States)

    Blair, Benjamin; Zimny-Schmitt, Daniel; Rudd, Murray A.

    2017-08-01

    Pharmaceutical pollution in the aquatic environment is an issue of concern that has attracted attention by the news media. Understanding the factors that contribute to media framing of pharmaceutical pollution may lead to a better understanding of the management and governance of this issue, including why these pollutants are generally unregulated at this time. This study conducted a content analysis of 405 newspaper articles (81 had substantive information on the topic) from 2007 to 2014, using the search terms "water" and "pharmaceuticals" in the Chicago Tribune, Denver Post, Los Angeles Times, New York Daily News, New York Times, USA Today, Wall Street Journal, and Washington Post. We sought to analyze the factors that contributed to the news media presentation of pharmaceutical pollution in the United States, including the presentation of the risks/safety and solutions by various actors. We found that the primary issues in the news media were uncertainty regarding public health and harm to the environment. The primary solutions recommended within the news media were implementing additional water treatment technologies, taking unused pharmaceuticals to predetermined sites for disposal (take-back programs), and trash disposal of unused pharmaceuticals. Water utilities and scientists presented improved water treatment technology, government actors presented take-back programs, and pharmaceutical representatives, while sparsely involved in the news media, presented trash disposal as their primary solutions. To advance the understanding of the management of pharmaceutical pollution, this article offers further insight into the debate and potential solutions within the news media presentation of this complex scientific topic.

  13. An analytical solution for stationary distribution of photon density in traveling-wave and reflective SOAs

    International Nuclear Information System (INIS)

    Totović, A R; Crnjanski, J V; Krstić, M M; Gvozdić, D M

    2014-01-01

    In this paper, we analyze two semiconductor optical amplifier (SOA) structures, traveling-wave and reflective, with the active region made of the bulk material. The model is based on the stationary traveling-wave equations for forward and backward propagating photon densities of the signal and the amplified spontaneous emission, along with the stationary carrier rate equation. We start by introducing linear approximation of the carrier density spatial distribution, which enables us to find solutions for the photon densities in a closed analytical form. An analytical approach ensures a low computational resource occupation and an easy analysis of the parameters influencing the SOA’s response. The comparison of the analytical and numerical results shows high agreement for a wide range of the input optical powers and bias currents. (paper)

  14. Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

    International Nuclear Information System (INIS)

    Onate, C.A.; Onyeaju, M.C.; Ikot, A.N.

    2016-01-01

    The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

  15. Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

    Energy Technology Data Exchange (ETDEWEB)

    Onate, C.A., E-mail: oaclems14@physicist.net [Physics Department, University of Benin (Nigeria); Onyeaju, M.C.; Ikot, A.N. [Theoretical Physics Group, Physics Department, University of Port Harcourt (Nigeria)

    2016-12-15

    The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

  16. Kernel method for air quality modelling. II. Comparison with analytic solutions

    Energy Technology Data Exchange (ETDEWEB)

    Lorimer, G S; Ross, D G

    1986-01-01

    The performance of Lorimer's (1986) kernel method for solving the advection-diffusion equation is tested for instantaneous and continuous emissions into a variety of model atmospheres. Analytical solutions are available for comparison in each case. The results indicate that a modest minicomputer is quite adequate for obtaining satisfactory precision even for the most trying test performed here, which involves a diffusivity tensor and wind speed which are nonlinear functions of the height above ground. Simulations of the same cases by the particle-in-cell technique are found to provide substantially lower accuracy even when use is made of greater computer resources.

  17. Analytical solution for stress, strain and plastic instability of pressurized pipes with volumetric flaws

    International Nuclear Information System (INIS)

    Cunha, Sérgio B.; Netto, Theodoro A.

    2012-01-01

    The mechanical behavior of internally pressurized pipes with volumetric flaws is analyzed. The two possible modes of circumferentially straining the pipe wall are identified and associated to hypothesized geometries. The radial deformation that takes place by bending the pipe wall is studied by means of axisymmetric flaws and the membrane strain developed by unequal hoop deformation is analyzed with the help of narrow axial flaws. Linear elastic shell solutions for stress and strain are developed, the plastic behavior is studied and the maximum hoop stress at the flaw is related to the undamaged pipe hoop stress by means of stress concentration factors. The stress concentration factors are employed to obtain equations predicting the pressure at which the pipe fails by plastic instability for both types of flaw. These analytical solutions are validated by comparison with burst tests on 3″ diameter pipes and finite element simulations. Forty-one burst tests were carried out and two materials with very dissimilar plastic behavior, carbon steel and austenitic stainless steel, were used in the experiments. Both the analytical and the numerical predictions showed good correlation with the experimentally observed burst pressures. - Highlights: ► An analytical model for the burst of a pipe with a volumetric flaw is developed. ► Deformation, strain and stress are modeled in the elastic and plastic domains. ► The model is comprehensively validated by experiments and numerical simulations. ► The burst pressure model’s accuracy is equivalent to finite element simulations.

  18. Media Komunitas dan Media Literacy

    Directory of Open Access Journals (Sweden)

    Pawito .

    2013-12-01

    Full Text Available Abstract:This essay deals with community media in relation to media literacy. After a short discussion on a number of community media characters is made the essay goes further with somewhat detail theoretical presumptions of the roles of media community with respect primarily to the development as Amartya Sen mentioned about. The author suggests that community media may play some significant roles in the development including (a disseminating information (from varieties of perspective, (b facilitating public discussion, (c helping to reach solutions of problems, (d encouraging participations, and (e encouraging the development of media literacy. Regarding the last point the author remarks that media community may have a dual-roles i.e facilitating community’s member in media participation and facilitating community’s member in media education.

  19. Analytical benchmarks for nuclear engineering applications. Case studies in neutron transport theory

    International Nuclear Information System (INIS)

    2008-01-01

    The developers of computer codes involving neutron transport theory for nuclear engineering applications seldom apply analytical benchmarking strategies to ensure the quality of their programs. A major reason for this is the lack of analytical benchmarks and their documentation in the literature. The few such benchmarks that do exist are difficult to locate, as they are scattered throughout the neutron transport and radiative transfer literature. The motivation for this benchmark compendium, therefore, is to gather several analytical benchmarks appropriate for nuclear engineering applications under one cover. We consider the following three subject areas: neutron slowing down and thermalization without spatial dependence, one-dimensional neutron transport in infinite and finite media, and multidimensional neutron transport in a half-space and an infinite medium. Each benchmark is briefly described, followed by a detailed derivation of the analytical solution representation. Finally, a demonstration of the evaluation of the solution representation includes qualified numerical benchmark results. All accompanying computer codes are suitable for the PC computational environment and can serve as educational tools for courses in nuclear engineering. While this benchmark compilation does not contain all possible benchmarks, by any means, it does include some of the most prominent ones and should serve as a valuable reference. (author)

  20. Benchmarking the invariant embedding method against analytical solutions in model transport problems

    International Nuclear Information System (INIS)

    Malin, Wahlberg; Imre, Pazsit

    2005-01-01

    The purpose of this paper is to demonstrate the use of the invariant embedding method in a series of model transport problems, for which it is also possible to obtain an analytical solution. Due to the non-linear character of the embedding equations, their solution can only be obtained numerically. However, this can be done via a robust and effective iteration scheme. In return, the domain of applicability is far wider than the model problems investigated in this paper. The use of the invariant embedding method is demonstrated in three different areas. The first is the calculation of the energy spectrum of reflected (sputtered) particles from a multiplying medium, where the multiplication arises from recoil production. Both constant and energy dependent cross sections with a power law dependence were used in the calculations. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel and unexpected application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and a half-space are interrelated through embedding-like integral equations, by the solution of which the reflected flux from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases the invariant embedding method proved to be robust, fast and monotonically converging to the exact solutions. (authors)

  1. Semi-analytical solution for flow in a leaky unconfined aquifer toward a partially penetrating pumping well

    Science.gov (United States)

    Malama, Bwalya; Kuhlman, Kristopher L.; Barrash, Warren

    2008-07-01

    SummaryA semi-analytical solution is presented for the problem of flow in a system consisting of unconfined and confined aquifers, separated by an aquitard. The unconfined aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace-Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined aquifer flow as we do not adopt the assumption of unidirectional flow in the confined aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than aquifer conductivities, the simpler models that restrict flow to the radial direction in aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in aquifer-aquitard systems where radial flow is significant in aquitards.

  2. Three-Dimensional Hermite—Bessel—Gaussian Soliton Clusters in Strongly Nonlocal Media

    International Nuclear Information System (INIS)

    Jin Hai-Qin; Yi Lin; Liang Jian-Chu; Cai Ze-Bin; Liu Fei

    2012-01-01

    We analytically and numerically demonstrate the existence of Hermite—Bessel—Gaussian spatial soliton clusters in three-dimensional strongly nonlocal media. It is found that the soliton clusters display the vortex, dipole azimuthon and quadrupole azimuthon in geometry, and the total number of solitons in the necklaces depends on the quantum number n and m of the Hermite functions and generalized Bessel polynomials. The numerical simulation is basically identical to the analytical solution, and white noise does not lead to collapse of the soliton, which confirms the stability of the soliton waves. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity

  3. Analytical solution to the circularity problem in the discounted cash flow valuation framework

    Directory of Open Access Journals (Sweden)

    Felipe Mejía-Peláez

    2011-12-01

    Full Text Available In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E, cost of levered equity (Ke, levered firm value (V, and the weighted average cost of capital (WACC. We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular “Rolling WACC” ignoring the circularity issue, setting a target leverage (usually constant with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors.

  4. Shielding computations for solution transfer lines from Analytical Lab to process cells of Demonstration Fast Reactor Plant (DFRP)

    International Nuclear Information System (INIS)

    Baskar, S.; Jose, M.T.; Baskaran, R.; Venkatraman, B.

    2018-01-01

    The diluted virgin solutions (both aqueous and organic) and aqueous analytical waste generated from experimental analysis of process solutions, pertaining to Fast Breeder Test Reactor (FBTR) and Prototype Fast Breeder Reactor (PFBR), in glove boxes of active analytical Laboratory (AAL) are pumped back to the process cells through a pipe in pipe arrangement. There are 6 transfer lines (Length 15-32 m), 2 for each type of transfer. The transfer lines passes through the area inside the AAL and also the operating area. Hence it is required to compute the necessary radial shielding requirement around the lines to limit the dose rates in both the areas to the permissible values as per the regulatory requirement

  5. Media identities and media-influenced indentifications Visibility and identity recognition in the media

    Directory of Open Access Journals (Sweden)

    Víctor Fco. Sampedro Blanco

    2004-10-01

    Full Text Available The media establish, in large part, the patterns of visibility and public recognition of collective identities. We define media identities as those that are the object of production and diffusion by the media. From this discourse, the communities and individuals elaborate media-influenced identifications; that is, processes of recognition or banishment; (rearticulating the identity markers that the media offer with other cognitive and emotional sources. The generation and appropriation of the identities are subjected to a media hierarchisation that influences their normalisation or marginalisation. The identities presented by the media and assumed by the audience as part of the official, hegemonic discourse are normalised, whereas the identities and identifications formulated in popular and minority terms are marginalised. After presenting this conceptual and analytical framework, this study attempts to outline the logics that condition the presentation, on the one hand, andthe public recognition, on the other hand, of contemporary identities.

  6. Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

    International Nuclear Information System (INIS)

    Olson, Gordon L.

    2016-01-01

    One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. Authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. In every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order. - Highlights: • Gray and multigroup radiation transport is done through 2D stochastic media. • Approximate models for the mean radiation field are found for all test problems. • Effective opacities are adjusted to fit the means of stochastic media transport. • Test problems include temperature dependent opacities and heat capacities • Transport solutions are done with angle orders n=1 and 5.

  7. Analytical solution of advection–diffusion equation in heterogeneous ...

    Indian Academy of Sciences (India)

    media like rivers as well as in porous media like aquifers. ... boundary conditions, and aquifer dimensions and dimensions of the ... tially dependent dispersion along non-uniform flow through ..... domain is initially pollutant free, i.e., c(x,0) = 0.

  8. Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces

    International Nuclear Information System (INIS)

    Brauner, N.; Rovinsky, J.; Maron, D.M.

    1995-01-01

    The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the 'flow monograms' describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the 'interface monograms', whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system 'operational monogram'. The 'operational monogram' enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop

  9. Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Brauner, N.; Rovinsky, J.; Maron, D.M. [Tel-Aviv Univ. (Israel)

    1995-09-01

    The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the `flow monograms` describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the `interface monograms`, whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system `operational monogram`. The `operational monogram` enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop.

  10. Use of rich-media resources by engineering undergraduates

    Science.gov (United States)

    Gillie, Martin; Dahli, Ranim; Saunders, Fiona C.; Gibson, Andrew

    2017-11-01

    The ability to develop and distribute digital teaching resources in higher education has developed rapidly over the last decade but research into how students use such resources has received limited attention. This study uses questionnaire results, Internet analytic data and semi-structured interviews to examine the use of three types of rich-media teaching resources - lecture podcasts, key-concept videos and tutorial solution videos - by engineering undergraduates. It is found that students value all three types of resource, especially for revision and as a supplement to lectures. Students find short, focused resources more useful than longer ones. Non-native English speakers and those with disabilities derive particular benefits from the resources. The effect of rich-media resources on lecture attendance is found to be small, and two-way.

  11. Limitless Analytic Elements

    Science.gov (United States)

    Strack, O. D. L.

    2018-02-01

    We present equations for new limitless analytic line elements. These elements possess a virtually unlimited number of degrees of freedom. We apply these new limitless analytic elements to head-specified boundaries and to problems with inhomogeneities in hydraulic conductivity. Applications of these new analytic elements to practical problems involving head-specified boundaries require the solution of a very large number of equations. To make the new elements useful in practice, an efficient iterative scheme is required. We present an improved version of the scheme presented by Bandilla et al. (2007), based on the application of Cauchy integrals. The limitless analytic elements are useful when modeling strings of elements, rivers for example, where local conditions are difficult to model, e.g., when a well is close to a river. The solution of such problems is facilitated by increasing the order of the elements to obtain a good solution. This makes it unnecessary to resort to dividing the element in question into many smaller elements to obtain a satisfactory solution.

  12. New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

    Science.gov (United States)

    S Saha, Ray

    2016-04-01

    In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

  13. Analytical chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Chae, Myeong Hu; Lee, Hu Jun; Kim, Ha Seok

    1989-02-15

    This book give explanations on analytical chemistry with ten chapters, which deal with development of analytical chemistry, the theory of error with definition and classification, sample and treatment gravimetry on general process of gravimetry in aqueous solution and non-aqueous solution, precipitation titration about precipitation reaction and types, complexometry with summary and complex compound, oxidation-reduction equilibrium on electrode potential and potentiometric titration, solvent extraction and chromatograph and experiment with basic operation for chemical experiment.

  14. Analytical chemistry

    International Nuclear Information System (INIS)

    Chae, Myeong Hu; Lee, Hu Jun; Kim, Ha Seok

    1989-02-01

    This book give explanations on analytical chemistry with ten chapters, which deal with development of analytical chemistry, the theory of error with definition and classification, sample and treatment gravimetry on general process of gravimetry in aqueous solution and non-aqueous solution, precipitation titration about precipitation reaction and types, complexometry with summary and complex compound, oxidation-reduction equilibrium on electrode potential and potentiometric titration, solvent extraction and chromatograph and experiment with basic operation for chemical experiment.

  15. Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

    Science.gov (United States)

    Shan, Zhendong; Ling, Daosheng

    2018-02-01

    This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

  16. Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

    International Nuclear Information System (INIS)

    Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

    2009-01-01

    A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

  17. Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary

    Science.gov (United States)

    Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing

    2016-04-01

    An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.

  18. A Complete First-Order Analytical Solution for Optimal Low-Thrust Limited-Power Transfers Between Coplanar Orbits with Small Eccentricities

    Science.gov (United States)

    Da Silva Fernandes, Sandro; Das Chagas Carvalho, Francisco; Vilhena de Moraes, Rodolpho

    The purpose of this work is to present a complete first order analytical solution, which includes short periodic terms, for the problem of optimal low-thrust limited power trajectories with large amplitude transfers (no rendezvous) between coplanar orbits with small eccentricities in Newtonian central gravity field. The study of these transfers is particularly interesting because the orbits found in practice often have a small eccentricity and the problem of transferring a vehicle from a low earth orbit to a high earth orbit is frequently found. Besides, the analysis has been motivated by the renewed interest in the use of low-thrust propulsion systems in space missions verified in the last two decades. Several researchers have obtained numerical and sometimes analytical solutions for a number of specific initial orbits and specific thrust profiles. Averaging methods are also used in such researches. Firstly, the optimization problem associated to the space transfer problem is formulated as a Mayer problem of optimal control with Cartesian elements - position and velocity vectors - as state variables. After applying the Pontryagin Maximum Principle, successive Mathieu transformations are performed and suitable sets of orbital elements are introduced. The short periodic terms are eliminated from the maximum Hamiltonian function through an infinitesimal canonical transformation built through Hori method - a perturbation canonical method based on Lie series. The new Hamiltonian function, which results from the infinitesimal canonical transformation, describes the extremal trajectories for long duration maneuvers. Closed-form analytical solutions are obtained for the new canonical system by solving the Hamilton-Jacobi equation through the separation of variables technique. By applying the transformation equations of the algorithm of Hori method, a first order analytical solution for the problem is obtained in non-singular orbital elements. For long duration maneuvers

  19. Method of model reduction and multifidelity models for solute transport in random layered porous media

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Zhijie; Tartakovsky, Alexandre M.

    2017-09-01

    This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.

  20. Multi-pathway model of nuclide transport in fractured media and its application

    International Nuclear Information System (INIS)

    Li Xun; Yang Zeping; Li Jinxuan

    2010-01-01

    In order to know the law of nuclide transport in fracture system, the basic differential equations of nuclide transport in fracture and matrix were obtained based on the dual media theory, and the general analytic solutions of nuclide transport in single fractured media with exponential attenuation source in fracture were deduced by Laplace transform, and one-dimensional multi-pathway model of nuclide transport was proposed based on dual media theory and stochastic distribution of fracture parameters. The transport of Th-229, Cs-135 and Se-79 were simulated with this model, the relative concentration of these nuclides in fracture system were predicted. Further more, it was deduced that aperture and velocity can distinctly influence transport of nuclide by comparing with the results which were simulated by single fracture model. (authors)

  1. Analytical solution for stress, strain and plastic instability of pressurized pipes with volumetric flaws

    Energy Technology Data Exchange (ETDEWEB)

    Cunha, Sergio B., E-mail: sbcunha@petrobras.com.br [PETROBRAS/TRANSPETRO, Av. Pres. Vargas 328 - 7th floor, Rio de Janeiro, RJ 20091-060 (Brazil); Netto, Theodoro A., E-mail: tanetto@lts.coppe.ufrj.br [COPPE, Federal University ot Rio de Janeiro, Ocean Engineering Department, PO BOX 68508, Rio de Janeiro - RJ (Brazil)

    2012-01-15

    The mechanical behavior of internally pressurized pipes with volumetric flaws is analyzed. The two possible modes of circumferentially straining the pipe wall are identified and associated to hypothesized geometries. The radial deformation that takes place by bending the pipe wall is studied by means of axisymmetric flaws and the membrane strain developed by unequal hoop deformation is analyzed with the help of narrow axial flaws. Linear elastic shell solutions for stress and strain are developed, the plastic behavior is studied and the maximum hoop stress at the flaw is related to the undamaged pipe hoop stress by means of stress concentration factors. The stress concentration factors are employed to obtain equations predicting the pressure at which the pipe fails by plastic instability for both types of flaw. These analytical solutions are validated by comparison with burst tests on 3 Double-Prime diameter pipes and finite element simulations. Forty-one burst tests were carried out and two materials with very dissimilar plastic behavior, carbon steel and austenitic stainless steel, were used in the experiments. Both the analytical and the numerical predictions showed good correlation with the experimentally observed burst pressures. - Highlights: Black-Right-Pointing-Pointer An analytical model for the burst of a pipe with a volumetric flaw is developed. Black-Right-Pointing-Pointer Deformation, strain and stress are modeled in the elastic and plastic domains. Black-Right-Pointing-Pointer The model is comprehensively validated by experiments and numerical simulations. Black-Right-Pointing-Pointer The burst pressure model's accuracy is equivalent to finite element simulations.

  2. Analytical solutions for the temperature field in a 2D incompressible inviscid flow through a channel with walls of solid fuel

    Directory of Open Access Journals (Sweden)

    Sorin BERBENTE

    2011-12-01

    Full Text Available A gas (oxidizer flows between two parallel walls of solid fuel. A combustion is initiated: the solid fuel is vaporized and a diffusive flame occurs. The hot combustion products are submitted both to thermal diffusion and convection. Analytical solutions can be obtained both for the velocity and temperature distributions by considering an equivalent mean temperature where the density and the thermal conductivity are evaluated. The main effects of heat transfer are due to heat convection at the flame. Because the detailed mechanism of the diffusion flame is not introduced the reference chemical reaction is the combustion of premixed fuel with oxidizer in excess. In exchange the analytical solution is used to define an ideal quasi-uniform combustion that could be realized by an n adequate control. The given analytical closed solutions prove themselves flexible enough to adjust the main data of some existing experiments and to suggest new approaches to the problem.

  3. An analytical longitudinal dielectric function of primitive electrolyte solutions and its application in predicting thermodynamic properties

    International Nuclear Information System (INIS)

    Xiao, Tiejun

    2015-01-01

    In this paper, the longitudinal dielectric function ϵ_l(k) of primitive electrolyte solutions is discussed. Starting from a modified mean spherical approximation, an analytical dielectric function in terms of two parameters is established. These two parameters can be related to the first two decay parameters k_1_,_2 of the dielectric response modes of the bulk system, and can be determined using constraints of k_1_,_2 from statistical theories. Furthermore, a combination of this dielectric function and the molecular Debye-Hückel theory[J. Chem. Phys. 135(2011)104104] leads to a self-consistent mean filed description of electrolyte solutions. Our theory reveals a relationship between the microscopic structure parameters of electrolyte solutions and the macroscopic thermodynamic properties, which is applied to concentrated electrolyte solutions.

  4. An algorithm for solving the optical problem for stratified anisotropic media

    Energy Technology Data Exchange (ETDEWEB)

    Palto, S P [Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii pr. 59, Moscow, 117333 (Russian Federation)

    2001-04-01

    An algorithm for solving the Maxwell equations for propagation of light through anisotropic stratified media is considered. The algorithm uses the Berreman matrices of order 4 x 4. In contrast to the numerical methods suggested by Berreman, the new method is exact. The Sylvester theorem for calculating functions of a matrix and the Laguerre method for determining eigenvalues provide the basis for an algorithm with an efficiency comparable to that of the algorithms based on analytic solutions, which exist only in the case of uniaxial media. The method suggested in this paper allows for the analysis of complex optical systems where the effects of biaxiality, magnetic anisotropy, and optical activity play an important role.

  5. Mechanism of nucleation and growth of hydrogen porosity in solidifying A356 aluminum alloy: an analytical solution

    International Nuclear Information System (INIS)

    Li, K.-D.; Chang, Edward

    2004-01-01

    This study derives an analytical solution for the mechanism of nucleation and growth of hydrogen pore in the solidifying A356 aluminum alloy. A model of initial transient hydrogen redistribution in the growing dendritic grain is used to modify the lever rule for the mechanism of nucleation of pore. The model predicts the fraction of solid at nucleation, the temperature range of nucleation, the radius of hydrogen diffusion cell, and the supersaturation of hydrogen needed for nucleation. The role of solidus velocity in nucleation is explained. The parameters calculated from the model of nucleation are used for analyzing the mechanism of kinetic diffusion-controlled growth of pore, in which the mathematical transformations of variables are introduced. With the transformations, it is argued that the diffusion problem involving the liquid and solid phases during solidification could be treated as a classic problem of precipitation in the single-phase medium treated by Ham or Avrami. The analytical solution for the nucleation of pore is compared with the mechanism of macrosegregation. The predicted volume percent of porosity and radius of pore based on the mechanism of growth of pore is discussed with respect to the thermodynamic solution, the published experimental data, the numerical solutions, and the role of interdendritic fluid flow governed by Darcy's law

  6. Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

    KAUST Repository

    Davit, Y.; Wood, B. D.; Debenest, G.; Quintard, M.

    2012-01-01

    In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time

  7. Analytical Solution of Displacements Around Circular Openings in Generalized Hoek-Brown Rocks

    Directory of Open Access Journals (Sweden)

    Huang Houxu

    2017-09-01

    Full Text Available The rock in plastic region is divided into numbers of elements by the slip lines, resulted from shear localization. During the deformation process, the elements will slip along the slip lines and the displacement field is discontinuous. Slip lines around circular opening in isotropic rock, subjected to hydrostatic stress are described by the logarithmic spirals. Deformation of the plastic region is mainly attributed to the slippage. Relationship between the shear stresses and slippage on slip lines is presented, based on the study of Revuzhenko and Shemyakin. Relations between slippage and rock failure are described, based on the elastic-brittle-plastic model. An analytical solution is presented for the plane strain analysis of displacements around circular openings in the Generalized Hoek-Brown rock. With properly choosing of slippage parameters, results obtained by using the proposed solution agree well with those presented in published sources.

  8. The Effects of Frequency of Media Utilization on Decision Making of Media Choice

    Science.gov (United States)

    Gotoh, Yasushi

    2014-01-01

    The purpose of this study is to use the Analytic Hierarchy Process in order to identify how frequency of media use in daily life affects decision-making in media choice. 276 university students took part in this research, They were asked to prioritize their ways of obtaining information about current affairs using sets of media such as TV, books,…

  9. Analytical solution for the electrical properties of a radio-frequency quadrupole (RFQ) with simple vanes

    International Nuclear Information System (INIS)

    Lancaster, H.

    1982-01-01

    Although the SUPERFISH program is used for calculating the design parameters of an RFQ structure with complex vanes, an analytical solution for electrical properties of an RFQ with simple vanes provides insight into the parametric behavior of these more complicated resonators. The fields in an inclined plane wave guide with proper boundary conditions match those in one quadrant of an RFQ. The principle of duality is used to exploit the solutions to a radial transmission line in solving the field equations. Calculated are the frequency equation, frequency sensitivity factors, electric field, magnetic field, stored energy (U), power dissipation, and quality factor

  10. Modeling of water and solute transport under variably saturated conditions: state of the art

    International Nuclear Information System (INIS)

    Lappala, E.G.

    1980-01-01

    This paper reviews the equations used in deterministic models of mass and energy transport in variably saturated porous media. Analytic, quasi-analytic, and numerical solution methods to the nonlinear forms of transport equations are discussed with respect to their advantages and limitations. The factors that influence the selection of a modeling method are discussed in this paper; they include the following: (1) the degree of coupling required among the equations describing the transport of liquids, gases, solutes, and energy; (2) the inclusion of an advection term in the equations; (3) the existence of sharp fronts; (4) the degree of nonlinearity and hysteresis in the transport coefficients and boundary conditions; (5) the existence of complex boundaries; and (6) the availability and reliability of data required by the models

  11. Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions

    International Nuclear Information System (INIS)

    Tran, H. N.; Demaziere, C.

    2012-01-01

    This paper presents the development of a neutronic and kinetic solver for hexagonal geometries. The tool is developed based on the diffusion theory with multi-energy groups and multi-groups of delayed neutron precursors allowing the solutions of forward and adjoint problems of static and dynamic states, and is applicable to both thermal and fast systems with hexagonal geometries. In the dynamic problems, the small stationary fluctuations of macroscopic cross sections are considered as noise sources, and then the induced first order noise is calculated fully in the frequency domain. Numerical algorithms for solving the static and noise equations are implemented with a spatial discretization based on finite differences and a power iterative solution. A coarse mesh finite difference method has been adopted for speeding up the convergence. Since no other numerical tool could calculate frequency-dependent noise in hexagonal geometry, validation calculations have been performed and benchmarked to analytical solutions based on a 2-D homogeneous system with two-energy groups and one-group of delayed neutron precursor, in which point-like perturbations of thermal absorption cross section at central and non-central positions are considered as noise sources. (authors)

  12. Violent media and hostile appraisals: A meta-analytic review.

    Science.gov (United States)

    Bushman, Brad J

    2016-11-01

    Hostile people tend to view the world as a hostile place. Although there are individual differences in hostile world-views, situational factors can also play a role. For example, scenes of violence in the mass media might influence people to view the world as a hostile place. This meta-analysis aggregates, for the first time, all studies that have investigated the link between exposure to violent media and hostile appraisals (e.g., perceiving the ambiguous actions by others as aggressive actions). This meta-analysis included 37 independent studies involving 10,410 participants. The results showed a "small" to "moderate" sized average correlation between exposure to violent media and hostile appraisals (r +  = .20, 95%CI = .14, .26). Significant correlations were found in experimental, cross-sectional, and longitudinal studies, indicating a triangulation of evidence. Effects were not correlated with participant gender. Effects were also stable over time. However, the link between exposure to violent media and hostile appraisals was positively related to age, perhaps because violent media can have cumulative effects over time. There was no evidence of publication bias. The findings from this meta-analysis are consistent with the General Aggression Model (e.g., Anderson, & Bushman, 2002; Annual Review of Psychology 53:27-51). These results compliment those from previous meta-analyses showing that violent media can increase aggressive thoughts, angry feelings, physiological arousal, and aggressive behavior. These findings also have practical significance, because people who view the world in a hostile manner are more likely to behave aggressively themselves. Aggr. Behav. 42:605-613, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

  13. The effect of loading solution and dissolution media on release of Diclofenac from ion exchange resins

    Directory of Open Access Journals (Sweden)

    "Atyabi F

    2002-07-01

    Full Text Available Drugs can be loaded on ion exchange resins in order to control their release. Loading of diclofenac sodium on the resin beads not only sustain its release but also reduce its gastrointestinal mucosal injury. In this study the effect of loading solution and concentration of diclofenac in loading solution on total amount of drug loaded on the resin beads (Amberlite IRA-900 and the release characteristic of drug in different media were examined. Results showed that diclofenac resin complex did not release their drug content in simulated gastric fluid but released it in simulated intestinal fluid independent of exposure time in acidic conditions. The effect of a number of parameters such as ionic strength and pH on the release characteristic of drug - resin complexes were also examined. Results showed that although ionic strength is an important factor, drug release is more affected by the pH of the media. NO ABSTRACT

  14. Class of analytic solutions for the thermally balanced magnetostatic prominence sheet

    International Nuclear Information System (INIS)

    Low, B.C.; Wu, S.T.

    1981-01-01

    This is a theoretical study of the nonlinear interplay between magnetostatic equilibrium and energy balance in a Kippenhahn-Schlueter type prominence sheet. The basic effects are illustrated explicitly with an analytic model in which a radiative loss proportional to rho 2 T balances against wave heating proportional to rho, with thermal conduction confined along magnetic field lines, where rho and T denote the plasma density and temperature, respectively. The particular choices of heat sink and source enable us to integrate the governing equations exactly while they are of the basic mathematical forms to simulate radiative loss in an optically thin plasma which is heated by wave dissipation. The steady solutions exhibit three different basic behaviors, characterized by the total wave heating in the prominence sheet being more than, equal to, or less than the total radiative loss. It is the compaction of the plasma along the field lines under its own weight combined with the effects of energy transport that determines which of the three basic behaviors obtains in a particular situation. The implications of the steady solutions for the formation of prominences are discussed. The exact solutions presented do not support the conclusion of Milne, Priest, and Roberts that there is an upper bound on the plasma beta for an equilibrium of the Kippenhahn-Schlueter prominence

  15. Analytical-scale separations of lanthanides : a review of techniques and fundamentals

    International Nuclear Information System (INIS)

    Nash, K. L.; Jensen, M. P.

    1999-01-01

    Separations chemistry is at the heart of most analytical procedures to determine the rare earth content of both man-made and naturally occurring materials. Such procedures are widely used in mineral exploration, fundamental geology and geochemistry, material science, and in the nuclear industry. Chromatographic methods that rely on aqueous solutions containing complexing agents sensitive to the lanthanide cationic radius and cation-exchange phase transfer reactions (using a variety of different solid media) have enjoyed the greatest success for these procedures. In this report, they will briefly summarize the most important methods for completing such analyses. they consider in some detail the basic aqueous (and two-phase) solution chemistry that accounts for separations that work well and offer explanations for why others are less successful

  16. Algorithms and analytical solutions for rapidly approximating long-term dispersion from line and area sources

    Science.gov (United States)

    Barrett, Steven R. H.; Britter, Rex E.

    Predicting long-term mean pollutant concentrations in the vicinity of airports, roads and other industrial sources are frequently of concern in regulatory and public health contexts. Many emissions are represented geometrically as ground-level line or area sources. Well developed modelling tools such as AERMOD and ADMS are able to model dispersion from finite (i.e. non-point) sources with considerable accuracy, drawing upon an up-to-date understanding of boundary layer behaviour. Due to mathematical difficulties associated with line and area sources, computationally expensive numerical integration schemes have been developed. For example, some models decompose area sources into a large number of line sources orthogonal to the mean wind direction, for which an analytical (Gaussian) solution exists. Models also employ a time-series approach, which involves computing mean pollutant concentrations for every hour over one or more years of meteorological data. This can give rise to computer runtimes of several days for assessment of a site. While this may be acceptable for assessment of a single industrial complex, airport, etc., this level of computational cost precludes national or international policy assessments at the level of detail available with dispersion modelling. In this paper, we extend previous work [S.R.H. Barrett, R.E. Britter, 2008. Development of algorithms and approximations for rapid operational air quality modelling. Atmospheric Environment 42 (2008) 8105-8111] to line and area sources. We introduce approximations which allow for the development of new analytical solutions for long-term mean dispersion from line and area sources, based on hypergeometric functions. We describe how these solutions can be parameterized from a single point source run from an existing advanced dispersion model, thereby accounting for all processes modelled in the more costly algorithms. The parameterization method combined with the analytical solutions for long-term mean

  17. Glycan characterization of the NIST RM monoclonal antibody using a total analytical solution: From sample preparation to data analysis.

    Science.gov (United States)

    Hilliard, Mark; Alley, William R; McManus, Ciara A; Yu, Ying Qing; Hallinan, Sinead; Gebler, John; Rudd, Pauline M

    Glycosylation is an important attribute of biopharmaceutical products to monitor from development through production. However, glycosylation analysis has traditionally been a time-consuming process with long sample preparation protocols and manual interpretation of the data. To address the challenges associated with glycan analysis, we developed a streamlined analytical solution that covers the entire process from sample preparation to data analysis. In this communication, we describe the complete analytical solution that begins with a simplified and fast N-linked glycan sample preparation protocol that can be completed in less than 1 hr. The sample preparation includes labelling with RapiFluor-MS tag to improve both fluorescence (FLR) and mass spectral (MS) sensitivities. Following HILIC-UPLC/FLR/MS analyses, the data are processed and a library search based on glucose units has been included to expedite the task of structural assignment. We then applied this total analytical solution to characterize the glycosylation of the NIST Reference Material mAb 8761. For this glycoprotein, we confidently identified 35 N-linked glycans and all three major classes, high mannose, complex, and hybrid, were present. The majority of the glycans were neutral and fucosylated; glycans featuring N-glycolylneuraminic acid and those with two galactoses connected via an α1,3-linkage were also identified.

  18. Creation of the CMB spectrum: precise analytic solutions for the blackbody photosphere

    Energy Technology Data Exchange (ETDEWEB)

    Khatri, Rishi; Sunyaev, Rashid A., E-mail: khatri@mpa-garching.mpg.de, E-mail: sunyaev@mpa-Garching.mpg.de [Max Planck Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)

    2012-06-01

    The blackbody spectrum of CMB was created in the blackbody photosphere at redshifts z∼>2 × 10{sup 6}. At these early times, the Universe was dense and hot enough that complete thermal equilibrium between baryonic matter (electrons and ions) and photons could be established on time scales much shorter than the age of the Universe. Any perturbation away from the blackbody spectrum was suppressed exponentially. New physics, for example annihilation and decay of dark matter, can add energy and photons to CMB at redshifts z∼>10{sup 5} and result in a Bose-Einstein spectrum with a non-zero chemical potential (μ). Precise evolution of the CMB spectrum around the critical redshift of z ≅ 2 × 10{sup 6} is required in order to calculate the μ-type spectral distortion and constrain the underlying new physics. Although numerical calculation of important processes involved (double Compton process, comptonization and bremsstrahlung) is not difficult with present day computers, analytic solutions are much faster and easier to calculate and provide valuable physical insights. We provide precise (better than 1%) analytic solutions for the decay of μ, created at an earlier epoch, including all three processes, double Compton, Compton scattering on thermal electrons and bremsstrahlung in the limit of small distortions. This is a significant improvement over the existing solutions with accuracy ∼ 10% or worse. We also give a census of important sources of energy injection into CMB in standard cosmology. In particular, calculations of distortions from electron-positron annihilation and primordial nucleosynthesis illustrate in a dramatic way the strength of the equilibrium restoring processes in the early Universe. Finally, we point out the triple degeneracy in standard cosmology, i.e., the μ and y distortions from adiabatic cooling of baryons and electrons, Silk damping and annihilation of thermally produced WIMP dark matter are of similar order of magnitude ( ∼ 10{sup

  19. Analytical solution describing pesticide volatilization from soil affected by a change in surface condition.

    Science.gov (United States)

    Yates, S R

    2009-01-01

    An analytical solution describing the fate and transport of pesticides applied to soils has been developed. Two pesticide application methods can be simulated: point-source applications, such as idealized shank or a hot-gas injection method, and a more realistic shank-source application method that includes a vertical pesticide distribution in the soil domain due to a soil fracture caused by a shank. The solutions allow determination of the volatilization rate and other information that could be important for understanding fumigant movement and in the development of regulatory permitting conditions. The solutions can be used to characterize differences in emissions relative to changes in the soil degradation rate, surface barrier conditions, application depth, and soil packing. In some cases, simple algebraic expressions are provided that can be used to obtain the total emissions and total soil degradation. The solutions provide a consistent methodology for determining the total emissions and can be used with other information, such as field and laboratory experimental data, to support the development of fumigant regulations. The uses of the models are illustrated by several examples.

  20. New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods

    International Nuclear Information System (INIS)

    Saha Ray, S

    2016-01-01

    In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov (KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation. (paper)

  1. Autowaves in moving excitable media

    Directory of Open Access Journals (Sweden)

    V.A.Davydov

    2004-01-01

    Full Text Available Within the framework of kinematic theory of autowaves we suggest a method for analytic description of stationary autowave structures appearing at the boundary between the moving and fixed excitable media. The front breakdown phenomenon is predicted for such structures. Autowave refraction and, particulary, one-side "total reflection" at the boundary is considered. The obtained analytical results are confirmed by computer simulations. Prospects of the proposed method for further studies of autowave dynamics in the moving excitable media are discussed.

  2. Upscaling solute transport in naturally fractured porous media with the continuous time random walk method

    Energy Technology Data Exchange (ETDEWEB)

    Geiger, S.; Cortis, A.; Birkholzer, J.T.

    2010-04-01

    Solute transport in fractured porous media is typically 'non-Fickian'; that is, it is characterized by early breakthrough and long tailing and by nonlinear growth of the Green function-centered second moment. This behavior is due to the effects of (1) multirate diffusion occurring between the highly permeable fracture network and the low-permeability rock matrix, (2) a wide range of advection rates in the fractures and, possibly, the matrix as well, and (3) a range of path lengths. As a consequence, prediction of solute transport processes at the macroscale represents a formidable challenge. Classical dual-porosity (or mobile-immobile) approaches in conjunction with an advection-dispersion equation and macroscopic dispersivity commonly fail to predict breakthrough of fractured porous media accurately. It was recently demonstrated that the continuous time random walk (CTRW) method can be used as a generalized upscaling approach. Here we extend this work and use results from high-resolution finite element-finite volume-based simulations of solute transport in an outcrop analogue of a naturally fractured reservoir to calibrate the CTRW method by extracting a distribution of retention times. This procedure allows us to predict breakthrough at other model locations accurately and to gain significant insight into the nature of the fracture-matrix interaction in naturally fractured porous reservoirs with geologically realistic fracture geometries.

  3. Gas-solute dispersivity ratio in granular porous media as related to particle size distribution and particle shape

    DEFF Research Database (Denmark)

    Pugliese, Lorenzo; Poulsen, Tjalfe; Straface, Salvatore

    2013-01-01

    Measurements of solute dispersion in porous media is generally much more time consuming than gas dispersion measurements performed under equivalent conditions. Significant time savings may therefore, be achieved if solute dispersion coefficients can be estimated based on measured gas dispersion...... data. This paper evaluates the possibility for estimating solute dispersion based on gas dispersion measurements. Breakthrough measurements were carried out at different fluid velocities (covering the same range in Reynolds number), using O2 and NaCl as gas and solute tracers, respectively. Three...... different, granular porous materials were used: (1) crushed granite (very angular particles), (2) gravel (particles of intermediate roundness) and (3) Leca® (almost spherical particles). For each material, 21 different particle size fractions were used. Gas and solute dispersion coefficients were determined...

  4. Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems: I. Analytical solutions under dipole-dipole correlations

    OpenAIRE

    Jiang, Shidong; Xu, Minzhong

    2005-01-01

    The analytical solutions for the general-four-wave-mixing hyperpolarizabilities $\\chi^{(3)}(-(w_1+w_2+w_3);w_1,w_2,w_3)$ on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of DC Kerr effect $\\chi^{(3)}(-w;0,0,w)$, DC-induced second harmonic generation $\\chi^{(3)}(-2w;0,w,w)$, optical Kerr effect $\\chi^{(3)}(-w;w,-w,w)$ and DC-electric-field-induced optica...

  5. Numerical simulation of inertial two-phase flow in heterogenous media

    International Nuclear Information System (INIS)

    Ali Akbar ABBASIAN ARANI; Didier LASSEUX; Azita AHMADI

    2005-01-01

    In this work, we present the development of a 3 D numerical tool for simulation of non-Darcy two-phase flow in heterogeneous porous media. The physical model selected is the generalized Darcy-Forchheimer model. A validation is performed first by comparing numerical results with a semi-analytical solution of the Buckley-Leverett type. Secondly, numerical results obtained on 1 D and 2 D heterogeneous configurations are presented and we highlight the importance of the inertial terms according to a Reynolds number of the flow. (authors)

  6. Electronic states of graphene nanoribbons and analytical solutions

    Directory of Open Access Journals (Sweden)

    Katsunori Wakabayashi, Ken-ichi Sasaki, Takeshi Nakanishi and Toshiaki Enoki

    2010-01-01

    Full Text Available Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.

  7. A new analytical approach for limit cycles and quasi-periodic solutions of nonlinear oscillators: the example of the forced Van der Pol Duffing oscillator

    International Nuclear Information System (INIS)

    Shukla, Anant Kant; Ramamohan, T R; Srinivas, S

    2014-01-01

    In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. (papers)

  8. SIMULTANEOUS ABSORPTION AND DESORPTION WITH REVERSIBLE 1ST-ORDER CHEMICAL-REACTION - ANALYTICAL SOLUTION AND NEGATIVE ENHANCEMENT FACTORS

    NARCIS (Netherlands)

    WINKELMAN, JGM; BEENACKERS, AACM

    The problem of ps absorption accompanied by a first-order reversible reaction, producing a volatile reaction product, is considered. A general analytical solution is developed for the film model, resulting in explicit relations for the concentration profiles in the film and for the mass transfer

  9. Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

    Science.gov (United States)

    Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

    2011-10-01

    This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

  10. A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

    KAUST Repository

    Gao, Kai

    2015-06-05

    The development of reliable methods for upscaling fine-scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. Therefore, we have proposed a numerical homogenization algorithm based on multiscale finite-element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that was similar to the rotated staggered-grid finite-difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity in which the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

  11. An open-source toolbox for multiphase flow in porous media

    Science.gov (United States)

    Horgue, P.; Soulaine, C.; Franc, J.; Guibert, R.; Debenest, G.

    2015-02-01

    Multiphase flow in porous media provides a wide range of applications: from the environmental understanding (aquifer, site-pollution) to industrial process improvements (oil production, waste management). Modeling of such flows involves specific volume-averaged equations and therefore specific computational fluid dynamics (CFD) tools. In this work, we develop a toolbox for modeling multiphase flow in porous media with OpenFOAM®, an open-source platform for CFD. The underlying idea of this approach is to provide an easily adaptable tool that can be used in further studies to test new mathematical models or numerical methods. The package provides the most common effective properties models of the literature (relative permeability, capillary pressure) and specific boundary conditions related to porous media flows. To validate this package, solvers based on the IMplicit Pressure Explicit Saturation (IMPES) method are developed in the toolbox. The numerical validation is performed by comparison with analytical solutions on academic cases. Then, a satisfactory parallel efficiency of the solver is shown on a more complex configuration.

  12. Analytical solution for the transport equation for neutral particles in cylindrical and Cartesian geometry

    International Nuclear Information System (INIS)

    Goncalves, Glenio Aguiar

    2003-01-01

    In this work, we are reported analytical solutions for the transport equation for neutral particles in cylindrical and cartesian geometry. For the cylindrical geometry, it is applied the Hankel transform of order zero in the S N approximation of the one-dimensional cylindrical transport equation, assuming azimuthal symmetry and isotropic scattering. This procedure is coined HTSN method. The anisotropic problem is handled using the decomposition method, generating a recursive approach, which the HTSN solution is used as initial condition. For cartesian geometry, the one and two dimensional transport equation is derived in the angular variable as many time as the degree of the anisotropic scattering. This procedure leads to set of integro-differential plus one differential equation that can be really solved by the variable separation method. Following this procedure, it was possible to come out with the Case solution for the one-dimensional problem. Numerical simulations are reported for the cylindrical transport problem both isotropic and anisotropic case of quadratic degree. (author)

  13. The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution

    Science.gov (United States)

    Fatyanov, A. G.; Burmin, V. Yu

    2018-04-01

    The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.

  14. Laboratory Experiments and Modeling of Pooled NAPL Dissolution in Porous Media

    Science.gov (United States)

    Copty, N. K.; Sarikurt, D. A.; Gokdemir, C.

    2017-12-01

    The dissolution of non-aqueous phase liquids (NAPLs) entrapped in porous media is commonly modeled at the continuum scale as the product of a chemical potential and an interphase mass transfer coefficient, the latter expressed in terms of Sherwood correlations that are related to flow and porous media properties. Because of the lack of precise estimates of the interface area separating the NAPL and aqueous phase, numerous studies have lumped the interfacial area into the interphase mass transfer coefficient. In this paper controlled dissolution experiments from a pooled NAPL were conducted. The immobile NAPL mass is placed at the bottom of a flow cell filled with porous media with water flowing on top. Effluent aqueous phase concentrations were measured for a wide range of aqueous phase velocities and for two types of porous media. To interpret the experimental results, a two-dimensional pore network model of the NAPL dissolution was developed. The well-defined geometry of the NAPL-water interface and the observed effluent concentrations were used to compute best-fit mass transfer coefficients and non-lumped Sherwood correlations. Comparing the concentrations predicted with the pore network model to simple previously used one-dimensional analytic solutions indicates that the analytic model which ignores the transverse dispersion can lead to over-estimation of the mass transfer coefficient. The predicted Sherwood correlations are also compared to previously published data and implications on NAPL remediation strategies are discussed.

  15. Social Data Analytics Using Tensors and Sparse Techniques

    Science.gov (United States)

    Zhang, Miao

    2014-01-01

    The development of internet and mobile technologies is driving an earthshaking social media revolution. They bring the internet world a huge amount of social media content, such as images, videos, comments, etc. Those massive media content and complicate social structures require the analytic expertise to transform those flood of information into…

  16. Analytical Solution and Physics of a Propellant Damping Device

    Science.gov (United States)

    Yang, H. Q.; Peugeot, John

    2011-01-01

    NASA design teams have been investigating options for "detuning" Ares I to prevent oscillations originating in the vehicle solid-rocket main stage from synching up with the natural resonance of the rest of the vehicle. An experimental work started at NASA MSFC center in 2008 using a damping device showed great promise in damping the vibration level of an 8 resonant tank. However, the mechanisms of the vibration damping were not well understood and there were many unknowns such as the physics, scalability, technology readiness level (TRL), and applicability for the Ares I vehicle. The objectives of this study are to understand the physics of intriguing slosh damping observed in the experiments, to further validate a Computational Fluid Dynamics (CFD) software in propellant sloshing against experiments with water, and to study the applicability and efficiency of the slosh damper to a full scale propellant tank and to cryogenic fluids. First a 2D fluid-structure interaction model is built to model the system resonance of liquid sloshing and structure vibration. A damper is then added into the above model to simulate experimentally observed system damping phenomena. Qualitative agreement is found. An analytical solution is then derived from the Newtonian dynamics for the thrust oscillation damper frequency, and a slave mass concept is introduced in deriving the damper and tank interaction dynamics. The paper will elucidate the fundamental physics behind the LOX damper success from the derivation of the above analytical equation of the lumped Newtonian dynamics. Discussion of simulation results using high fidelity multi-phase, multi-physics, fully coupled CFD structure interaction model will show why the LOX damper is unique and superior compared to other proposed mitigation techniques.

  17. On the analytical solution of the SN equation in a rectangle assuming an exponential exiting angular flux boundary

    International Nuclear Information System (INIS)

    Goncalez, Tifani T.; Segatto, Cynthia F.; Vilhena, Marco Tullio

    2011-01-01

    In this work, we report an analytical solution for the set of S N equations for the angular flux, in a rectangle, using the double Laplace transform technique. Its main idea comprehends the steps: application of the Laplace transform in one space variable, solution of the resulting equation by the LTS N method and reconstruction of the double Laplace transformed angular flux using the inversion theorem of the Laplace transform. We must emphasize that we perform the Laplace inversion by the LTS N method in the x direction, meanwhile we evaluate the inversion in the y direction performing the calculation of the corresponding line integral solution by the Stefest method. We have also to figure out that the application of Laplace transform to this type of boundary value problem introduces additional unknown functions associated to the partial derivatives of the angular flux at boundary. Based on the good results attained by the nodal LTS N method, we assume that the angular flux at boundary is also approximated by an exponential function. By analytical we mean that no approximation is done along the solution derivation except for the exponential hypothesis for the exiting angular flux at boundary. For sake of completeness, we report numerical comparisons of the obtained results against the ones of the literature. (author)

  18. An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

    Science.gov (United States)

    Swidinsky, Andrei; Liu, Lifei

    2017-11-01

    We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

  19. Prestack traveltimes for dip-constrained TI media

    KAUST Repository

    Golikov, Pavel; Alkhalifah, Tariq Ali; Stovas, Alexey

    2012-01-01

    The double-square-root (DSR) formula is an integral part of many wavefield based imaging tools. A transversely isotropic medium with a titled symmetry axis (TI) version of the DSR formula is nearly impossible to obtain analytically. As a result, we develop an approximate version of the DSR formula valid for media with the symmetry axis normal to the dip of the reflector (DTI). The accuracy of this approximate solution is enhanced using Shanks transform to a point where the errors are extremely small for practical anisotropic values. Under this assumption, we also do not need to compute the symmetry axis field as it is inherently included in the formulation.

  20. Prestack traveltimes for dip-constrained TI media

    KAUST Repository

    Golikov, Pavel

    2012-11-04

    The double-square-root (DSR) formula is an integral part of many wavefield based imaging tools. A transversely isotropic medium with a titled symmetry axis (TI) version of the DSR formula is nearly impossible to obtain analytically. As a result, we develop an approximate version of the DSR formula valid for media with the symmetry axis normal to the dip of the reflector (DTI). The accuracy of this approximate solution is enhanced using Shanks transform to a point where the errors are extremely small for practical anisotropic values. Under this assumption, we also do not need to compute the symmetry axis field as it is inherently included in the formulation.