A discussion of the kamlet-jacobs formula for the detonation pressure
Energy Technology Data Exchange (ETDEWEB)
Kazandjian, Luc; Danel, Jean-Francois [Commissariat a l' Energie Atomique, Centre CEA-DIF, B. P. 12, F-91680 Bruyeres-le-Chatel (France)
2006-02-15
The main features of the Kamlet-Jacobs formula for the detonation pressure of C-H-N-O explosives are analytically derived from a BKW (Becker-Kistiakowsky-Wilson) equation of state of the detonation products. In the derivation, well-known typical values at the Chapman-Jouguet state, in particular the nearly constant value of the relative volume of the detonation products, are used. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Li, Xiao-hong; Yin, Geng-xin; Zhang, Xian-zhou
2012-10-01
Based on the full optimized molecular geometrical structures at the DFT-B3LYP/6-311+G** level, there exists intramolecular hydrogen bond interaction for cyclic 2-diazo-4,6-dinitrophenol. The assigned infrared spectrum is obtained and used to compute the thermodynamic properties. The results show that there are four main characteristic regions in the calculated IR spectra of the title compound. The detonation velocities and pressures are also evaluated by using Kamlet-Jacobs equations based on the calculated density and condensed phase heat of formation. Thermal stability and the pyrolysis mechanism of 2-diazo-4,6-dinitrophenol are investigated by calculating the bond dissociation energies at the B3LYP/6-311+G** level.
Plasma balance equations based on orbit theory
International Nuclear Information System (INIS)
Lehnert, B.
1982-01-01
A set of plasma balance equations is proposed which is based on orbit theory and the particle distribution function, to provide means for theoretical analysis of a number of finite Larmor radius (FLR) phenomena without use of the Vlasov equation. Several important FLR effects originate from the inhomogeneity of an electric field in the plasma. The exact solution of a simple case shows that this inhomogeneity introduces fundamental changes in the physics of the particle motion. Thus, the periodic Larmor motion (gyration) is shifted in frequency and becomes elliptically polarized. Further, the non-periodic guiding-centre drift obtains additional components, part of which are accelerated such as to make the drift orbits intersect the equipotential surfaces of a static electric field. An attempt is finally made to classify the FLR effects, also with the purpose of identifying phenomena which have so far not been investigated. (author)
Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
International Nuclear Information System (INIS)
Znojil, Miloslav
2004-01-01
Witten's the non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations
Solution of partial differential equations by agent-based simulation
International Nuclear Information System (INIS)
Szilagyi, Miklos N
2014-01-01
The purpose of this short note is to demonstrate that partial differential equations can be quickly solved by agent-based simulation with high accuracy. There is no need for the solution of large systems of algebraic equations. This method is especially useful for quick determination of potential distributions and demonstration purposes in teaching electromagnetism. (letters and comments)
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed
2012-09-06
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed; Zidan, Mohammed A.; Salama, Khaled N.
2012-01-01
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation
Directory of Open Access Journals (Sweden)
Shu-Li Mei
2013-01-01
Full Text Available Based on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a nonlinear matrix ordinary differential equation. In order to obtain the analytical solution of the system of ODEs, the homotopy analysis method (HAM proposed by Shijun Liao was developed to solve the system of ODEs by combining the precise integration method (PIM which can be employed to get the analytical solution of linear system of ODEs. The numerical experiences show that HAM is not sensitive to the time step, and so the arithmetic error is mainly derived from the discrete in physical space.
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem
2018-01-01
In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.
Directory of Open Access Journals (Sweden)
Azmat Ullah
Full Text Available In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA with Interior Point Algorithm (IPA is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.
Numerical solution of modified differential equations based on symmetry preservation.
Ozbenli, Ersin; Vedula, Prakash
2017-12-01
In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.
Tokamak plasma shape identification based on the boundary integral equations
International Nuclear Information System (INIS)
Kurihara, Kenichi; Kimura, Toyoaki
1992-05-01
A necessary condition for tokamak plasma shape identification is discussed and a new identification method is proposed in this article. This method is based on the boundary integral equations governing a vacuum region around a plasma with only the measurement of either magnetic fluxes or magnetic flux intensities. It can identify various plasmas with low to high ellipticities with the precision determined by the number of the magnetic sensors. This method is applicable to real-time control and visualization using a 'table-look-up' procedure. (author)
Stochastic Differential Equation-Based Flexible Software Reliability Growth Model
Directory of Open Access Journals (Sweden)
P. K. Kapur
2009-01-01
Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
2012-01-01
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Abdulle, Assyr
2012-01-01
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.
DEFF Research Database (Denmark)
Hattel, Jesper; Hansen, Preben
1995-01-01
This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....
A new pseudorandom number generator based on a complex number chaotic equation
International Nuclear Information System (INIS)
Liu Yang; Tong Xiao-Jun
2012-01-01
In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties
Tielemans, E.; Kupper, L.L.; Kromhout, H.; Heederik, D.; Houba, R.
1998-01-01
Basically, two strategies can be considered for the analysis of hazardous pollutants in the work environment: group-based and individual-based strategies. This paper provides existing and recently derived equations for both strategies describing the influence of several factors on attenuation and on
Solution of wave-like equation based on Haar wavelet
Directory of Open Access Journals (Sweden)
Naresh Berwal
2012-11-01
Full Text Available Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.
Cauchy problem for Laplace equation: An observer based approach
Majeed, Muhammad Usman; Zayane-Aissa, Chadia; Laleg-Kirati, Taous Meriem
2013-01-01
domain from the observations on outer boundary. Proposed approach adapts one of the space variables as a time variable. The observer developed to solve Cauchy problem for the Laplace's equation is compuationally robust and accurate. © 2013 IEEE.
Sandia equation of state data base: seslan File
Energy Technology Data Exchange (ETDEWEB)
Kerley, G.I. [Sandia National Labs., Albuquerque, NM (US); Christian-Frear, T.L. [RE/SPEC Inc., Albuquerque, NM (US)
1993-06-24
Sandia National Laboratories maintains several libraries of equation of state tables, in a modified Sesame format, for use in hydrocode calculations and other applications. This report discusses one of those libraries, the seslan file, which contains 78 tables from the Los Alamos equation of state library. Minor changes have been made to these tables, making them more convenient for code users and reducing numerical difficulties that occasionally arise in hydrocode calculations.
Dominant height-based height-diameter equations for trees in southern Indiana
John A., Jr. Kershaw; Robert C. Morrissey; Douglass F. Jacobs; John R. Seifert; James B. McCarter
2008-01-01
Height-diameter equations are developed based on dominant tree data collected in 1986 in 8- to 17-year-old clearcuts and the phase 2 Forest Inventory and Analysis plots on the Hoosier National Forest in south central Indiana. Two equation forms are explored: the basic, three-parameter Chapman-Richards function, and a modification of the three-parameter equation...
DEFF Research Database (Denmark)
Marcussen, Lis; Aasberg-Petersen, K.; Krøll, Annette Elisabeth
2000-01-01
An adsorption isotherm equation for nonideal pure component adsorption based on vacancy solution theory and the Non-Random-Two-Liquid (NRTL) equation is found to be useful for predicting pure component adsorption equilibria at a variety of conditions. The isotherm equation is evaluated successfully...... adsorption systems, spreading pressure and isosteric heat of adsorption are also calculated....
Wills, John M.; Mattsson, Ann E.
2012-02-01
Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Computations of Wall Distances Based on Differential Equations
Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.
2004-01-01
The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.
Validation of a numerical algorithm based on transformed equations
International Nuclear Information System (INIS)
Xu, H.; Barron, R.M.; Zhang, C.
2003-01-01
Generally, a typical equation governing a physical process, such as fluid flow or heat transfer, has three types of terms that involve partial derivatives, namely, the transient term, the convective terms and the diffusion terms. The major difficulty in obtaining numerical solutions of these partial differential equations is the discretization of the convective terms. The transient term is usually discretized using the first-order forward or backward differencing scheme. The diffusion terms are usually discretized using the central differencing scheme and no difficulty arises since these terms involve second-order spatial derivatives of the flow variables. The convective terms are non-linear and contain first-order spatial derivatives. The main difference between various numerical algorithms is the discretization of the convective terms. In the present study, an alternative approach to discretizing the governing equations is presented. In this algorithm, the governing equations are first transformed by introducing an exponential function to eliminate the convective terms in the equations. The proposed algorithm is applied to simulate some fluid flows with exact solutions to validate the proposed algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. The comparisons with the power-law scheme indicate that the proposed scheme exhibits better performance. (author)
Electromagnetic equations based on the law of Biot and Savart
International Nuclear Information System (INIS)
Yan, C.-C.
1983-01-01
The law of Biot and Savart is given some interpretations that may be of some help in presenting the law. Some possible consequences and the whole set of Maxwell-Lorentz equations are shown to be derivable from the law of Biot and Savart. It is pointed out that the failure or success of deriving the set of Maxwell-Lorentz equation from the law of Biot and Savart is intimately connected to the basic ideas of the theory of special relativity of Einstein. (Author) [pt
Cauchy problem for Laplace equation: An observer based approach
Majeed, Muhammad Usman
2013-10-01
A method to solve Cauchy Problem for Laplace equation using state observers is proposed. It is known that this problem is ill-posed. The domain under consideration is simple lipschitz in 2 with a hole. The idea is to recover the solution over whole domain from the observations on outer boundary. Proposed approach adapts one of the space variables as a time variable. The observer developed to solve Cauchy problem for the Laplace\\'s equation is compuationally robust and accurate. © 2013 IEEE.
A Gradient Based Iterative Solutions for Sylvester Tensor Equations
Directory of Open Access Journals (Sweden)
Zhen Chen
2013-01-01
proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective.
Stature estimation equations for South Asian skeletons based on DXA scans of contemporary adults.
Pomeroy, Emma; Mushrif-Tripathy, Veena; Wells, Jonathan C K; Kulkarni, Bharati; Kinra, Sanjay; Stock, Jay T
2018-05-03
Stature estimation from the skeleton is a classic anthropological problem, and recent years have seen the proliferation of population-specific regression equations. Many rely on the anatomical reconstruction of stature from archaeological skeletons to derive regression equations based on long bone lengths, but this requires a collection with very good preservation. In some regions, for example, South Asia, typical environmental conditions preclude the sufficient preservation of skeletal remains. Large-scale epidemiological studies that include medical imaging of the skeleton by techniques such as dual-energy X-ray absorptiometry (DXA) offer new potential datasets for developing such equations. We derived estimation equations based on known height and bone lengths measured from DXA scans from the Andhra Pradesh Children and Parents Study (Hyderabad, India). Given debates on the most appropriate regression model to use, multiple methods were compared, and the performance of the equations was tested on a published skeletal dataset of individuals with known stature. The equations have standard errors of estimates and prediction errors similar to those derived using anatomical reconstruction or from cadaveric datasets. As measured by the number of significant differences between true and estimated stature, and the prediction errors, the new equations perform as well as, and generally better than, published equations commonly used on South Asian skeletons or based on Indian cadaveric datasets. This study demonstrates the utility of DXA scans as a data source for developing stature estimation equations and offer a new set of equations for use with South Asian datasets. © 2018 Wiley Periodicals, Inc.
Indirect Inference for Stochastic Differential Equations Based on Moment Expansions
Ballesio, Marco
2016-01-06
We provide an indirect inference method to estimate the parameters of timehomogeneous scalar diffusion and jump diffusion processes. We obtain a system of ODEs that approximate the time evolution of the first two moments of the process by the approximation of the stochastic model applying a second order Taylor expansion of the SDE s infinitesimal generator in the Dynkin s formula. This method allows a simple and efficient procedure to infer the parameters of such stochastic processes given the data by the maximization of the likelihood of an approximating Gaussian process described by the two moments equations. Finally, we perform numerical experiments for two datasets arising from organic and inorganic fouling deposition phenomena.
A rational function based scheme for solving advection equation
International Nuclear Information System (INIS)
Xiao, Feng; Yabe, Takashi.
1995-07-01
A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author)
Ford, Neville J.; Connolly, Joseph A.
2009-07-01
We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.
Predictive model for early math skills based on structural equations.
Aragón, Estíbaliz; Navarro, José I; Aguilar, Manuel; Cerda, Gamal; García-Sedeño, Manuel
2016-12-01
Early math skills are determined by higher cognitive processes that are particularly important for acquiring and developing skills during a child's early education. Such processes could be a critical target for identifying students at risk for math learning difficulties. Few studies have considered the use of a structural equation method to rationalize these relations. Participating in this study were 207 preschool students ages 59 to 72 months, 108 boys and 99 girls. Performance with respect to early math skills, early literacy, general intelligence, working memory, and short-term memory was assessed. A structural equation model explaining 64.3% of the variance in early math skills was applied. Early literacy exhibited the highest statistical significance (β = 0.443, p < 0.05), followed by intelligence (β = 0.286, p < 0.05), working memory (β = 0.220, p < 0.05), and short-term memory (β = 0.213, p < 0.05). Correlations between the independent variables were also significant (p < 0.05). According to the results, cognitive variables should be included in remedial intervention programs. © 2016 Scandinavian Psychological Associations and John Wiley & Sons Ltd.
PolyRES: A polygon-based Richards equation solver
International Nuclear Information System (INIS)
Hills, R.G.
1995-12-01
This document describes the theory, implementation, and use of a software package designed to solve the transient, two-dimensional, Richards equation for water flow in unsaturated-saturated soils. This package was specifically designed to model complex geometries with minimal input from the user and to simulate groundwater flow related to assessment of low-level radioactive waste disposal sites and engineered facilities. The spatial variation of the hydraulic properties can be defined across individual polygon-shaped subdomains, called objects. These objects combine to form a polygon-shaped model domain. Each object can have its own distribution of hydraulic parameters. The resulting model domain and polygon-shaped internal objects are mapped onto a rectangular, finite-volume, computational grid by a preprocessor. This allows the user to specify model geometry independently of the underlying grid and greatly simplifies user input for complex geometries. In addition, this approach significantly reduces the computational requirements since complex geometries are actually modeled on a rectangular grid. This results in well-structured, finite difference-like systems of equations that require minimal storage and are very efficient to solve. The documentation for this software package includes a user's manual, a detailed description of the underlying theory, and a detailed discussion of program flow. Several example problems are presented that show the use and features of the software package. The water flow predictions for several of these example problems are compared to those of another algorithm to test for prediction equivalency
Equation-based model for the stock market.
Xavier, Paloma O C; Atman, A P F; de Magalhães, A R Bosco
2017-09-01
We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.
Fourier-Based Fast Multipole Method for the Helmholtz Equation
Cecka, Cris
2013-01-01
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions rather than spherical harmonics. By modifying the transfer function in the precomputation stage of the FMM, time-critical stages of the algorithm are accelerated by causing the interpolation operators to become straightforward applications of fast Fourier transforms, retaining the diagonality of the transfer function, and providing a simplified error analysis. Using Fourier analysis, constructive algorithms are derived to a priori determine an integration quadrature for a given error tolerance. Sharp error bounds are derived and verified numerically. Various optimizations are considered to reduce the number of quadrature points and reduce the cost of computing the transfer function. © 2013 Society for Industrial and Applied Mathematics.
Graph-Based Cooperative Localization Using Symmetric Measurement Equations.
Gulati, Dhiraj; Zhang, Feihu; Clarke, Daniel; Knoll, Alois
2017-06-17
Precise localization is a key requirement for the success of highly assisted or autonomous vehicles. The diminishing cost of hardware has resulted in a proliferation of the number of sensors in the environment. Cooperative localization (CL) presents itself as a feasible and effective solution for localizing the ego-vehicle and its neighboring vehicles. However, one of the major challenges to fully realize the effective use of infrastructure sensors for jointly estimating the state of a vehicle in cooperative vehicle-infrastructure localization is an effective data association. In this paper, we propose a method which implements symmetric measurement equations within factor graphs in order to overcome the data association challenge with a reduced bandwidth overhead. Simulated results demonstrate the benefits of the proposed approach in comparison with our previously proposed approach of topology factors.
Equation-based model for the stock market
Xavier, Paloma O. C.; Atman, A. P. F.; de Magalhães, A. R. Bosco
2017-09-01
We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.
Materials data base and design equations for the UCLA solid breeder blanket
International Nuclear Information System (INIS)
Sharafat, S.; Amodeo, R.; Ghoniem, N.M.
1986-02-01
The materials and properties investigated for this blanket study are listed. The phenomenological equations and mathematical fits for all materials and properties considered are given. Efforts to develop a swelling equation based on the few experimental data points available for breeder materials are described. The sintering phenomena for ceramics is investigated
Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping
2018-06-01
As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.
Iterative observer based method for source localization problem for Poisson equation in 3D
Majeed, Muhammad Usman; Laleg-Kirati, Taous-Meriem
2017-01-01
A state-observer based method is developed to solve point source localization problem for Poisson equation in a 3D rectangular prism with available boundary data. The technique requires a weighted sum of solutions of multiple boundary data
Collage-based approaches for elliptic partial differential equations inverse problems
Yodzis, Michael; Kunze, Herb
2017-01-01
The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.
A variational solution of transport equation based on spherical geometry
International Nuclear Information System (INIS)
Liu Hui; Zhang Ben'ai
2002-01-01
A variational method with differential forms gives better precision for numerical solution of transport critical problem based on spherical geometry, and its computation seems simple than other approximate methods
From Equation to Inequality Using a Function-Based Approach
Verikios, Petros; Farmaki, Vassiliki
2010-01-01
This article presents features of a qualitative research study concerning the teaching and learning of school algebra using a function-based approach in a grade 8 class, of 23 students, in 26 lessons, in a state school of Athens, in the school year 2003-2004. In this article, we are interested in the inequality concept and our aim is to…
Optimal harvesting for a predator-prey agent-based model using difference equations.
Oremland, Matthew; Laubenbacher, Reinhard
2015-03-01
In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.
Estimation of Supercapacitor Energy Storage Based on Fractional Differential Equations.
Kopka, Ryszard
2017-12-22
In this paper, new results on using only voltage measurements on supercapacitor terminals for estimation of accumulated energy are presented. For this purpose, a study based on application of fractional-order models of supercapacitor charging/discharging circuits is undertaken. Parameter estimates of the models are then used to assess the amount of the energy accumulated in supercapacitor. The obtained results are compared with energy determined experimentally by measuring voltage and current on supercapacitor terminals. All the tests are repeated for various input signal shapes and parameters. Very high consistency between estimated and experimental results fully confirm suitability of the proposed approach and thus applicability of the fractional calculus to modelling of supercapacitor energy storage.
Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions
Directory of Open Access Journals (Sweden)
Yeguo Sun
2012-01-01
Full Text Available We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.
Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.
Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung
2018-01-01
A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.
Jamali, R. M. Jalal Uddin; Hashem, M. M. A.; Hasan, M. Mahfuz; Rahman, Md. Bazlar
2013-01-01
Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods especially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxation factor, {\\omega}. Recently, hybridization of classical Gauss-Seidel based successive relaxation t...
Modeling of superconductors based on the timedependent Ginsburg-Landau equations
Grishakov, K. S.; Degtyarenko, P. N.; Degtyarenko, N. N.; Elesin, V. F.; Kruglov, V. S.
2009-11-01
Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors.
CORE-COLLAPSE SUPERNOVA EQUATIONS OF STATE BASED ON NEUTRON STAR OBSERVATIONS
International Nuclear Information System (INIS)
Steiner, A. W.; Hempel, M.; Fischer, T.
2013-01-01
Many of the currently available equations of state for core-collapse supernova simulations give large neutron star radii and do not provide large enough neutron star masses, both of which are inconsistent with some recent neutron star observations. In addition, one of the critical uncertainties in the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully explored by the currently available equations of state. In this article, we construct two new equations of state which match recent neutron star observations and provide more flexibility in studying the dependence on nuclear matter properties. The equations of state are also provided in tabular form, covering a wide range in density, temperature, and asymmetry, suitable for astrophysical simulations. These new equations of state are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics with three-flavor Boltzmann neutrino transport. The results are compared with commonly used equations of state in supernova simulations of 11.2 and 40 M ☉ progenitors. We consider only equations of state which are fitted to nuclear binding energies and other experimental and observational constraints. We find that central densities at bounce are weakly correlated with L and that there is a moderate influence of the symmetry energy on the evolution of the electron fraction. The new models also obey the previously observed correlation between the time to black hole formation and the maximum mass of an s = 4 neutron star
Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art
Directory of Open Access Journals (Sweden)
Herb E. Kunze
2014-01-01
Full Text Available We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.
Splines and their reciprocal-bases in volume-integral equations
International Nuclear Information System (INIS)
Sabbagh, H.A.
1993-01-01
The authors briefly outline the use of higher-order splines and their reciprocal-bases in discretizing the volume-integral equations of electromagnetics. The discretization is carried out by means of the method of moments, in which the expansion functions are the higher-order splines, and the testing functions are the corresponding reciprocal-basis functions. These functions satisfy an orthogonality condition with respect to the spline expansion functions. Thus, the method is not Galerkin, but the structure of the resulting equations is quite regular, nevertheless. The theory is applied to the volume-integral equations for the unknown current density, or unknown electric field, within a scattering body, and to the equations for eddy-current nondestructive evaluation. Numerical techniques for computing the matrix elements are also given
Directory of Open Access Journals (Sweden)
Luning Shi
2014-01-01
Full Text Available A prestress force identification method for externally prestressed concrete uniform beam based on the frequency equation and the measured frequencies is developed. For the purpose of the prestress force identification accuracy, we first look for the appropriate method to solve the free vibration equation of externally prestressed concrete beam and then combine the measured frequencies with frequency equation to identify the prestress force. To obtain the exact solution of the free vibration equation of multispan externally prestressed concrete beam, an analytical model of externally prestressed concrete beam is set up based on the Bernoulli-Euler beam theory and the function relation between prestress variation and vibration displacement is built. The multispan externally prestressed concrete beam is taken as the multiple single-span beams which must meet the bending moment and rotation angle boundary conditions, the free vibration equation is solved using sublevel simultaneous method and the semi-analytical solution of the free vibration equation which considered the influence of prestress on section rigidity and beam length is obtained. Taking simply supported concrete beam and two-span concrete beam with external tendons as examples, frequency function curves are obtained with the measured frequencies into it and the prestress force can be identified using the abscissa of the crosspoint of frequency functions. Identification value of the prestress force is in good agreement with the test results. The method can accurately identify prestress force of externally prestressed concrete beam and trace the trend of effective prestress force.
Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem
2016-01-01
In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear
Alirezaei, M.; Kanarachos, S.A.; Scheepers, B.T.M.; Maurice, J.P.
2013-01-01
Development and experimentally evaluation of an optimal Vehicle Dynamic Control (VDC) strategy based on the State Dependent Riccati Equation (SDRE) control technique is presented. The proposed nonlinear controller is based on a nonlinear vehicle model with nonlinear tire characteristics. A novel
A multivariate family-based association test using generalized estimating equations : FBAT-GEE
Lange, C; Silverman, SK; Xu, [No Value; Weiss, ST; Laird, NM
In this paper we propose a multivariate extension of family-based association tests based on generalized estimating equations. The test can be applied to multiple phenotypes and to phenotypic data obtained in longitudinal studies without making any distributional assumptions for the phenotypic
Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye
2018-04-01
The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.
A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver
Liu, Yang
2015-10-26
© 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.
Energy Technology Data Exchange (ETDEWEB)
Wang, Gui-Xiang; Xiao, He-Ming; Xu, Xiao-Juan; Ju, Xue-Hai [Department of Chemistry, Nanjing University of Science and Technology, Nanjing, 210094 (China)
2006-04-15
The DFT-B3LYP method, with basis set 6-31G*, is employed to optimize molecular geometries and electronic structures of eighteen nitramines. The averaged molar volume (V) and theoretical density ({rho}) are estimated using the Monte-Carlo method based on 0.001 electrons/bohr{sup 3} density space. Subsequently, the detonation velocity (D) and pressure (P) of the explosives are estimated by using the Kamlet-Jacobs equation on the basis of the theoretical density and heat of formation ({delta}{sub f}H), which is calculated using the PM3 method. The reliability of this theoretical method and results are tested by comparing the theoretical values of {rho} and D with the experimental or referenced values. The theoretical values of D and P are compared with the experimental values of electric spark sensitivity (E{sub ES}). It is found that for the compounds with metylenenitramine units (-CH{sub 2}N(NO{sub 2})-) in their molecules (such as ORDX, AcAn and HMX) or with the better symmetrical cyclic nitramines but excluding metylenenitramine units (such as DNDC and TNAD), there is a excellent linear relationship between the square of detonation velocity (D{sup 2}) or the logarithm of detonation pressure (lg P) and electric spark sensitivity (E{sub ES}). This suggests that in the molecular design of energetic materials, such a theoretical approach can be used to predict their E{sub ES} values, which have been proven to be difficult to predict quantitatively or to synthesize. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Existing creatinine-based equations overestimate glomerular filtration rate in Indians.
Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand
2018-02-01
Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the
Sun, Bo; Liu, Yu; Li, Jing Xian; Li, Haipeng; Chen, Peijie
2013-01-01
Purpose: This study set out to examine the relationship between step frequency and velocity to develop a step frequency-based equation to predict Chinese youth's energy expenditure (EE) during walking and running. Method: A total of 173 boys and girls aged 11 to 18 years old participated in this study. The participants walked and ran on a…
A surface-integral-equation approach to the propagation of waves in EBG-based devices
Lancellotti, V.; Tijhuis, A.G.
2012-01-01
We combine surface integral equations with domain decomposition to formulate and (numerically) solve the problem of electromagnetic (EM) wave propagation inside finite-sized structures. The approach is of interest for (but not limited to) the analysis of devices based on the phenomenon of
Introduction of the Notion of Differential Equations by Modelling Based Teaching
Budinski, Natalija; Takaci, Djurdjica
2011-01-01
This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…
Mei, Shu-Li; Lv, Hong-Liang; Ma, Qin
2008-01-01
Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.
Ortiz-Hernández, Luis; Vega López, A Valeria; Ramos-Ibáñez, Norma; Cázares Lara, L Joana; Medina Gómez, R Joab; Pérez-Salgado, Diana
To develop and validate equations to estimate the percentage of body fat of children and adolescents from Mexico using anthropometric measurements. A cross-sectional study was carried out with 601 children and adolescents from Mexico aged 5-19 years. The participants were randomly divided into the following two groups: the development sample (n=398) and the validation sample (n=203). The validity of previously published equations (e.g., Slaughter) was also assessed. The percentage of body fat was estimated by dual-energy X-ray absorptiometry. The anthropometric measurements included height, sitting height, weight, waist and arm circumferences, skinfolds (triceps, biceps, subscapular, supra-iliac, and calf), and elbow and bitrochanteric breadth. Linear regression models were estimated with the percentage of body fat as the dependent variable and the anthropometric measurements as the independent variables. Equations were created based on combinations of six to nine anthropometric variables and had coefficients of determination (r 2 ) equal to or higher than 92.4% for boys and 85.8% for girls. In the validation sample, the developed equations had high r 2 values (≥85.6% in boys and ≥78.1% in girls) in all age groups, low standard errors (SE≤3.05% in boys and ≤3.52% in girls), and the intercepts were not different from the origin (p>0.050). Using the previously published equations, the coefficients of determination were lower, and/or the intercepts were different from the origin. The equations developed in this study can be used to assess the percentage of body fat of Mexican schoolchildren and adolescents, as they demonstrate greater validity and lower error compared with previously published equations. Copyright © 2017 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.
Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication
DEFF Research Database (Denmark)
Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi
2015-01-01
We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser...... characterization and carrier recovery in coherent communication. Two rate equation based Bayesian filters, the particle filter and extended Kalman filter, are used in conjunction with a coherent receiver to measure frequency noise spectrum of a photonic crystal cavity laser with less than 20 nW of fiber...
Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots
Directory of Open Access Journals (Sweden)
Ching-Long Shih
2012-08-01
Full Text Available This paper aims to demonstrate a clear relationship between Lagrange equations and Newton-Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method for using either symbolic or on-line numerical computations. Based on the decomposition approach and cross-product operation, a computing method for robot dynamics can be easily developed. The advantages of this computing framework are that: it can be used for both symbolic and on-line numeric computation purposes, and it can also be applied to biped systems, as well as some simple closed-chain robot systems.
Bai, Shirong; Skodje, Rex T
2017-08-17
A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
Asiri, Sharefa M.
2013-05-25
Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2015-04-01
This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.
Fluid flow in porous media using image-based modelling to parametrize Richards' equation.
Cooper, L J; Daly, K R; Hallett, P D; Naveed, M; Koebernick, N; Bengough, A G; George, T S; Roose, T
2017-11-01
The parameters in Richards' equation are usually calculated from experimentally measured values of the soil-water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The Cahn-Hilliard-Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil-water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.
Xu, Peiliang
2018-06-01
The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking
Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation
Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.
2017-10-01
There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.
Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations
Directory of Open Access Journals (Sweden)
Vladimir P. Gerdt
2006-05-01
Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.
International Nuclear Information System (INIS)
Kataoka, Isao; Tomiyama, Akio
2004-01-01
The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill
CRPropa 3.1—a low energy extension based on stochastic differential equations
Energy Technology Data Exchange (ETDEWEB)
Merten, Lukas; Tjus, Julia Becker; Eichmann, Björn [Theoretische Physik IV: Plasma-Astroteilchenphysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum (Germany); Fichtner, Horst [Theoretische Physik IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, Universitätsstrasse 150, 44801 Bochum (Germany); Sigl, Günter, E-mail: lukas.merten@rub.de, E-mail: julia.tjus@rub.de, E-mail: hf@tp4.rub.de, E-mail: eiche@tp4.rub.de, E-mail: guenter.sigl@desy.de [II Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
2017-06-01
The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ{sub ∥} and perpendicular κ{sub ⊥} diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.
CRPropa 3.1—a low energy extension based on stochastic differential equations
International Nuclear Information System (INIS)
Merten, Lukas; Tjus, Julia Becker; Eichmann, Björn; Fichtner, Horst; Sigl, Günter
2017-01-01
The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ ∥ and perpendicular κ ⊥ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.
Padrino, Juan C.; Sprittles, James; Lockerby, Duncan
2017-11-01
Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).
Exergy analysis on throttle reduction efficiency based on real gas equations
International Nuclear Information System (INIS)
Luo, Yuxi; Wang, Xuanyin
2010-01-01
This paper proposes an approach to calculate the efficiency of throttling in which the exergy (available energy) is used to evaluate the energy conversion processes. In the exergy calculation for real gases, a difficult part of integration can be removed by judiciously advised thermodynamic paths; the compressibility factor is calculated by using Peng-Robinson (P-R) equation. It is found that the largest deviation between the exergies calculated by the real gas equation and ideal gas assumption is about 1%. Because the exergy is a function of the pressure and temperature, the Joule-Thomson coefficients are used to calculate the temperature changes of throttling, based on the compressibility factors of the Soave-Redlich-Kwong (S-R-K) and P-R equations, and the temperature decreases are compared with those calculated by empirical formula. The result shows that the heat exergy contributes very little in throttling. The simple equation of ideal gas is suggested to calculate the efficiency of throttling for air at atmospheric temperatures.
CRPropa 3.1—a low energy extension based on stochastic differential equations
Merten, Lukas; Becker Tjus, Julia; Fichtner, Horst; Eichmann, Björn; Sigl, Günter
2017-06-01
The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel κ∥ and perpendicular κ⊥ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.
Research on the Collinear Equation Model of Visual Positioning Based on Visible Light Communication
Directory of Open Access Journals (Sweden)
Wang Yuqi
2015-01-01
Full Text Available A positioning method based on visible light communication is proposed, which receiving visible light information by low-resolution photodiode array and receiving visual information by the front camera of mobile phone. The terminal position is determined by matching spot information provided by photodiode array with visual information and position information provided by visible light communication. A collinear equation model is derived which based on mobile phone front camera. A hardware-in-loop simulation has been conducted to verify the collinear equation. The three-dimensional positioning error is on the level of decimeter. Moreover, the main factors which affect the positioning accuracy are analyzed in order to further improve the positioning accuracy.
Iterative observer based method for source localization problem for Poisson equation in 3D
Majeed, Muhammad Usman
2017-07-10
A state-observer based method is developed to solve point source localization problem for Poisson equation in a 3D rectangular prism with available boundary data. The technique requires a weighted sum of solutions of multiple boundary data estimation problems for Laplace equation over the 3D domain. The solution of each of these boundary estimation problems involves writing down the mathematical problem in state-space-like representation using one of the space variables as time-like. First, system observability result for 3D boundary estimation problem is recalled in an infinite dimensional setting. Then, based on the observability result, the boundary estimation problem is decomposed into a set of independent 2D sub-problems. These 2D problems are then solved using an iterative observer to obtain the solution. Theoretical results are provided. The method is implemented numerically using finite difference discretization schemes. Numerical illustrations along with simulation results are provided.
Correction of the calculation of beam loading based in the RF power diffusion equation
International Nuclear Information System (INIS)
Silva, R. da.
1980-01-01
It is described an empirical correction based upon experimental datas of others authors in ORELA, GELINA and SLAC accelerators, to the calculation of the energy loss due to the beam loading effect as stated by the RF power diffusion equation theory an accelerating structure. It is obtained a dependence of this correction with the electron pulse full width half maximum, but independent of the electron energy. (author) [pt
Solution of the Lorentz-Dirac equation based on a new momentum expression
Yan, C C
1998-01-01
The Lorentz-Dirac equation is solved based on a new momentum expression given by p sup a =1/c sup 2 (u submu p supmu)u sup a +k du sup a /d tau. This new momentum expression is the form proposed by Barut modified to satisfy the condition imposed by Dirac. The solution turns out to be well behaved without violating causality or causing runaway. (author)
Investigating market efficiency through a forecasting model based on differential equations
de Resende, Charlene C.; Pereira, Adriano C. M.; Cardoso, Rodrigo T. N.; de Magalhães, A. R. Bosco
2017-05-01
A new differential equation based model for stock price trend forecast is proposed as a tool to investigate efficiency in an emerging market. Its predictive power showed statistically to be higher than the one of a completely random model, signaling towards the presence of arbitrage opportunities. Conditions for accuracy to be enhanced are investigated, and application of the model as part of a trading strategy is discussed.
Directory of Open Access Journals (Sweden)
Ayşe Betül Koç
2014-01-01
Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
International Nuclear Information System (INIS)
Green, B I; Vedula, Prakash
2013-01-01
An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)
Comment on the consistency of truncated nonlinear integral equation based theories of freezing
International Nuclear Information System (INIS)
Cerjan, C.; Bagchi, B.; Rice, S.A.
1985-01-01
We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions
[New topics regarding equations for GFR estimation based on serum creatinine and cystatin C].
Horio, Masaru
2014-02-01
Japanese GFR equations and CKD-EPI equations based on standardized serum creatinine and standardized cystatin C are recommended in recent Japanese CKD guides and KDIGO guidelines for CKD management, respectively. CKD-EPIcreat overestimates GFR in Japanese subjects, probably due to the difference in muscle mass between Japanese and Caucasians. Unlike CKD-EPIcreat, CKD-EPIcys performs well in Japanese subjects, indicating the advantages of using cystatin C as a GFR marker. KDIGO guidelines suggest measuring eGFRcys in adults with eGFRcreat of 45-59 ml/min/1.73 m2 who do not have markers of kidney damage if confirmation of CKD is required. Creatinine is excreted by glomerular filtration, but also secreted by the tubules. Alteration of the tubular secretion of creatinine may influence the performance of GFR equations based on serum creatinine. Multivariate analysis showed that GFR and serum albumin levels were independent parameters affecting the fractional excretion of creatinine (FE-Cr). Alteration of FE-Cr according to the serum albumin levels may be one of the reasons for the bias of GFR equations based on serum creatinine. Low GFR is a risk factor for all-cause and cardiovascular mortality in a general population. However, the relationship between eGFR and the hazard risk of events is different depending on whether cystatin C or creatinine is used to calculate eGFR. The association between eGFRcys and the hazard risk is much stronger compared with eGFRcreat. Cystatin C may be a useful alternative to creatinine for detecting a high risk of complications in a general population and subjects with CKD.
Partial differential equation-based localization of a monopole source from a circular array.
Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa
2013-10-01
Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.
Generalized structured component analysis a component-based approach to structural equation modeling
Hwang, Heungsun
2014-01-01
Winner of the 2015 Sugiyama Meiko Award (Publication Award) of the Behaviormetric Society of Japan Developed by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured component analysis allows researchers to evaluate the adequacy of a model as a whole, compare a model to alternative specifications, and conduct complex analyses in a straightforward manner. Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling provides a detailed account of this novel statistical methodology and its various extensions. The authors present the theoretical underpinnings of generalized structured component analysis and demonstrate how it can be applied to various empirical examples. The book enables quantitative methodologists, applied researchers, and practitioners to grasp the basic concepts behind this new a...
A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying
2018-04-01
Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.
Directory of Open Access Journals (Sweden)
Hamid A. Jalab
2014-01-01
Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.
Materials data base and design equations for the UCLA solid breeder blanket
International Nuclear Information System (INIS)
Sharafat, S.; Amodeo, R.; Ghoniem, N.M.
1986-01-01
The need for a complete and coherent material data base for fusion reactor systems has been an important issue for some time now. Since the choices for materials used in fusion reactors are becoming more apparent, it is important to be able to quickly access this data to facilitate reactor design. The philosophy of a data base is one of expansion and modification. This will lead to a constantly growing collection of most recently acquired information. Based on this philosophy special care has been given to the structure, the accessibility and ease of modification. The data base is developed primarily for use on Personal Computers (PC's). In Section 10.2. materials and properties investigated for this blanket study are listed. Section 10.3. is a list of phenomenological equations and mathematical fits for all materials and properties considered. Section 10.4. describes the authors efforts to develop a swelling equations based on the few experimental data points available for breeder materials. In Section 10.5. the sintering phenomena for ceramics is investigated
The adjoint method for general EEG and MEG sensor-based lead field equations
International Nuclear Information System (INIS)
Vallaghe, Sylvain; Papadopoulo, Theodore; Clerc, Maureen
2009-01-01
Most of the methods for the inverse source problem in electroencephalography (EEG) and magnetoencephalography (MEG) use a lead field as an input. The lead field is the function which relates any source in the brain to its measurements at the sensors. For complex geometries, there is no analytical formula of the lead field. The common approach is to numerically compute the value of the lead field for a finite number of point sources (dipoles). There are several drawbacks: the model of the source space is fixed (a set of dipoles), and the computation can be expensive for as much as 10 000 dipoles. The common idea to bypass these problems is to compute the lead field from a sensor point of view. In this paper, we use the adjoint method to derive general EEG and MEG sensor-based lead field equations. Within a simple framework, we provide a complete review of the explicit lead field equations, and we are able to extend these equations to non-pointlike sensors.
UNIFIED MODELS OF ELEMENTS OF POWER SUPPLY SYSTEMS BASED ON EQUATIONS IN PHASE COORDINATES
Directory of Open Access Journals (Sweden)
Yu.N. Vepryk
2015-12-01
Full Text Available Purpose. The models of electrical machines in the phase coordinates, the universal algorithm for the simulation of separate elements in a d-q coordinates system and in a phase-coordinates system are proposed. Methodology. Computer methods of investigation of transients in electrical systems are based on a compilation of systems of differential equations and their numerical integration solution methods. To solve differential equations an implicit method of numerical integration was chosen. Because it provides to complete structural simulation possibility: firstly developing models of separate elements and then forming a model of the complex system. For the mathematical simulation of electromagnetic transients in the elements of the electrical systems has been accepted the implicit Euler-Cauchy method, because it provides a higher precision and stability of the computing processes. Results. In developing the model elements identified two groups of elements: - Static elements and electrical machines in the d-q coordinates; - Rotating electrical machines in phase coordinates. As an example, the paper provides a model of synchronous and asynchronous electric machines in the d-q coordinates system and the phase coordinate system. The generalization algorithm and the unified notation form of equations of elements of an electrical system are obtained. It provides the possibility of using structural methods to develop a mathematical model of power systems under transient conditions. Practical value. In addition, the using of a computer model allows to implement multivariant calculations for research and study of factors affecting the quantitative characteristics of the transients.
Nayak, Bishnupriya; Menon, S. V. G.
2018-01-01
Enthalpy-based equation of state based on a modified soft sphere model for the fluid phase, which includes vaporization and ionization effects, is formulated for highly porous materials. Earlier developments and applications of enthalpy-based approach had not accounted for the fact that shocked states of materials with high porosity (e.g., porosity more than two for Cu) are in the expanded fluid region. We supplement the well known soft sphere model with a generalized Lennard-Jones formula for the zero temperature isotherm, with parameters determined from cohesive energy, specific volume and bulk modulus of the solid at normal condition. Specific heats at constant pressure, ionic and electronic enthalpy parameters and thermal excitation effects are calculated using the modified approach and used in the enthalpy-based equation of state. We also incorporate energy loss from the shock due to expansion of shocked material in calculating porous Hugoniot. Results obtained for Cu, even up to initial porosities ten, show good agreement with experimental data.
Anak Gisen, Jacqueline Isabella; Nijzink, Remko C.; Savenije, Hubert H. G.
2014-05-01
Dispersion mathematical representation of tidal mixing between sea water and fresh water in The definition of dispersion somehow remains unclear as it is not directly measurable. The role of dispersion is only meaningful if it is related to the appropriate temporal and spatial scale of mixing, which are identified as the tidal period, tidal excursion (longitudinal), width of estuary (lateral) and mixing depth (vertical). Moreover, the mixing pattern determines the salt intrusion length in an estuary. If a physically based description of the dispersion is defined, this would allow the analytical solution of the salt intrusion problem. The objective of this study is to develop a predictive equation for estimating the dispersion coefficient at tidal average (TA) condition, which can be applied in the salt intrusion model to predict the salinity profile for any estuary during different events. Utilizing available data of 72 measurements in 27 estuaries (including 6 recently studied estuaries in Malaysia), regressions analysis has been performed with various combinations of dimensionless parameters . The predictive dispersion equations have been developed for two different locations, at the mouth D0TA and at the inflection point D1TA (where the convergence length changes). Regressions have been carried out with two separated datasets: 1) more reliable data for calibration; and 2) less reliable data for validation. The combination of dimensionless ratios that give the best performance is selected as the final outcome which indicates that the dispersion coefficient is depending on the tidal excursion, tidal range, tidal velocity amplitude, friction and the Richardson Number. A limitation of the newly developed equation is that the friction is generally unknown. In order to compensate this problem, further analysis has been performed adopting the hydraulic model of Cai et. al. (2012) to estimate the friction and depth. Keywords: dispersion, alluvial estuaries, mixing, salt
Peng, NaiFu; Guan, Hui; Wu, ChuiJie
2016-04-01
In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano; Gomes, Diogo A.; Machado Velho, Roberto
2017-01-01
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano
2017-03-22
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
Questioning the quantity equation using an agent-based computational model
DEFF Research Database (Denmark)
Bruun, Charlotte
2000-01-01
by Stutzel (1954), argues that the functional relationship may as well be negative. Even focusing the money needed to carry out transactions, there is no immediate answer to the question of the functional relationship between trade turnover and money demand. An agent-based computational model is used......In the literature we find two opposing hypotheses relating the volume of money to the volume of transactions or national income. The classic hypothesis, implicitly entailed in the quantity equation, argues that this relation must be positive, while an opposing hypothesis, most strongly presented...
Hussain, Nur Farahin Mee; Zahid, Zalina
2014-12-01
Nowadays, in the job market demand, graduates are expected not only to have higher performance in academic but they must also be excellent in soft skill. Problem-Based Learning (PBL) has a number of distinct advantages as a learning method as it can deliver graduates that will be highly prized by industry. This study attempts to determine the satisfaction level of engineering students on the PBL Approach and to evaluate their determinant factors. The Structural Equation Modeling (SEM) was used to investigate how the factors of Good Teaching Scale, Clear Goals, Student Assessment and Levels of Workload affected the student satisfaction towards PBL approach.
A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints
Li, Jinquan; Feng, Shuang; Mi, Honghai
In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.
Local Ray-Based Traveltime Computation Using the Linearized Eikonal Equation
Almubarak, Mohammed S.
2013-05-01
The computation of traveltimes plays a critical role in the conventional implementations of Kirchhoff migration. Finite-difference-based methods are considered one of the most effective approaches for traveltime calculations and are therefore widely used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging. In this thesis, I improved the accuracy of the solution of the linearized eikonal equation by constructing a linear system of equations (LSE) based on finite-difference approximation, which is of second-order accuracy. The ill-conditioned LSE is initially regularized and subsequently solved to calculate the traveltime update. Numerical tests proved that this method is as accurate as the second-order eikonal solver. Later arrivals are picked using ray tracing. These traveltimes are binned to the nearest node on a regular grid and empty nodes are estimated by interpolating the known values. The resulting traveltime field is used as an input to the linearized eikonal algorithm, which improves the accuracy of the interpolated nodes and yields a local ray-based traveltime. This is a preliminary study and further investigation is required to test the efficiency and the convergence of the solutions.
Theoretical Maxwell's Equations, Gauge Field and Their Universality Based on One Conservation Law
Institute of Scientific and Technical Information of China (English)
Liu Changmao
2005-01-01
The notion of the inner product of vectors is extended to tensors of different orders, which may replace the vector product usually. The essences of the differential and the codifferential forms are pointed out: they represent the tangent surface and the normal surface fluxes of a tensor, respectively. The definitions of the divergence and the curl of a 2D surface flux of a tensor are obtained.Maxwell's equations, namely, the construction law of field, which were usually established based on two conservation laws of electric charge and imaginary magnetic charge, are derived by the author only by using one conservation law ( mass or fluid flux quantity and so on) and the feature of central field ( or its composition). By the feature of central field ( or its composition), the curl of 2D flux is zero. Both universality of gauge field and the difficulty of magnetic monopole theory ( a magnetic monopole has no effect on electric current just like a couple basing no effect on the sum of forces) are presented: magnetic monopole has no the feature of magnet. Finally it is pointed out that the base of relation of mass and energy is already involved in Maxwell's equations.
Huang, Guanghui; Wan, Jianping; Chen, Hui
2013-02-01
Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.
Majeed, Muhammad Usman
2017-07-19
Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
Newtonian nudging for a Richards equation-based distributed hydrological model
Paniconi, Claudio; Marrocu, Marino; Putti, Mario; Verbunt, Mark
The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model's behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation
Fermion unification model based on the intrinsic SU(8 symmetry of a generalized Dirac equation
Directory of Open Access Journals (Sweden)
Eckart eMarsch
2015-10-01
Full Text Available A natural generalization of the original Dirac spinor into a multi-component spinor is achieved, which corresponds to the single lepton and the three quarks of the first family of the standard model of elementary particle physics. Different fermions result from similarity transformations of the Dirac equation, but apparently there can be no more fermions according to the maximal multiplicity revealed in this study. Rotations in the fermion state space are achieved by the unitary generators of the U(1 and the SU(3 groups, corresponding to quantum electrodynamics (QED based on electric charge and chromodynamics (QCD based on colour charge. In addition to hypercharge the dual degree of freedom of hyperspin emerges, which occurs due to the duplicity implied by the two related (Weyl and Dirac representations of the Dirac equation. This yields the SU(2 symmetry of the weak interaction, which can be married to U(1 to generate the unified electroweak interaction as in the standard model. Therefore, the symmetry group encompassing all the three groups mentioned above is SU(8, which can accommodate and unify the observed eight basic stable fermions.
Strong plasma shock structures based on the Navier--Stokes equations
International Nuclear Information System (INIS)
Abe, K.
1975-01-01
The structure of a plasma collisional shock wave is examined on the basis of the Navier--Stokes equations and simultaneously on the basis of the Fokker--Planck equation. The resultant structures are compared to check the validity of the Navier--Stokes equations applied to the structures of strong shock waves. The Navier--Stokes equations give quite correct structures for weak shock waves. For the strong shock waves, the detailed structures obtained from the Navier--Stokes equations differ from the results of the Fokker--Planck equation, but the shock thicknesses of the two shock waves are in relatively close agreement
Asiri, Sharefa M.
2016-10-20
In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.
Directory of Open Access Journals (Sweden)
Pengjie Hu
2018-06-01
Full Text Available Phosphorus is the primary factor that limits eutrophication of surface waters in aquatic environments. Sediment particles have a strong affinity to phosphorus due to the high specific surface areas and surface active sites. In this paper, a numerical model containing hydrodynamics, sediment, and phosphorus module based on improved Langmuir equation is established, where the processes of adsorption and desorption are considered. Through the statistical analysis of the physical experiment data, the fitting formulas of two important parameters in the Langmuir equation are obtained, which are the adsorption coefficient, ka, and the ratio k between the adsorption coefficient and the desorption coefficient. In order to simulate the experimental flume and get a constant and uniform water flow, a periodical numerical flume is built by adding a streamwise body force, Fx. The adsorbed phosphorus by sediment and the dissolved phosphorus in the water are separately added into the Advection Diffusion equation as a source term to simulate the interaction between them. The result of the numerical model turns out to be well matched with that of the physical experiment and can thus provide the basis for further analysis. With the application of the numerical model to some new and relative cases, the conclusion will be drawn through an afterwards analysis. The concentration of dissolved phosphorus proves to be unevenly distributed along the depth and the maximum value approximately appears in the 3/4 water depth because both the high velocity in the top layer and the high turbulence intensity in the bottom layer can promote sediment adsorption on phosphorus.
Asiri, Sharefa M.
2017-10-08
Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions\\' parameters. (iii) Propose an effective algorithm for selecting the method\\'s design parameters
Silva, A L; DeVries, T J; Tedeschi, L O; Marcondes, M I
2018-04-16
There is a lack of studies that provide models or equations capable of predicting starter feed intake (SFI) for milk-fed dairy calves. Therefore, a multi-study analysis was conducted to identify variables that influence SFI, and to develop equations to predict SFI in milk-fed dairy calves up to 64 days of age. The database was composed of individual data of 176 calves from eight experiments, totaling 6426 daily observations of intake. The information collected from the studies were: birth BW (kg), SFI (kg/day), fluid milk or milk replacer intake (MI; l/day), sex (male or female), breed (Holstein or Holstein×Gyr crossbred) and age (days). Correlations between SFI and the quantitative variables MI, birth BW, metabolic birth BW, fat intake, CP intake, metabolizable energy intake, and age were calculated. Subsequently, data were graphed, and based on a visual appraisal of the pattern of the data, an exponential function was chosen. Data were evaluated using a meta-analysis approach to estimate fixed and random effects of the experiments using nonlinear mixed coefficient statistical models. A negative correlation between SFI and MI was observed (r=-0.39), but age was positively correlated with SFI (r=0.66). No effect of liquid feed source (milk or milk replacer) was observed in developing the equation. Two equations, significantly different for all parameters, were fit to predict SFI for calves that consume less than 5 (SFI5) l/day of milk or milk replacer: ${\\rm SFI}_{{\\,\\lt\\,5}} {\\equals}0.1839_{{\\,\\pm\\,0.0581}} {\\times}{\\rm MI}{\\times}{\\rm exp}^{{\\left( {\\left( {0.0333_{{\\,\\pm\\,0.0021 }} {\\minus}0.0040_{{\\,\\pm\\,0.0011}} {\\times}{\\rm MI}} \\right){\\times}\\left( {{\\rm A}{\\minus}{\\rm }\\left( {0.8302_{{\\,\\pm\\,0.5092}} {\\plus}6.0332_{{\\,\\pm\\,0.3583}} {\\times}{\\rm MI}} \\right)} \\right)} \\right)}} {\\minus}\\left( {0.12{\\times}{\\rm MI}} \\right)$ ; ${\\rm SFI}_{{\\,\\gt\\,5}} {\\equals}0.1225_{{\\,\\pm\\,0.0005 }} {\\times
Use of chemistry software to teach and assess model-based reaction and equation knowledge
Directory of Open Access Journals (Sweden)
Kevin Pyatt
2014-12-01
Full Text Available This study investigated the challenges students face when learning chemical reactions in a first-year chemistry course and the effectiveness of a curriculum and software implementation that was used to teach and assess student understanding of chemical reactions and equations. This study took place over a two year period in a public suburban high-school, in southwestern USA. Two advanced placement (AP chemistry classes participated, referred to here as study group A (year 1, N = 14; and study group B (year 2, N = 21. The curriculum for a first-year chemistry course (group A was revised to include instruction on reaction-types. The second year of the study involved the creation and implementation of a software solution which promoted mastery learning of reaction-types. Students in both groups benefited from the reaction-type curriculum and achieved proficiency in chemical reactions and equations. The findings suggest there was an added learning benefit to using the reaction-type software solution. This study also found that reaction knowledge was a moderate to strong predictor of chemistry achievement. Based on regression analysis, reaction knowledge significantly predicted chemistry achievement for both groups.
Multi-dimensional upwinding-based implicit LES for the vorticity transport equations
Foti, Daniel; Duraisamy, Karthik
2017-11-01
Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.
International Nuclear Information System (INIS)
Senol, Aynur
2013-01-01
Highlights: • Vapour pressures of (solvent + salt) systems have been estimated through a solvation-based model. • Two structural forms of the generalized solvation model using the Antoine equation have been performed. • A simplified concentration-dependent vapour pressure model has been also processed. • The model reliability analysis has been performed in terms of a log-ratio objective function. • The reliability of the models has been interpreted in terms of the statistical design factors. -- Abstract: This study deals with modelling the vapour pressure of a (solvent + salt) system on the basis of the principles of LSER. The solvation model framework clarifies the simultaneous impact of several physical variables such as the vapour pressure of a pure solvent estimated by the Antoine equation, the solubility and solvatochromic parameters of the solvent and the physical properties of the ionic salt. It has been analyzed independently the performance of two structural forms of the generalized model, i.e., a relation depending on an integration of the properties of the solvent and the ionic salt and a relation on a reduced property-basis. A simplified concentration-dependent vapour pressure model has been also explored and implemented on the relevant systems. The vapour pressure data of sixteen (solvent + salt) systems have been processed to analyze statistically the reliability of existing models in terms of a log–ratio objective function. The proposed vapour pressure models match relatively well the observed performance, yielding the overall design factors of 1.066 and 1.073 for the solvation-based models with the integrated and reduced properties, and 1.008 for the concentration-based model, respectively
Niang, Oumar; Thioune, Abdoulaye; El Gueirea, Mouhamed Cheikh; Deléchelle, Eric; Lemoine, Jacques
2012-09-01
The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.
Multi criteria evaluation for universal soil loss equation based on geographic information system
Purwaamijaya, I. M.
2018-05-01
The purpose of this research were to produce(l) a conceptual, functional model designed and implementation for universal soil loss equation (usle), (2) standard operational procedure for multi criteria evaluation of universal soil loss equation (usle) using geographic information system, (3) overlay land cover, slope, soil and rain fall layers to gain universal soil loss equation (usle) using multi criteria evaluation, (4) thematic map of universal soil loss equation (usle) in watershed, (5) attribute table of universal soil loss equation (usle) in watershed. Descriptive and formal correlation methods are used for this research. Cikapundung Watershed, Bandung, West Java, Indonesia was study location. This research was conducted on January 2016 to May 2016. A spatial analysis is used to superimposed land cover, slope, soil and rain layers become universal soil loss equation (usle). Multi criteria evaluation for universal soil loss equation (usle) using geographic information system could be used for conservation program.
International Nuclear Information System (INIS)
Leung Shingyu; Qian Jianliang
2010-01-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
Quantitative phase microscopy for cellular dynamics based on transport of intensity equation.
Li, Ying; Di, Jianglei; Ma, Chaojie; Zhang, Jiwei; Zhong, Jinzhan; Wang, Kaiqiang; Xi, Teli; Zhao, Jianlin
2018-01-08
We demonstrate a simple method for quantitative phase imaging of tiny transparent objects such as living cells based on the transport of intensity equation. The experiments are performed using an inverted bright field microscope upgraded with a flipping imaging module, which enables to simultaneously create two laterally separated images with unequal defocus distances. This add-on module does not include any lenses or gratings and is cost-effective and easy-to-alignment. The validity of this method is confirmed by the measurement of microlens array and human osteoblastic cells in culture, indicating its potential in the applications of dynamically measuring living cells and other transparent specimens in a quantitative, non-invasive and label-free manner.
Energy Technology Data Exchange (ETDEWEB)
Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)
2016-07-01
We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.
A Kohn–Sham equation solver based on hexahedral finite elements
International Nuclear Information System (INIS)
Fang Jun; Gao Xingyu; Zhou Aihui
2012-01-01
We design a Kohn–Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C 60 , C 120 , and C 275 H 172 . It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.
Hu, Junbao; Meng, Xin; Wei, Qi; Kong, Yan; Jiang, Zhilong; Xue, Liang; Liu, Fei; Liu, Cheng; Wang, Shouyu
2018-03-01
Wide-field microscopy is commonly used for sample observations in biological research and medical diagnosis. However, the tilting error induced by the oblique location of the image recorder or the sample, as well as the inclination of the optical path often deteriorates the imaging quality. In order to eliminate the tilting in microscopy, a numerical tilting compensation technique based on wavefront sensing using transport of intensity equation method is proposed in this paper. Both the provided numerical simulations and practical experiments prove that the proposed technique not only accurately determines the tilting angle with simple setup and procedures, but also compensates the tilting error for imaging quality improvement even in the large tilting cases. Considering its simple systems and operations, as well as image quality improvement capability, it is believed the proposed method can be applied for tilting compensation in the optical microscopy.
Fast integration-based prediction bands for ordinary differential equation models.
Hass, Helge; Kreutz, Clemens; Timmer, Jens; Kaschek, Daniel
2016-04-15
To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature a large number of parameters, sparse observations of the model components and lack of information in the available data. Due to the curse of dimensionality, classical and sampling approaches propagating parameter uncertainties to predictions are hardly feasible and insufficient. However, for experimental design and to discriminate between competing models, prediction and confidence bands are essential. To circumvent the hurdles of the former methods, an approach to calculate a profile likelihood on arbitrary observations for a specific time point has been introduced, which provides accurate confidence and prediction intervals for nonlinear models and is computationally feasible for high-dimensional models. In this article, reliable and smooth point-wise prediction and confidence bands to assess the model's uncertainty on the whole time-course are achieved via explicit integration with elaborate correction mechanisms. The corresponding system of ordinary differential equations is derived and tested on three established models for cellular signalling. An efficiency analysis is performed to illustrate the computational benefit compared with repeated profile likelihood calculations at multiple time points. The integration framework and the examples used in this article are provided with the software package Data2Dynamics, which is based on MATLAB and freely available at http://www.data2dynamics.org helge.hass@fdm.uni-freiburg.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e
Equation-free analysis of agent-based models and systematic parameter determination
Thomas, Spencer A.; Lloyd, David J. B.; Skeldon, Anne C.
2016-12-01
Agent based models (ABM)s are increasingly used in social science, economics, mathematics, biology and computer science to describe time dependent systems in circumstances where a description in terms of equations is difficult. Yet few tools are currently available for the systematic analysis of ABM behaviour. Numerical continuation and bifurcation analysis is a well-established tool for the study of deterministic systems. Recently, equation-free (EF) methods have been developed to extend numerical continuation techniques to systems where the dynamics are described at a microscopic scale and continuation of a macroscopic property of the system is considered. To date, the practical use of EF methods has been limited by; (1) the over-head of application-specific implementation; (2) the laborious configuration of problem-specific parameters; and (3) large ensemble sizes (potentially) leading to computationally restrictive run-times. In this paper we address these issues with our tool for the EF continuation of stochastic systems, which includes algorithms to systematically configuration problem specific parameters and enhance robustness to noise. Our tool is generic and can be applied to any 'black-box' simulator and determines the essential EF parameters prior to EF analysis. Robustness is significantly improved using our convergence-constraint with a corrector-repeat (C3R) method. This algorithm automatically detects outliers based on the dynamics of the underlying system enabling both an order of magnitude reduction in ensemble size and continuation of systems at much higher levels of noise than classical approaches. We demonstrate our method with application to several ABM models, revealing parameter dependence, bifurcation and stability analysis of these complex systems giving a deep understanding of the dynamical behaviour of the models in a way that is not otherwise easily obtainable. In each case we demonstrate our systematic parameter determination stage for
McDonald, A. David; Sandal, Leif Kristoffer
1998-01-01
Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per replication. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic, put forward by Hurn and Lin...
Directory of Open Access Journals (Sweden)
Jinping Tang
2017-01-01
Full Text Available Optical tomography is an emerging and important molecular imaging modality. The aim of optical tomography is to reconstruct optical properties of human tissues. In this paper, we focus on reconstructing the absorption coefficient based on the radiative transfer equation (RTE. It is an ill-posed parameter identification problem. Regularization methods have been broadly applied to reconstruct the optical coefficients, such as the total variation (TV regularization and the L1 regularization. In order to better reconstruct the piecewise constant and sparse coefficient distributions, TV and L1 norms are combined as the regularization. The forward problem is discretized with the discontinuous Galerkin method on the spatial space and the finite element method on the angular space. The minimization problem is solved by a Jacobian-based Levenberg-Marquardt type method which is equipped with a split Bregman algorithms for the L1 regularization. We use the adjoint method to compute the Jacobian matrix which dramatically improves the computation efficiency. By comparing with the other imaging reconstruction methods based on TV and L1 regularizations, the simulation results show the validity and efficiency of the proposed method.
Two-level method for unsteady Navier-Stokes equations based on a new projection
International Nuclear Information System (INIS)
Hou Yanren; Li Kaitai
2004-12-01
A two-level algorithm for the two dimensional unsteady Navier-Stokes equations based on a new projection is proposed and investigated. The approximate solution is solved as a sum of a large eddy component and a small eddy component, which are in the sense of the new projection, constructed in this paper. These two terms advance in time explicitly. Actually, the new algorithm proposed here can be regarded as a sort of postprocessing algorithm for the standard Galerkin method (SGM). The large eddy part is solved by SGM in the usual L 2 -based large eddy subspace while the small eddy part (the correction part) is obtained in its complement subspace in the sense of the new projection. The stability analysis indicates the improvement of the stability comparing with SGM of the same scale, and the L 2 -error estimate shows that the scheme can improve the accuracy of SGM approximation for half order. We also propose a numerical implementation based on Lagrange multiplier for this two-level algorithm. (author)
Development of uncertainty-based work injury model using Bayesian structural equation modelling.
Chatterjee, Snehamoy
2014-01-01
This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.
International Nuclear Information System (INIS)
Elfelsoufi, Z.; Azrar, L.
2016-01-01
In this paper, a mathematical modeling of flutter and divergence analyses of fluid conveying pipes based on integral equation formulations is presented. Dynamic stability problems related to fluid pressure, velocity, tension, topography slope and viscoelastic supports and foundations are formulated. A methodological approach is presented and the required matrices, associated to the influencing fluid and pipe parameters, are explicitly given. Internal discretizations are used allowing to investigate the deformation, the bending moment, slope and shear force at internal points. Velocity–frequency, pressure-frequency and tension-frequency curves are analyzed for various fluid parameters and internal elastic supports. Critical values of divergence and flutter behaviors with respect to various fluid parameters are investigated. This model is general and allows the study of dynamic stability of tubes crossed by stationary and instationary fluid on various types of supports. Accurate predictions can be obtained and are of particular interest for a better performance and for an optimal safety of piping system installations. - Highlights: • Modeling the flutter and divergence of fluid conveying pipes based on RBF. • Dynamic analysis of a fluid conveying pipe with generalized boundary conditions. • Considered parameters fluid are the pressure, tension, slopes topography, velocity. • Internal support increase the critical velocity value. • This methodologies determine the fluid parameters effects.
Directory of Open Access Journals (Sweden)
Yunjiao Bai
2015-01-01
Full Text Available The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.
Chemical and physical FET-based sensors or variations on an equation
Olthuis, Wouter
2005-01-01
This paper exposes the continuous thread of Bergveld’s work: the model equation of the field-effect transistor (FET) derived and repeated in the theoretical section. Zooming in on some of the variables of this equation leads us to several of his important projects. A short description and typical
Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations
Bhowmik, S.K.; Stolk, C.C.
2011-01-01
We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given
Zhang, Chuang; Guo, Zhaoli; Chen, Songze
2017-12-01
An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
International Nuclear Information System (INIS)
Krishnaswami, Govind S.
2006-01-01
Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren't differential equations as they involve left annihilation, which doesn't satisfy the Leibnitz rule with concatenation. But left annihilation is a derivation of the commutative shuffle product. Moreover shuffle and concatenation combine to define a bialgebra. Motivated by deformation quantization, we expand concatenation around shuffle in powers of q, whose physical value is 1. At zeroth order the loop equations become quadratic PDEs in the shuffle algebra. If the variation of the action is linear in iterated commutators of left annihilations, these quadratic PDEs linearize by passage to shuffle reciprocal of correlations. Remarkably, this is true for regularized versions of the Yang-Mills, Chern-Simons and Gaussian actions. But the linear equations are underdetermined just as the loop equations were. For any particular solution, the shuffle reciprocal is explicitly inverted to get the zeroth order gluon correlations. To go beyond zeroth order, we find a Poisson bracket on the shuffle algebra and associative q-products interpolating between shuffle and concatenation. This method, and a complementary one of deforming annihilation rather than product are shown to give over and underestimates for correlations of a gaussian matrix model
Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu
2016-08-01
Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.
A clutter removal method for the Doppler ultrasound signal based on a nonlinear diffusion equation
International Nuclear Information System (INIS)
Li Peng; Xin Pengcheng; Bian Zhengzhong; Yu Gang
2008-01-01
Strong clutter components produced by stationary and slow-moving tissue structures render the lower frequency part of the spectrogram useless and degrade the accuracy of clinical ultrasound indices. An adaptive method based on the nonlinear forward-and-backward diffusion equation (FAB-DE) is proposed to remove strong clutter components from the contaminated Doppler signal. The clutter signal is extracted first by the FAB-DE accurately, in which the nonlinear diffusion coefficient function of the FAB-DE locally adjusts according to signal features and the diffusion adaptively switches between forward and backward mode. The present method has been validated by simulated and realistic pulse wave Doppler signals, and compared with the conventional high pass filter and the matching pursuit method. The simulation results, including spectrogram, mean velocity error, standard deviation of mean velocity and signal-to-clutter ratio of a decontaminated signal, demonstrate that the present FAB-DE method can remove clutter sufficiently and retain more low blood components simultaneously as compared with the other two methods. Results of the realistic Doppler blood signal, including spectrogram and low-frequency part of the spectrum, support the conclusion drawn from simulation cases
International Nuclear Information System (INIS)
Kitazumi, Yuki; Shirai, Osamu; Yamamoto, Masahiro; Kano, Kenji
2013-01-01
Graphical abstract: - Highlights: • Diffuse double layers overlap with each other in the micropore. • The overlapping of the diffuse double layer affects the double layer capacitance. • The electric field becomes weak in the micropore. • The electroneutrality is unsatisfactory in the micropore. - Abstract: The structure of the diffuse double layer around a nm-sized micropore on porous electrodes has been studied by numerical simulation using the Poisson–Boltzmann equation. The double layer capacitance of the microporous electrode strongly depends on the electrode potential, the electrolyte concentration, and the size of the micropore. The potential and the electrolyte concentration dependence of the capacitance is different from that of the planner electrode based on the Gouy's theory. The overlapping of the diffuse double layer becomes conspicuous in the micropore. The overlapped diffuse double layer provides the mild electric field. The intensified electric field exists at the rim of the orifice of the micropore because of the expansion of the diffuse double layers. The characteristic features of microporous electrodes are caused by the heterogeneity of the electric field around the micropores
Simulation of flux during electro-membrane extraction based on the Nernst-Planck equation.
Gjelstad, Astrid; Rasmussen, Knut Einar; Pedersen-Bjergaard, Stig
2007-12-07
The present work has for the first time described and verified a theoretical model of the analytical extraction process electro-membrane extraction (EME), where target analytes are extracted from an aqueous sample, through a thin layer of 2-nitrophenyl octylether immobilized as a supported liquid membrane (SLM) in the pores in the wall of a porous hollow fibre, and into an acceptor solution present inside the lumen of the hollow fibre by the application of an electrical potential difference. The mathematical model was based on the Nernst-Planck equation, and described the flux over the SLM. The model demonstrated that the magnitude of the electrical potential difference, the ion balance of the system, and the absolute temperature influenced the flux of analyte across the SLM. These conclusions were verified by experimental data with five basic drugs. The flux was strongly dependent of the potential difference over the SLM, and increased potential difference resulted in an increase in the flux. The ion balance, defined as the sum of ions in the donor solution divided by the sum of ions in the acceptor solution, was shown to influence the flux, and high ionic concentration in the acceptor solution relative to the sample solution was advantageous for high flux. Different temperatures also led to changes in the flux in the EME system.
Study of carbon dioxide gas treatment based on equations of kinetics in plasma discharge reactor
Abedi-Varaki, Mehdi
2017-08-01
Carbon dioxide (CO2) as the primary greenhouse gas, is the main pollutant that is warming earth. CO2 is widely emitted through the cars, planes, power plants and other human activities that involve the burning of fossil fuels (coal, natural gas and oil). Thus, there is a need to develop some method to reduce CO2 emission. To this end, this study investigates the behavior of CO2 in dielectric barrier discharge (DBD) plasma reactor. The behavior of different species and their reaction rates are studied using a zero-dimensional model based on equations of kinetics inside plasma reactor. The results show that the plasma reactor has an effective reduction on the CO2 density inside the reactor. As a result of reduction in the temporal variations of reaction rate, the speed of chemical reactions for CO2 decreases and very low concentration of CO2 molecules inside the plasma reactor is generated. The obtained results are compared with the existing experimental and simulation findings in the literature.
A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations
International Nuclear Information System (INIS)
Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q
2013-01-01
Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field
Application of a mechanism-based rate equation to black liquor gasification rate data
Energy Technology Data Exchange (ETDEWEB)
Overacker, N.L.; Waag, K.J.; Frederick, W.J. [Oregon State University, OR (United States). Dept. of Chemical Engineering; Whitty, K.J.
1995-09-01
There is growing interest worldwide to develop alternate chemical recovery processes for paper mills which are cheaper, safer, more efficient and more environmentally sound than traditional technology. Pressurized gasification of black liquor is the basis for many proposed schemes and offers the possibility to double the amount of electricity generated per unit of dry black liquor solids. Such technology also has capital, safety and environmental advantages. One of the most important considerations regarding this emerging technology is the kinetics of the gasification reaction. This has been studied empirically at Aabo Akademi University for the pressurized gasification with carbon dioxide and steam. For the purposes of reactor modeling and scale-up, however, a thorough understanding of the mechanism behind the reaction is desirable. This report discusses the applicability of a mechanism-based rate equation to gasification of black liquor. The mechanism considered was developed for alkali-catalyzed gasification of carbon and is tested using black liquor gasification data obtained during simultaneous reaction with H{sub 2}O and CO. Equilibrium considerations and the influence of the water-gas shift reaction are also discussed. The work presented here is a cooperative effort between Aabo Akademi University and Oregon State University. The experimental work and some of the data analysis was performed at Aabo Akademi University. Development of the models and consideration of their applicability was performed primarily at Oregon State University
Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System
Directory of Open Access Journals (Sweden)
Wenyu Yang
2014-01-01
Full Text Available Particle swarm optimization (PSO is inspired by sociological behavior. In this paper, we interpret PSO as a finite difference scheme for solving a system of stochastic ordinary differential equations (SODE. In this framework, the position points of the swarm converge to an equilibrium point of the SODE and the local attractors, which are easily defined by the present position points, also converge to the global attractor. Inspired by this observation, we propose a class of modified PSO iteration methods (MPSO based on local attractors of the SODE. The idea of MPSO is to choose the next update state near the present local attractor, rather than the present position point as in the original PSO, according to a given probability density function. In particular, the quantum-behaved particle swarm optimization method turns out to be a special case of MPSO by taking a special probability density function. The MPSO methods with six different probability density functions are tested on a few benchmark problems. These MPSO methods behave differently for different problems. Thus, our framework not only gives an interpretation for the ordinary PSO but also, more importantly, provides a warehouse of PSO-like methods to choose from for solving different practical problems.
Hugoniot-based equations of state for two filled EPDM rubbers
Pacheco, Adam; Dattelbaum, Dana; Orler, E.; Gustavsen, R.
2013-06-01
The shock response of silica filled and Kevlar filled ethylene-propylene-diene (EPDM) rubbers was studied using gas gun-driven plate impact experiments. Both materials are proprietary formulations made by Kirkhill-TA, Brea CA USA, and are used for ablative internal rocket motor insulation. Two types of experiments were performed. In the first, the filled-EPDM sample was mounted on the front of the projectile and impacted a Lithium Fluoride (LiF) window. The Hugoniot state was determined from the measured projectile velocity, the EPDM/LiF interface velocity (measured using VISAR) and impedance matching to LiF. In the second type of experiment, electromagnetic particle velocity gauges were embedded between layers of filled-EPDM. These provided in situ particle velocity and shock velocity measurements. Experiments covered a pressure range of 0.34 - 14 GPa. Hugoniot-based equations of state were obtained for both materials, and will be compared to those of other filled elastomers such as silica-filled polydimethylsiloxane and adiprene. Work performed while at Los Alamos National Laboratory.
Energy Technology Data Exchange (ETDEWEB)
Fox, Zachary [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Neuert, Gregor [Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, Tennessee 37232 (United States); Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, Tennessee 37232 (United States); Department of Biomedical Engineering, Vanderbilt University School of Engineering, Nashville, Tennessee 37232 (United States); Munsky, Brian [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States)
2016-08-21
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.
Directory of Open Access Journals (Sweden)
Qing Chen
2017-01-01
Full Text Available Shale gas is an effective gas resource all over the world. The evaluation of pore structure plays a critical role in exploring shale gas efficiently. Nitrogen adsorption experiment is one of the significant approaches to analyze pore size structure of shale. Shale is extremely heterogeneous due to component diversity and structure complexity. Therefore, adsorption isotherms for homogeneous adsorbents and empirical isotherms may not apply to shale. The shape of adsorption-desorption curve indicates that nitrogen adsorption on shale includes monolayer adsorption, multilayer adsorption, and capillary condensation. Usually, Langmuir isotherm is a monolayer adsorption model for ideal interfaces; BET (Brunauer, Emmett, Teller adsorption isotherm is a multilayer adsorption model based on specific assumptions; Freundlich isotherm is an empirical equation widely applied in liquid phase adsorption. In this study, a new nitrogen adsorption isotherm is applied to simultaneously depict monolayer adsorption, multilayer adsorption, and capillary condensation, which provides more real and accurate representation of nitrogen adsorption on shale. In addition, parameters are discussed in relation to heat of adsorption which is relevant to the shape of the adsorption isotherm curve. The curve fitting results indicate that our new nitrogen adsorption isotherm can appropriately describe the whole process of nitrogen adsorption on shale.
A spatial discretization of the MHD equations based on the finite volume - spectral method
International Nuclear Information System (INIS)
Miyoshi, Takahiro
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
DAE Tools: equation-based object-oriented modelling, simulation and optimisation software
Directory of Open Access Journals (Sweden)
Dragan D. Nikolić
2016-04-01
Full Text Available In this work, DAE Tools modelling, simulation and optimisation software, its programming paradigms and main features are presented. The current approaches to mathematical modelling such as the use of modelling languages and general-purpose programming languages are analysed. The common set of capabilities required by the typical simulation software are discussed, and the shortcomings of the current approaches recognised. A new hybrid approach is introduced, and the modelling languages and the hybrid approach are compared in terms of the grammar, compiler, parser and interpreter requirements, maintainability and portability. The most important characteristics of the new approach are discussed, such as: (1 support for the runtime model generation; (2 support for the runtime simulation set-up; (3 support for complex runtime operating procedures; (4 interoperability with the third party software packages (i.e. NumPy/SciPy; (5 suitability for embedding and use as a web application or software as a service; and (6 code-generation, model exchange and co-simulation capabilities. The benefits of an equation-based approach to modelling, implemented in a fourth generation object-oriented general purpose programming language such as Python are discussed. The architecture and the software implementation details as well as the type of problems that can be solved using DAE Tools software are described. Finally, some applications of the software at different levels of abstraction are presented, and its embedding capabilities and suitability for use as a software as a service is demonstrated.
Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation
Directory of Open Access Journals (Sweden)
Xiaoyan Deng
2009-01-01
into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.
International Nuclear Information System (INIS)
Gao Wen-Wu; Wang Zhi-Gang
2014-01-01
Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions. (general)
Gas-evolution oscillators. 10. A model based on a delay equation
Energy Technology Data Exchange (ETDEWEB)
Bar-Eli, K.; Noyes, R.M. [Univ. of Oregon, Eugene, OR (United States)
1992-09-17
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas.
Gas-evolution oscillators. 10. A model based on a delay equation
International Nuclear Information System (INIS)
Bar-Eli, K.; Noyes, R.M.
1992-01-01
This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas
Asiri, Sharefa M.
2017-01-01
Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
Directory of Open Access Journals (Sweden)
Maisarah Jalalonmuhali
2018-01-01
Full Text Available Background. To assess the performance of different GFR estimating equations, test the diagnostic value of serum cystatin-C, and compare the applicability of cystatin-C based equation with serum creatinine based equation for estimating GFR (eGFR in comparison with measured GFR in the elderly Malaysian patients. Methods. A cross-sectional study recruiting volunteered patients 65 years and older attending medical outpatient clinic. 51 chromium EDTA (51Cr-EDTA was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA, four-variable Modification of Diet in Renal Disease (4-MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations using serum creatinine (CKD-EPIcr as well as serum cystatin-C (CKD-EPIcys were calculated. Results. A total of 40 patients, 77.5% male, with mean measured GFR 41.2±18.9 ml/min/1.73 m2 were enrolled. Mean bias was the smallest for 4-MDRD; meanwhile, CKD-EPIcr had the highest precision and accuracy with lower limit of agreement among other equations. CKD-EPIcys equation did not show any improvement in GFR estimation in comparison to CKD-EPIcr and MDRD. Conclusion. The CKD-EPIcr formula appears to be more accurate and correlates better with measured GFR in this cohort of elderly patients.
Jalalonmuhali, Maisarah; Elagel, Salma Mohamed Abouzriba; Tan, Maw Pin; Lim, Soo Kun; Ng, Kok Peng
2018-01-01
To assess the performance of different GFR estimating equations, test the diagnostic value of serum cystatin-C, and compare the applicability of cystatin-C based equation with serum creatinine based equation for estimating GFR (eGFR) in comparison with measured GFR in the elderly Malaysian patients. A cross-sectional study recruiting volunteered patients 65 years and older attending medical outpatient clinic. 51 chromium EDTA ( 51 Cr-EDTA) was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA), four-variable Modification of Diet in Renal Disease (4-MDRD), and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations using serum creatinine (CKD-EPIcr) as well as serum cystatin-C (CKD-EPIcys) were calculated. A total of 40 patients, 77.5% male, with mean measured GFR 41.2 ± 18.9 ml/min/1.73 m 2 were enrolled. Mean bias was the smallest for 4-MDRD; meanwhile, CKD-EPIcr had the highest precision and accuracy with lower limit of agreement among other equations. CKD-EPIcys equation did not show any improvement in GFR estimation in comparison to CKD-EPIcr and MDRD. The CKD-EPIcr formula appears to be more accurate and correlates better with measured GFR in this cohort of elderly patients.
International Nuclear Information System (INIS)
Klose, Alexander D.
2010-01-01
This note serves as an introduction to two papers by Klose et al. and provides a brief review of the latest developments in optical tomography of scattering tissue. We discuss advancements made in solving the forward model for light propagation based on the radiative transfer equation, in reconstructing scattering and absorption cross sections of tissue, and in molecular imaging of luminescent sources.
Low-lying qq(qq)-bar states in a relativistic model based on the Bethe-Salpeter equation
International Nuclear Information System (INIS)
Ram, B.; Kriss, V.
1985-01-01
Low-lying qq(qq)-bar states are analysed in a previously given relativistic model based on the Bethe-Salpeter equation. It is not got M-diquonia, P-mesonia, or meson molecules, but it is got T-diquonia
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik
2009-06-01
The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.
Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes
Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca
2018-01-01
Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.
Bartels, Robert E.
2002-01-01
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo
2007-01-01
A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.
International Nuclear Information System (INIS)
Hecht, M.J.; Catton, I.; Kastenberg, W.E.
1976-12-01
An equation of state based on the properties of normal fluids, the law of rectilinear averages, and the second law of thermodynamics can be derived for advanced LMFBR fuels on the basis of the vapor pressure, enthalpy of vaporization, change in heat capacity upon vaporization, and liquid density at the melting point. The method consists of estimating an equation of state by means of the law of rectilinear averages and the second law of thermodynamics, integrating by means of the second law until an instability is reached, and then extrapolating by means of a self-consistent estimation of the enthalpy of vaporization
A Forward GPS Multipath Simulator Based on the Vegetation Radiative Transfer Equation Model.
Wu, Xuerui; Jin, Shuanggen; Xia, Junming
2017-06-05
Global Navigation Satellite Systems (GNSS) have been widely used in navigation, positioning and timing. Nowadays, the multipath errors may be re-utilized for the remote sensing of geophysical parameters (soil moisture, vegetation and snow depth), i.e., GPS-Multipath Reflectometry (GPS-MR). However, bistatic scattering properties and the relation between GPS observables and geophysical parameters are not clear, e.g., vegetation. In this paper, a new element on bistatic scattering properties of vegetation is incorporated into the traditional GPS-MR model. This new element is the first-order radiative transfer equation model. The new forward GPS multipath simulator is able to explicitly link the vegetation parameters with GPS multipath observables (signal-to-noise-ratio (SNR), code pseudorange and carrier phase observables). The trunk layer and its corresponding scattering mechanisms are ignored since GPS-MR is not suitable for high forest monitoring due to the coherence of direct and reflected signals. Based on this new model, the developed simulator can present how the GPS signals (L1 and L2 carrier frequencies, C/A, P(Y) and L2C modulations) are transmitted (scattered and absorbed) through vegetation medium and received by GPS receivers. Simulation results show that the wheat will decrease the amplitudes of GPS multipath observables (SNR, phase and code), if we increase the vegetation moisture contents or the scatters sizes (stem or leaf). Although the Specular-Ground component dominates the total specular scattering, vegetation covered ground soil moisture has almost no effects on the final multipath signatures. Our simulated results are consistent with previous results for environmental parameter detections by GPS-MR.
A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.
Harrison, Jonathan U; Yates, Christian A
2016-09-01
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.
Refraction traveltime tomography based on damped wave equation for irregular topographic model
Park, Yunhui; Pyun, Sukjoon
2018-03-01
Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography. This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem. As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography
International Nuclear Information System (INIS)
Bessho, Y.; Uchikawa, S.
1985-01-01
A subchannel analysis program, MENUETT, is developed for evaluation of thermal-hydraulic characteristics in boiling water reactor fuel bundles. This program is based on five conservation equations of two-phase flow with the drift-flux correlation. The cross flows are calculated separately for liquid and vapor phases from the lateral momentum conservation equation. The effects of turbulent mixing and void drift are accounted for in the program. The conservation equations are implicitly differentiated with the convective terms by the donor-cell method, and are solved iteratively in the axial and lateral directions. Data of the 3 X 3 rod bundle experiments are used for program verification. The lateral distributions of equilibrium quality and mass flow rate at the bundle exit calculated by the program compare satisfactorily with the experimental results
Directory of Open Access Journals (Sweden)
Partov Doncho
2017-01-01
Full Text Available The paper presents analysis of the stress-strain behaviour and deflection changes due to creep in statically determinate composite steel-concrete beam according to EUROCODE 2, ACI209R-92 and Gardner&Lockman models. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann - Volterra for the concrete part considering the above mentioned models. On the basis of the theory of viscoelastic body of Maslov-Arutyunian-Trost-Zerna-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time 't', two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernel function in the integral equation is presented. Example with the model proposed is investigated.
Si, Guo-Ning; Chen, Lan; Li, Bao-Guo
2014-04-01
Base on the Kawakita powder compression equation, a general theoretical model for predicting the compression characteristics of multi-components pharmaceutical powders with different mass ratios was developed. The uniaxial flat-face compression tests of powder lactose, starch and microcrystalline cellulose were carried out, separately. Therefore, the Kawakita equation parameters of the powder materials were obtained. The uniaxial flat-face compression tests of the powder mixtures of lactose, starch, microcrystalline cellulose and sodium stearyl fumarate with five mass ratios were conducted, through which, the correlation between mixture density and loading pressure and the Kawakita equation curves were obtained. Finally, the theoretical prediction values were compared with experimental results. The analysis showed that the errors in predicting mixture densities were less than 5.0% and the errors of Kawakita vertical coordinate were within 4.6%, which indicated that the theoretical model could be used to predict the direct compaction characteristics of multi-component pharmaceutical powders.
Method of constructing a fundamental equation of state based on a scaling hypothesis
Rykov, V. A.; Rykov, S. V.; Kudryavtseva, I. V.; Sverdlov, A. V.
2017-11-01
The work studies the issues associated with the construction of the equation of state (EOS) taking due account of substance behavior in the critical region and associated with the scaling theory of critical phenomena (ST). The authors have developed a new version of the scaling hypothesis; this approach uses the following: a) substance equation of state having a form of a Schofield-Litster-Ho linear model (LM) and b) the Benedek hypothesis. The Benedek hypothesis has found a similar behavior character for a number of properties (isochoric and isobaric heat capacities, isothermal compressibility coefficient) at critical and near-critical isochors in the vicinity of the critical point. A method is proposed to build the fundamental equation of state (FEOS) which satisfies the ST power laws. The FEOS building method is verified by building the equation of state for argon within the state parameters range: up to 1000 MPa in terms of pressure, and from 83.056 К to 13000 К in terms of temperature. The executed comparison with the fundamental equations of state of Stewart-Jacobsen (1989), of Kozlov at al (1996), of Tegeler-Span-Wagner (1999), of has shown that the FEOS describes the known experimental data with an essentially lower error.
Modeling for cardiac excitation propagation based on the Nernst-Planck equation and homogenization.
Okada, Jun-ichi; Sugiura, Seiryo; Hisada, Toshiaki
2013-06-01
The bidomain model is a commonly used mathematical model of the electrical properties of the cardiac muscle that takes into account the anisotropy of both the intracellular and extracellular spaces. However, the equations contain self-contradiction such that the update of ion concentrations does not consider intracellular or extracellular ion movements due to the gradient of electric potential and the membrane charge as capacitive currents in spite of the fact that those currents are taken into account in forming Kirchhoff's first law. To overcome this problem, we start with the Nernst-Planck equation, the ionic conservation law, and the electroneutrality condition at the cellular level, and by introducing a homogenization method and assuming uniformity of variables at the microscopic scale, we derive rational bidomain equations at the macroscopic level.
Treatment of pairing correlations based on the equations of motion for zero-coupled pair operators
International Nuclear Information System (INIS)
Andreozzi, F.; Covello, A.; Gargano, A.; Ye, L.J.; Porrino, A.
1985-01-01
The pairing problem is treated by means of the equations of motion for zero-coupled pair operators. Exact equations for the seniority-v states of N particles are derived. These equations can be solved by a step-by-step procedure which consists of progressively adding pairs of particles to a core. The theory can be applied at several levels of approximation depending on the number of core states which are taken into account. Some numerical applications to the treatment of v = 0, v = 1, and v = 2 states in the Ni isotopes are performed. The accuracy of various approximations is tested by comparison with exact results. For the seniority-one and seniority-two problems it turns out that the results obtained from the first-order theory are very accurate, while those of higher order calculations are practically exact. Concerning the seniority-zero problem, a fifth-order calculation reproduces quite well the three lowest states
An integral equation-based numerical solver for Taylor states in toroidal geometries
O'Neil, Michael; Cerfon, Antoine J.
2018-04-01
We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation
Plante, Ianik; Wu, Honglu
2014-01-01
Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the
Simulation of quantum dynamics based on the quantum stochastic differential equation.
Li, Ming
2013-01-01
The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.
Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish
2011-08-01
We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.
Filters in topology optimization based on Helmholtz‐type differential equations
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Sigmund, Ole
2011-01-01
The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology...... from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation...
An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation
Asiri, Sharefa M.; Zayane, Chadia; Laleg-Kirati, Taous-Meriem
2015-01-01
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.
Elbanna, Hesham M.; Carlson, Leland A.
1992-01-01
The quasi-analytical approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. Results are compared to those obtained by the direct finite difference approach and both methods are evaluated to determine their computational accuracy and efficiency. The quasi-analytical approach is shown to be accurate and efficient for large aerodynamic systems.
T-4 handbook of material properties data bases. Volume 1c. Equations of state
International Nuclear Information System (INIS)
Holian, K.S.
1984-11-01
This manual is a compilation of descriptions of the equations of state (EOS) in the T-4 computerized library of material properties tables. The introduction gives a brief descriptions of the library and of the physics theories and models which were used to calculate the equations of state. Then each EOS is described in detail. First, various physical parameters of each theoretical EOS are tabulated and compared with experiments when available. Then the method of generating the EOS is briefly described. Finally, the tabels are plotted in terms of pressure and energy vs density along line of constant temperature
An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation
Asiri, Sharefa M.
2015-08-31
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.
A Comparison of Resonant Tunneling Based on Schrödinger's Equation and Quantum Hydrodynamics
Directory of Open Access Journals (Sweden)
Naoufel Ben Abdallah
2002-01-01
Full Text Available Smooth quantum hydrodynamic (QHD model simulations of the current–voltage curve of a resonant tunneling diode at 300K are compared with that predicted by the mixed-state Schrödinger equation approach. Although the resonant peak for the QHD simulation occurs at 0.15V instead of the Schrödinger equation value of 0.2V, there is good qualitative agreement between the current–voltage curves for the two models, including the predicted peak current values.
Fresnel Lens Solar Concentrator Design Based on Geometric Optics and Blackbody Radiation Equations
Watson, Michael D.; Jayroe, Robert, Jr.
1999-01-01
Fresnel lenses have been used for years as solar concentrators in a variety of applications. Several variables effect the final design of these lenses including: lens diameter, image spot distance from the lens, and bandwidth focused in the image spot. Defining the image spot as the geometrical optics circle of least confusion and applying blackbody radiation equations the spot energy distribution can be determined. These equations are used to design a fresnel lens to produce maximum flux for a given spot size, lens diameter, and image distance. This approach results in significant increases in solar efficiency over traditional single wavelength designs.
Structural equation modelling based data fusion for technology forecasting: A generic framework
CSIR Research Space (South Africa)
Staphorst, L
2013-07-01
Full Text Available to explain the variations in independent variables as functions (commonly referred to regression functions) of variations in dependent variables [13]. With this knowledge it is then possible to perform prediction and forecasting of the values that dependent....G.; “A General Method for Estimating a Linear Structural Equation System,” in Structural Equation Models in the Social Sciences, eds.: A.S. Goldberger and O. D. Duncan, New York: Seminar, 1973. [15] Steinberg, A.N. and Rogova, G.; "Situation...
Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method
Directory of Open Access Journals (Sweden)
Ying Wang
2014-06-01
Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica
2000-07-01
Full text follows: There is a common opinion that the construction of a consistent relativistic quantum mechanics on the base of a relativistic wave equation meets well-known difficulties related to the existence of infinite number of negative energy levels, to the existence of negative vector norms, and so on, which may be only solved in a second-quantized theory, see, for example, two basic papers devoted to the problem L.Foldy, S.Wouthuysen, Phys. Rep.78 (1950) 29; H.Feshbach, F.Villars, Rev. Mod. Phys. 30 (1958) 24, whose arguments are repeated in all handbooks in relativistic quantum theory. Even Dirac trying to solve the problem had turned last years to infinite-component relativistic wave equations, see P.A.M. Dirac, Proc. R. Soc. London, A328 (1972) 1. We believe that a consistent relativistic quantum mechanics may be constructed on the base of an extended (charge symmetric) equation, which unite both a relativistic wave equation for a particle and for an antiparticle. We present explicitly the corresponding construction, see for details hep-th/0003112. We support such a construction by two demonstrations: first, in course of a careful canonical quantization of the corresponding classical action of a relativistic particle we arrive just to such a consistent quantum mechanics; second, we demonstrate that a reduction of the QFT of a corresponding field (scalar, spinor, etc.) to one-particle sector, if such a reduction may be done, present namely this quantum mechanics. (author)
A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation
Oruç, Ömer
2018-04-01
In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.
Accelerating 3D Elastic Wave Equations on Knights Landing based Intel Xeon Phi processors
Sourouri, Mohammed; Birger Raknes, Espen
2017-04-01
In advanced imaging methods like reverse-time migration (RTM) and full waveform inversion (FWI) the elastic wave equation (EWE) is numerically solved many times to create the seismic image or the elastic parameter model update. Thus, it is essential to optimize the solution time for solving the EWE as this will have a major impact on the total computational cost in running RTM or FWI. From a computational point of view applications implementing EWEs are associated with two major challenges. The first challenge is the amount of memory-bound computations involved, while the second challenge is the execution of such computations over very large datasets. So far, multi-core processors have not been able to tackle these two challenges, which eventually led to the adoption of accelerators such as Graphics Processing Units (GPUs). Compared to conventional CPUs, GPUs are densely populated with many floating-point units and fast memory, a type of architecture that has proven to map well to many scientific computations. Despite its architectural advantages, full-scale adoption of accelerators has yet to materialize. First, accelerators require a significant programming effort imposed by programming models such as CUDA or OpenCL. Second, accelerators come with a limited amount of memory, which also require explicit data transfers between the CPU and the accelerator over the slow PCI bus. The second generation of the Xeon Phi processor based on the Knights Landing (KNL) architecture, promises the computational capabilities of an accelerator but require the same programming effort as traditional multi-core processors. The high computational performance is realized through many integrated cores (number of cores and tiles and memory varies with the model) organized in tiles that are connected via a 2D mesh based interconnect. In contrary to accelerators, KNL is a self-hosted system, meaning explicit data transfers over the PCI bus are no longer required. However, like most
Chen, Xueli; Zhang, Qitan; Yang, Defu; Liang, Jimin
2014-01-01
To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP3 equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP3) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.
International Nuclear Information System (INIS)
Chen, Xueli; Zhang, Qitan; Yang, Defu; Liang, Jimin
2014-01-01
To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP 3 equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP 3 ) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions
Is classical mechanics based on Newton's laws or Eulers analytical equations?
Directory of Open Access Journals (Sweden)
H.Iro
2005-01-01
Full Text Available In an example I illustrate how my picture of physics is enriched due to my frequent conversations with Reinhard Folk. The subject is: Who wrote down the basic equations of motion of classical mechanics for the first time? (To be sure, it was not Newton.
Comparison of stator-mounted permanent-magnet machines based on a general power equation
DEFF Research Database (Denmark)
Chen, Zhe; Hua, Wei; Cheng, Ming
2009-01-01
The stator-mounted permanent-magnet (SMPM) machines have some advantages compared with its counterparts, such as simple rotor, short winding terminals, and good thermal dissipation conditions for magnets. In this paper, a general power equation for three types of SMPM machine is introduced first...
A new differential equations-based model for nonlinear history-dependent magnetic behaviour
International Nuclear Information System (INIS)
Aktaa, J.; Weth, A. von der
2000-01-01
The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations
Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models
Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning
2012-01-01
The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…
Transverse momentum spectra and elliptic flow: Hydrodynamics with QCD-based equations of state
Bluhm, M; Heinz, U
2008-01-01
We present a family of equations of state within a quasiparticle model adjusted to lattice QCD and study the impact on azimuthal flow anisotropies and transverse momentum spectra within hydrodynamic simulations for heavy-ion collisions at energies relevant for LHC.
Molecular-based Equation of State for TIP4P Water
Czech Academy of Sciences Publication Activity Database
Jirsák, Jan; Nezbeda, Ivo
2007-01-01
Roč. 136, č. 3 (2007), s. 310-316 ISSN 0167-7322 R&D Projects: GA AV ČR 1ET400720409; GA AV ČR IAA4072303 Institutional research plan: CEZ:AV0Z40720504 Keywords : equation of state * perturbation theory * primitive models Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 0.982, year: 2007
Exact solutions of a Schrodinger equation based on the Lambert function
International Nuclear Information System (INIS)
Williams, Brian Wesley
2005-01-01
An exactly solvable Schrodinger equation of the confluent Natanzon class is derived using the differential properties of the Lambert W function. This potential involves two constant parameters and is defined along the entire real line. Specific spatial forms demonstrating wells and deformed positive barriers are presented
Shock-wave structure based on the Navier-Stokes-Fourier equations
Uribe, F. J.; Velasco, R. M.
2018-04-01
We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature.
Equations of State of Elements Based on the Generalized Fermi-Thomas Theory
Feynman, R. P.; Metropolis, N.; Teller, E.
1947-04-28
The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures. Calculations have been carried out both without and with the exchange terms. Discussion of similarity transformations lead to the virial theorem and to correlation of solutions for different Z-values.
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations
International Nuclear Information System (INIS)
Yotsuji, K.; Tachi, Y.; Nishimaki, Y.
2012-01-01
Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3
International Nuclear Information System (INIS)
Jetana, Thongsuk; Abdullah, Norhani; Liang, Boo Juan; Syed Salim, Syed Jalaludin; Ho, Wan Yin
2003-06-01
Three experiments were conducted at the farm of the Universiti Putra Malaysia, Serdang, Selangor, Malaysia, to establish a model as an index for estimating rumen microbial protein production. In Experiment 1, six Ferral male goats (wt. 40.2±4.6 kg) were used to determine the endogenous purine derivatives (PD) excreted in the urine by fasting. In Experiment 2, four Ferral male goats (wt. 39.6±1.8 kg) were used to measure the proportion of plasma PD excreted in the urine by using [ 14 C]-uric acid as a marker at two levels of feed intake (40% and 80% voluntary intake), using an incomplete 2x4 Latin square experimental design. The feed consisted of 40% oil palm frond and 60% concentrate (OPFC). In Experiment 3, four Ferral male goats fed (OPFC)) were slaughtered and rumen contents were taken for measurements of purine and total nitrogen contents of mixed rumen microbes. The results showed that endogenous PD (allantoin, uric acid, xanthine and hypoxanthine) excreted in the urine obtained by the fasting trial was 202±17 μmol/kg BW 0 . 75 d - 1. The average percentage recovery of plasma PD excretion in the urine by using [ 14 C)-uric acid as a marker was 83±2.0% (cv=6.88, ranged 76.3-91.4%, n=8). Percentage recovery was not affected by levels of feed intake. The ratio of purine N: total N in the mixed rumen liquid associated bacteria (LAB) was 0.085. In this study, a preliminary model for goats was established by using the information from the recovery of labeled PD [ 14 C]-uric acid and the fasting PD excretion. The model obtained was Y 0.83X + 0.202 x BW 0 . 75 , where Y = PD excretion in the urine (mmol/d) X PD absorption at small intestine (mmol/d) BW 0 . 75 = Metabolic body weight (kg) Thus the microbial nitrogen based on total PD (MNpd) can be calculated as follows: MNpd = 70 x X = 0.992 x X (g/d) 0.085 x 0.83 x 1000 where 0.085 is the ratio of purine-N: total N in mixed rumen microbes, 0.83 is the average of digestibility of microbial purine from published
International Nuclear Information System (INIS)
Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho; Pyeon, Cheol Ho
2015-01-01
In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r g , E g , t g ) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the neutron sources
Energy Technology Data Exchange (ETDEWEB)
Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)
2015-10-15
In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the
Campbell, D A; Chkrebtii, O
2013-12-01
Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Valle G, E. del; Mugica R, C.A.
2005-01-01
In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)
Chen, Xiangyong; Qiu, Jianlong
2014-01-01
This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example i...
Stability study of pre-stack seismic inversion based on the full Zoeppritz equation
Liang, Lifeng; Zhang, Hongbing; Guo, Qiang; Saeed, Wasif; Shang, Zuoping; Huang, Guojiao
2017-10-01
Pre-stack seismic inversion is highly important and complicated. Its result is non-unique, and the process is unstable because pre-stack seismic inversion is an ill-posed problem that simultaneously obtains the results of multiple parameters. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization (EPR) can help mitigate the problem. To achieve this combination, we developed an inversion method by constructing a new objective function, which includes the EPR and the Markov random field. The method directly gains reflectivity R PP by the full Zoeppritz equation instead of its approximations and effectively controls the stability of simultaneous inversion by two additional assumptions: the sectional constant V S/V P and the generalized Gardner equation. Thus, the simultaneous inversion of multiple parameters is directed toward to V P, ΔL S (the fitting deviation of V S) and density, and the generalized Gardner equation is regarded as a constraint from which the fitting relationship is derived. We applied the fast simulated annealing algorithm to solve the nonlinear optimization problem. The test results on 2D synthetic data indicated that the stability of simultaneous inversion for V P, ΔL S and density is better than these for V P, V S, and density. The inverted result of density gradually worsens as the deviation ΔL D (the fitting deviation of the density) increases. Moreover, the inverted results were acceptable when using the fitting relationships with error, although they showed varying degrees of influence. We constructed time-varying and space-varying fitting relationships using the logging data in pre-stack inversion of the field seismic data. This improved the inverted results of the simultaneous inversion for complex geological models. Finally, the inverted results of the field data distinctly revealed more detailed information about the layers and matched well with the logging data along the wells over most
Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations
International Nuclear Information System (INIS)
Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.
2003-01-01
We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations
Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh
International Nuclear Information System (INIS)
Zhang Dier; Shen Lihua; Zhou Aihui; Gong Xingao
2008-01-01
A finite element (FE) method with self-adaptive mesh-refinement technique is developed for solving the density functional Kohn-Sham equations. The FE method adopts local piecewise polynomials basis functions, which produces sparsely structured matrices of Hamiltonian. The method is well suitable for parallel implementation without using Fourier transform. In addition, the self-adaptive mesh-refinement technique can control the computational accuracy and efficiency with optimal mesh density in different regions
International Nuclear Information System (INIS)
Savidge, I.R.; Gladden, J.B.; Campbell, K.P.; Ziesenis, J.S.
1988-01-01
A central and unresolved problem in assessing the impact of power plant operations on Hudson River fish populations was the prediction of long-term population changes resulting from impingement and entrainment mortality. A series of equations was developed from the Ricker and Beverton-Holt stock-recruitment models to address this issue. It was assumed that compensation occurs during a brief period early in the life cycle rather than throughout the life cycle. Equations were developed for the added power plant-induced mortality occurring before or after compensation in each model. Mortality added after compensation resulted in larger estimates of population reduction than mortality added before compensation. The simple deterministic and more complex age-structured models provided identical predictions of long-term changes in population size in most cases. Similarly, the simple models predicted population changes that were nearly identical to the average age-structured model with variable survival except when levels of variation were quite high and the population modeled was semelparous. Advantages of the equations developed herein are their simplicity, generality, and minimal data requirements. The predictions of long-term population changes resulting from impingement and entrainment mortality were not attained. The magnitude and form of the compensatory responses of Hudson River fish populations remained undetermined, so that an agreement on this critical component of prediction models could not be reached. 33 refs., 4 figs., 2 tabs
Interpolation problem for the solutions of linear elasticity equations based on monogenic functions
Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii
2017-11-01
Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.
Pieprzyk, S.; Brańka, A. C.; Maćkowiak, Sz.; Heyes, D. M.
2018-03-01
The equation of state (EoS) of the Lennard-Jones fluid is calculated using a new set of molecular dynamics data which extends to higher temperature than in previous studies. The modified Benedict-Webb-Rubin (MBWR) equation, which goes up to ca. T ˜ 6, is reparametrized with new simulation data. A new analytic form for the EoS, which breaks the fluid range into two regions with different analytic forms and goes up to ca. T ≃ 35, is also proposed. The accuracy of the new formulas is at least as good as the MBWR fit and goes to much higher temperature allowing it to now encompass the Amagat line. The fitted formula extends into the high temperature range where the system can be well represented by inverse power potential scaling, which means that our specification of the equation of state covers the entire (ρ, T) plane. Accurate analytic fit formulas for the Boyle, Amagat, and inversion curves are presented. Parametrizations of the extrema loci of the isochoric, CV, and isobaric, CP, heat capacities are given. As found by others, a line maxima of CP terminates in the critical point region, and a line of minima of CP terminates on the freezing line. The line of maxima of CV terminates close to or at the critical point, and a line of minima of CV terminates to the right of the critical point. No evidence for a divergence in CV in the critical region is found.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
International Nuclear Information System (INIS)
Zheng, Lin; Zheng, Song; Zhai, Qinglan
2016-01-01
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
Sembiring, S. A.
2018-02-01
The objective of this research is to analyze the impacts of rice policy on the household food security. The research used cross section data, were collected from 74 respondent as determined by purposive sampling in Sei Rejo villages, the Sub District of Sei Rampah, Serdang Bedagai District in the Province of North Sumatera. Rice policy model specification uses the simultaneous equations consisting of 6 structural equations and 6 identity equations which was estimated using Two Stages Least Squares (2SLS) method. The results show that the effectiveness of government purchase price of dried harvest paddy gave a positive impact on paddy planted area and lead to an increase paddy production and an increase of the rice production gave a positive impact on household rice availability and household rice surplus, and the increase of household rice surplus gave the quantity of Raskin decrease, whereas the increase of fertilizers gave a negative impact on paddy planted area and lead to decrease paddy production and to decrease in rice production was followed by an decrease in household rice availability and household rice surplus, and the decrease of household rice surplus gave the quantity of Raskin increase.
Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow
Energy Technology Data Exchange (ETDEWEB)
Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)
2016-02-05
In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.
Shaikh, Saijuddin; Schulze, Kerry J; Kurpad, Anura; Ali, Hasmot; Shamim, Abu Ahmed; Mehra, Sucheta; Wu, Lee S-F; Rashid, Mahbubar; Labrique, Alain B; Christian, Parul; West, Keith P
2013-02-28
Equations for predicting body composition from bioelectrical impedance analysis (BIA) parameters are age-, sex- and population-specific. Currently there are no equations applicable to women of reproductive age in rural South Asia. Hence, we developed equations for estimating total body water (TBW), fat-free mass (FFM) and fat mass in rural Bangladeshi women using BIA, with ²H₂O dilution as the criterion method. Women of reproductive age, participating in a community-based placebo-controlled trial of vitamin A or β-carotene supplementation, were enrolled at 19·7 (SD 9·3) weeks postpartum in a study to measure body composition by ²H₂O dilution and impedance at 50 kHz using multi-frequency BIA (n 147), and resistance at 50 kHz using single-frequency BIA (n 82). TBW (kg) by ²H2O dilution was used to derive prediction equations for body composition from BIA measures. The prediction equation was applied to resistance measures obtained at 13 weeks postpartum in a larger population of postpartum women (n 1020). TBW, FFM and fat were 22·6 (SD 2·7), 30·9 (SD 3·7) and 10·2 (SD 3·8) kg by ²H₂O dilution. Height²/impedance or height²/resistance and weight provided the best estimate of TBW, with adjusted R² 0·78 and 0·76, and with paired absolute differences in TBW of 0·02 (SD 1·33) and 0·00 (SD 1·28) kg, respectively, between BIA and ²H₂O. In the larger sample, values for TBW, FFM and fat were 23·8, 32·5 and 10·3 kg, respectively. BIA can be an important tool for assessing body composition in women of reproductive age in rural South Asia where poor maternal nutrition is common.
ten Haaf, Twan; Weijs, Peter J M
2014-01-01
Resting energy expenditure (REE) is expected to be higher in athletes because of their relatively high fat free mass (FFM). Therefore, REE predictive equation for recreational athletes may be required. The aim of this study was to validate existing REE predictive equations and to develop a new recreational athlete specific equation. 90 (53 M, 37 F) adult athletes, exercising on average 9.1 ± 5.0 hours a week and 5.0 ± 1.8 times a week, were included. REE was measured using indirect calorimetry (Vmax Encore n29), FFM and FM were measured using air displacement plethysmography. Multiple linear regression analysis was used to develop a new FFM-based and weight-based REE predictive equation. The percentage accurate predictions (within 10% of measured REE), percentage bias, root mean square error and limits of agreement were calculated. Results: The Cunningham equation and the new weight-based equation REE(kJ / d) = 49.940* weight(kg) + 2459.053* height(m) - 34.014* age(y) + 799.257* sex(M = 1,F = 0) + 122.502 and the new FFM-based equation REE(kJ / d) = 95.272*FFM(kg) + 2026.161 performed equally well. De Lorenzo's equation predicted REE less accurate, but better than the other generally used REE predictive equations. Harris-Benedict, WHO, Schofield, Mifflin and Owen all showed less than 50% accuracy. For a population of (Dutch) recreational athletes, the REE can accurately be predicted with the existing Cunningham equation. Since body composition measurement is not always possible, and other generally used equations fail, the new weight-based equation is advised for use in sports nutrition.
A modelling of robot manipulator dynamics based on Newton-Euler's equations
International Nuclear Information System (INIS)
Sasaki, Shinobu
1990-09-01
In this paper is presented an algorithm for solving the inverse dynamics of robot manipulators. In comparison with the dynamical equations derived from the Lagrange's mechanics, the relations to be treated are of simple forms due to recursive expressions of relative link motions. A computer simulation for applying the algorithm to a six-link manipulator indicated that the present method might be most appropriate among the existing approaches from the viewpoint of computational efficiency. In particular, it is noted that the increase of the number of links has hardly great effect on the intricacy of calculation. (author)
International Nuclear Information System (INIS)
Furuya, Atsushi; Yagi, Masatoshi; Itoh, Sanae-I.
2003-01-01
The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if Δ' > 0. (author)
Directory of Open Access Journals (Sweden)
Xiangyong Chen
2014-01-01
Full Text Available This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example illustrates the effectiveness of the presented optimal schemes. Our proposed results provide a theoretical guide for both making warfare command decision and assessing military actions.
Regularity criteria for the Navier–Stokes equations based on one component of velocity
Czech Academy of Sciences Publication Activity Database
Guo, Z.; Caggio, M.; Skalák, Zdeněk
2017-01-01
Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China (CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.659, year: 2016
Directory of Open Access Journals (Sweden)
Murat Osmanoglu
2013-01-01
Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
Regularity criteria for the Navier–Stokes equations based on one component of velocity
Czech Academy of Sciences Publication Activity Database
Guo, Z.; Caggio, M.; Skalák, Zdeněk
2017-01-01
Roč. 35, June (2017), s. 379-396 ISSN 1468-1218 R&D Projects: GA ČR GA14-02067S Grant - others:Západočeská univerzita(CZ) SGS-2016-003; National Natural Science Foundation of China(CN) 11301394 Institutional support: RVO:67985874 Keywords : Navier–Stokes equations * regularity of solutions * regularity criteria * Anisotropic Lebesgue spaces Subject RIV: BK - Fluid Dynamics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.659, year: 2016
Integral equation based stability analysis of short wavelength drift modes in tokamaks
International Nuclear Information System (INIS)
Hirose, A.; Elia, M.
2003-01-01
Linear stability of electron skin-size drift modes in collisionless tokamak discharges has been investigated in terms of electromagnetic, kinetic integral equations in which neither ions nor electrons are assumed to be adiabatic. A slab-like ion temperature gradient mode persists in such a short wavelength regime. However, toroidicity has a strong stabilizing influence on this mode. In the electron branch, the toroidicity induced skin-size drift mode previously predicted in terms of local kinetic analysis has been recovered. The mode is driven by positive magnetic shear and strongly stabilized for negative shear. The corresponding mixing length anomalous thermal diffusivity exhibits favourable isotope dependence. (author)
The investigation of relativistic microscopic optical potential based on RBBG equation
International Nuclear Information System (INIS)
Chen Baoqiu; Ma Zhongyu
1992-01-01
The relativistic microscopic optical potential is derived from the RBBG equation. The nucleon complex effective mass is determined phenomenologically by a fit to 200 MeV proton-nucleus scattering data. Then the relativistic microscopic optical potentials of proton scattered from different targets: 16 O, 40 Ca, 90 Zr and 208 Pb in the energies range from 160 to 800 MeV have been got. The relativistic microscopic optical potentials have been used to study proton- 40 Ca scattering at 200 MeV. Theoretical predictions for cross section and spin observables are compared with experimental data and phenomenological Dirac optical potential
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
Yan, Liping; Chen, Benyong; Zhang, Enzheng; Zhang, Shihua; Yang, Ye
2015-08-01
A novel method for the precision measurement of refractive index of air (n(air)) based on the combining of the laser synthetic wavelength interferometry with the Edlén equation estimation is proposed. First, a n(air_e) is calculated from the modified Edlén equation according to environmental parameters measured by low precision sensors with an uncertainty of 10(-6). Second, a unique integral fringe number N corresponding to n(air) is determined based on the calculated n(air_e). Then, a fractional fringe ε corresponding to n(air) with high accuracy can be obtained according to the principle of fringe subdivision of laser synthetic wavelength interferometry. Finally, high accurate measurement of n(air) is achieved according to the determined fringes N and ε. The merit of the proposed method is that it not only solves the problem of the measurement accuracy of n(air) being limited by the accuracies of environmental sensors, but also avoids adopting complicated vacuum pumping to measure the integral fringe N in the method of conventional laser interferometry. To verify the feasibility of the proposed method, comparison experiments with Edlén equations in short time and in long time were performed. Experimental results show that the measurement accuracy of n(air) is better than 2.5 × 10(-8) in short time tests and 6.2 × 10(-8) in long time tests.
Yang, Ting; Dong, Jianji; Lu, Liangjun; Zhou, Linjie; Zheng, Aoling; Zhang, Xinliang; Chen, Jianping
2014-07-04
Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.
Hou, Jie; Dong, Jianji; Zhang, Xinliang
2017-06-15
Systems of ordinary differential equations (SODEs) are crucial for describing the dynamic behaviors in various systems such as modern control systems which require observability and controllability. In this Letter, we propose and experimentally demonstrate an all-optical SODE solver based on the silicon-on-insulator platform. We use an add/drop microring resonator to construct two different ordinary differential equations (ODEs) and then introduce two external feedback waveguides to realize the coupling between these ODEs, thus forming the SODE solver. A temporal coupled mode theory is used to deduce the expression of the SODE. A system experiment is carried out for further demonstration. For the input 10 GHz NRZ-like pulses, the measured output waveforms of the SODE solver agree well with the calculated results.
DEFF Research Database (Denmark)
Huang, Liping; Crino, Michelle; Wu, Jason Hy
2016-01-01
to a standard format. Individual participant records will be compiled and a series of analyses will be completed to: (1) compare existing equations for estimating 24-hour salt intake from spot urine samples with 24-hour urine samples, and assess the degree of bias according to key demographic and clinical......BACKGROUND: Methods based on spot urine samples (a single sample at one time-point) have been identified as a possible alternative approach to 24-hour urine samples for determining mean population salt intake. OBJECTIVE: The aim of this study is to identify a reliable method for estimating mean...... population salt intake from spot urine samples. This will be done by comparing the performance of existing equations against one other and against estimates derived from 24-hour urine samples. The effects of factors such as ethnicity, sex, age, body mass index, antihypertensive drug use, health status...
DEFF Research Database (Denmark)
D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar
2012-01-01
and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent...... flexors. Results: Males were signifantly stronger than females across all age groups. Elbow peak torque (EPT) was better preserved from 60s to 70s whereas knee peak torque (KPT) reduced significantly (PGender, thigh mass and age best...... predicted KPT (R2=0.60). Gender, forearm mass and age best predicted EPT (R2=0.75). Good crossvalidation was established for both elbow and knee models. Conclusion: This cross-sectional study of muscle strength created and validated strength scaled equations of EPT and KPT using only gender, segment mass...
International Nuclear Information System (INIS)
Saez, D.G.; Hernandez, L.; Borroto, M.; Figueredo, M.
1996-01-01
A semiempirical equation of polynomial-exponential type is presented to describe the transmission data of Co-60 gamma radiation in finite materials of concrete and lead. This equation and the expression obtained for the relationship of scatter-to-incident exposure made easy the developing in computer of an analytical solution for shielding calculations of Co 60 teletherapy rooms, based on the procedures of the NCRP 49 and Simpkin's method. The standard error in the estimation of parameters is less than 1.7 % except for the attenuation of 150 'o' scattered radiation in concrete that resulted in 6.3 % for one of them. The shielding calculations were compared with the data in NCRP 49 for the same conditions with a correlation better than 99 %
Directory of Open Access Journals (Sweden)
Yidong Xu
2017-07-01
Full Text Available In this paper, a novel method based on the Poggio–Miller–Chang-Harrington–Wu–Tsai (PMCHWT integral equation is presented to study the electromagnetic fields excited by vertical or horizontal electric dipoles in the presence of a layered region which consists of K-layered dissipative media and the air above. To transform the continuous integral equation into a block tridiagonal matrix with the feature of convenient solution, the Rao–Wilton–Glisson (RWG functions are introduced as expansion and testing functions. The electromagnetic fields excited by an electric dipole are calculated and compared with the available results, where the electric dipole antenna is buried in the non-planar air–sea–seabed, air–rock–earth–mine, and multilayered sphere structures. The analysis and computations demonstrate that the method exhibits high accuracy and solving performance in the near field propagation region.
Gambi, J. M.; García del Pino, M. L.; Gschwindl, J.; Weinmüller, E. B.
2017-12-01
This paper deals with the problem of throwing middle-sized low Earth orbit debris objects into the atmosphere via laser ablation. The post-Newtonian equations here provided allow (hypothetical) space-based acquisition, pointing and tracking systems endowed with very narrow laser beams to reach the pointing accuracy presently prescribed. In fact, whatever the orbital elements of these objects may be, these equations will allow the operators to account for the corrections needed to balance the deviations of the line of sight directions due to the curvature of the paths the laser beams are to travel along. To minimize the respective corrections, the systems will have to perform initial positioning manoeuvres, and the shooting point-ahead angles will have to be adapted in real time. The enclosed numerical experiments suggest that neglecting these measures will cause fatal errors, due to differences in the actual locations of the objects comparable to their size.
Directory of Open Access Journals (Sweden)
Ming-Lu Wu
2013-12-01
Full Text Available This paper links professional service firms’ resource-based strategies to their customer-focused performance for formulating service quality improvement priorities. The research applies the structural equation modelling approach to survey data from Hong Kong construction consultants to test some hypotheses. The study validates the various measures of firms’ resource-based strategies and customer-focused performance and bridges the gaps in firms’ organizational learning, core competences and customer-focused performance mediated by their strategic flexibility. The research results have practical implications for professional service firms to deploy resources appropriately to first enhance different competences and then improve customerfocused performance using their different competences.
Wavelet-like bases for thin-wire integral equations in electromagnetics
Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.
2005-03-01
In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.
Using Bronson Equation to Accurately Predict the Dog Brain Weight Based on Body Weight Parameter
Directory of Open Access Journals (Sweden)
L. Miguel Carreira
2016-12-01
Full Text Available The study used 69 brains (n = 69 from adult dog cadavers, divided by their skull type into three groups, brachi (B, dolicho (D and mesaticephalic (M (n = 23 each, and aimed: (1 to determine whether the Bronson equation may be applied, without reservation, to estimate brain weight (BW in brachy (B, dolicho (D, and mesaticephalic (M dog breeds; and (2 to evaluate which breeds are more closely related to each other in an evolutionary scenario. All subjects were identified by sex, age, breed, and body weight (bw. An oscillating saw was used for a circumferential craniotomy to open the skulls; the brains were removed and weighed using a digital scale. For statistical analysis, p-values < 0.05 were considered significant. The work demonstrated a strong relationship between the observed and predicted BW by using the Bronson equation. It was possible to hypothesize that groups B and D present a greater encephalization level than M breeds, that B and D dog breeds are more closely related to each other than to M, and from the three groups, the D individuals presented the highest brain mass mean.
Aczél, J
1987-01-01
Recently I taught short courses on functional equations at several universities (Barcelona, Bern, Graz, Hamburg, Milan, Waterloo). My aim was to introduce the most important equations and methods of solution through actual (not artifi cial) applications which were recent and with which I had something to do. Most of them happened to be related to the social or behavioral sciences. All were originally answers to questions posed by specialists in the respective applied fields. Here I give a somewhat extended version of these lectures, with more recent results and applications included. As previous knowledge just the basic facts of calculus and algebra are supposed. Parts where somewhat more (measure theory) is needed and sketches of lengthier calcula tions are set in fine print. I am grateful to Drs. J. Baker (Waterloo, Ont.), W. Forg-Rob (Innsbruck, Austria) and C. Wagner (Knoxville, Tenn.) for critical remarks and to Mrs. Brenda Law for care ful computer-typing of the manuscript (in several versions). A...
Integral representations of solutions of the wave equation based on relativistic wavelets
International Nuclear Information System (INIS)
Perel, Maria; Gorodnitskiy, Evgeny
2012-01-01
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed. (paper)
Thermodynamics of Highly Concentrated Aqueous Electrolytes: Based on Boltzmann's eponymous equation
Energy Technology Data Exchange (ETDEWEB)
Ally, Moonis Raza [ORNL
2018-05-01
This sharply focused book invites the reader to explore the chemical thermodynamics of highly concentrated aqueous electrolytes from a different vantage point than traditional methods. The book's foundation is deeply rooted in Ludwig Boltzmann's eponymous equation. The pathway from micro to macro thermodynamics is explained heuristically, in a step-by-step approach. Concepts and mathematical formalism are explained in detail to captivate and maintain interest as the algebra twists and turns. Every significant result is derived in a lucid and piecemeal fashion. Application of the theory is exemplified with examples. It is amazing to realize that Boltamann's simple equation contains sufficient information from which such an elaborate theory can emerge. This book is suitable for undergraduate and graduate level classes in chemical engineering, chemistry, geochemistry, environmental sciences, and those studying aerosol particles in the troposphere. Students interested in understanding how thermodynamic theories may be developed would be inspired by the methodology. The author wishes that readers get as much excitement reading this book as he did writing it.
Wu, Hulin; Xue, Hongqi; Kumar, Arun
2012-06-01
Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.
On a model for baryons based on a Dirac equation with confining potentials
International Nuclear Information System (INIS)
Ferreira, P.L.
1977-06-01
An independent particle model for baryons is studied in which the quarks obey a Dirac equation with an average potential of the form V(r) = 1/2 (1 + β)(V 0 + lambda r - γ/r). A numerical solution is obtained for S-waves. Several properties of the 1/2 + baryons such as the ratio (G sub(A)/G sub(V)) sub (N) for nucleons and baryon magnetic moments are analysed in terms of the model. A comparison with the case of a pure linear potential and with a pure harmonic oscillator is made, showing that it is possible to obtain a better agreement with the data in the present case
Modelling of proton exchange membrane fuel cell performance based on semi-empirical equations
Energy Technology Data Exchange (ETDEWEB)
Al-Baghdadi, Maher A.R. Sadiq [Babylon Univ., Dept. of Mechanical Engineering, Babylon (Iraq)
2005-08-01
Using semi-empirical equations for modeling a proton exchange membrane fuel cell is proposed for providing a tool for the design and analysis of fuel cell total systems. The focus of this study is to derive an empirical model including process variations to estimate the performance of fuel cell without extensive calculations. The model take into account not only the current density but also the process variations, such as the gas pressure, temperature, humidity, and utilization to cover operating processes, which are important factors in determining the real performance of fuel cell. The modelling results are compared well with known experimental results. The comparison shows good agreements between the modeling results and the experimental data. The model can be used to investigate the influence of process variables for design optimization of fuel cells, stacks, and complete fuel cell power system. (Author)
Optical properties reconstruction using the adjoint method based on the radiative transfer equation
Addoum, Ahmad; Farges, Olivier; Asllanaj, Fatmir
2018-01-01
An efficient algorithm is proposed to reconstruct the spatial distribution of optical properties in heterogeneous media like biological tissues. The light transport through such media is accurately described by the radiative transfer equation in the frequency-domain. The adjoint method is used to efficiently compute the objective function gradient with respect to optical parameters. Numerical tests show that the algorithm is accurate and robust to retrieve simultaneously the absorption μa and scattering μs coefficients for lowly and highly absorbing medium. Moreover, the simultaneous reconstruction of μs and the anisotropy factor g of the Henyey-Greenstein phase function is achieved with a reasonable accuracy. The main novelty in this work is the reconstruction of g which might open the possibility to image this parameter in tissues as an additional contrast agent in optical tomography.
A new equation of state Based on Nuclear Statistical Equilibrium for Core-Collapse Simulations
Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki
2012-09-01
We calculate a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.
Beyond the Cahn-Hilliard equation: a vacancy-based kinetic theory
International Nuclear Information System (INIS)
Nastar, M.
2011-01-01
A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description of the vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equilibrium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. The resulting analytical expression of the structure function highlights the contribution of the vacancy diffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, the linearized SCMF kinetic equations involve three constant rates, first one describing the vacancy relaxation kinetics, second one related to the kinetic coupling between local concentrations and pair correlations and the third one representing the spinodal amplification rate. Starting from the same vacancy diffusion model, we perform kinetic Monte Carlo simulations of a Body Centered Cubic (BCC) demixting alloy. The resulting spherically averaged structure function is compared to the SCMF predictions. Both qualitative and quantitative agreements are satisfying. (authors)
Tamellini, L.; Le Maî tre, O.; Nouy, A.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
Directory of Open Access Journals (Sweden)
A. A. Shevtsov
2015-01-01
Full Text Available Spray drying of solutions and suspensions is among the most common methods of producing a wide range of powdered products in chemical, food and pharmaceutical industries. For the drying of heat-sensitive materials, which is fully applicable to the distillery stillage filtrate continuous-flow type of contact of drying agent and the solution droplets is examined. Two-phase simulation method of computational hydrodynamics in a stationary state for studying the process of drying of the distillery stillage filtrate in the pilot spray dryer under the following assumptions was used. The components form an ideal mixture, the properties of which are calculated directly from the properties of the components and their proportions. The droplets were presented in spherical form. The density and specific heat of the solution and the coefficient of vapors diffusion in the gas phase remained unchanged. To solve the heat exchange equations between the drying agent and the drops by the finite volume method the software package ANSYS CFX was used. The bind between the two phases was established by Navier-Stokes equations. The continuous phase (droplets of the distillery stillage filtrate was described by the k-ε turbulence model. The results obtained showed that the interaction of "drop-wall" causes a significant change of velocity, temperature and humidity both of a drying agent and the product particles. The behavior of the particles by spraying, collision with walls and deposition of the finished product allowed to determine the dependence of physical parameters of the drying process, of the geometric dimensions of the dryer. Comparison of simulation results with experimental data showed satisfactory convergence of the results: for the temperature of the powder 10% its humidity of 12% and temperature of the spent drying agent at the outlet from the drier of 13%. The possibility of using the model in the spray dryers designing, and control of the drying process
The intrinsic periodic fluctuation of forest: a theoretical model based on diffusion equation
Zhou, J.; Lin, G., Sr.
2015-12-01
Most forest dynamic models predict the stable state of size structure as well as the total basal area and biomass in mature forest, the variation of forest stands are mainly driven by environmental factors after the equilibrium has been reached. However, although the predicted power-law size-frequency distribution does exist in analysis of many forest inventory data sets, the estimated distribution exponents are always shifting between -2 and -4, and has a positive correlation with the mean value of DBH. This regular pattern can not be explained by the effects of stochastic disturbances on forest stands. Here, we adopted the partial differential equation (PDE) approach to deduce the systematic behavior of an ideal forest, by solving the diffusion equation under the restricted condition of invariable resource occupation, a periodic solution was gotten to meet the variable performance of forest size structure while the former models with stable performance were just a special case of the periodic solution when the fluctuation frequency equals zero. In our results, the number of individuals in each size class was the function of individual growth rate(G), mortality(M), size(D) and time(T), by borrowing the conclusion of allometric theory on these parameters, the results perfectly reflected the observed "exponent-mean DBH" relationship and also gave a logically complete description to the time varying form of forest size-frequency distribution. Our model implies that the total biomass of a forest can never reach a stable equilibrium state even in the absence of disturbances and climate regime shift, we propose the idea of intrinsic fluctuation property of forest and hope to provide a new perspective on forest dynamics and carbon cycle research.
Liang, Jie; Qian, Hong
2010-01-01
Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand "complex behavior" and complexity theory, and from which important biological insight can be gained.
International Nuclear Information System (INIS)
Buy, Francois; Voltz, Christophe; Llorca, Fabrice
2006-01-01
This work is devoted to the evaluation of complex behavior of metals under shock wave loading. It presents a methodology for the design of specific experiments performed for validation of models and the evaluation of a multiphase equation of state for tin. This material has been selected because of the numerous works completed during the past years on its equation of state. We focus on the solid diagram which presents two solid phases. A thermodynamically based equation of state is developed which gives the opportunity to search for singularities which could be activated under particular shock wave loading. In the temperature -- pressure diagram, the superimposed Hugoniot and release paths make apparent a double shock, release shock configurations. We propose the design and the VISAR results of a calibrated shock -- reshock test for investigating the validity and the efficiency of the model for predicting the thermodynamical state of tin (phases mixing, temperature...). Comparison between numerical and experimental data shows the good accuracy of the results given by the EOS
International Nuclear Information System (INIS)
Carvalho Gonçalves, Wemerson de; Martinez, Aquilino Senra; Carvalho da Silva, Fernando
2015-01-01
Highlights: • We define the new function importance. • We calculate the kinetic parameters Λ, β, Γ and Q to: 0.95, 0.96, 0.97, 0.98 and 0.99. • We compared the results with those obtained by the main important functions. • We found that the calculated kinetic parameters are physically consistent. - Abstract: This paper aims to determine the parameters for a new set of equations of point kinetic subcritical systems, based on the concept of importance of Heuristic Generalized Perturbation Theory (HGPT). The importance function defined here is related to both the subcriticality and the external neutron source worth (which keeps the system at steady state). The kinetic parameters defined in this work are compared with the corresponding parameters when adopting the importance functions proposed by Gandini and Salvatores (2002), Dulla et al. (2006) and Nishihara et al. (2003). Furthermore, the point kinetics equations developed here are solved for two different transients, considering the parameters obtained with different importance functions. The results collected show that there is a similar behavior of the solution of the point kinetics equations, when used with the parameters obtained by the importance functions proposed by Gandini and Salvatores (2002) and Dulla et al. (2006), specially near the criticality. However, this is not verified as the system gets farther from criticality
International Nuclear Information System (INIS)
Foucart, F; Kasen, D; Desai, D; Brege, W; Duez, M D; Hemberger, D A; Scheel, M A; Kidder, L E; Pfeiffer, H P
2017-01-01
Neutron star-black hole binaries are among the strongest sources of gravitational waves detectable by current observatories. They can also power bright electromagnetic signals (gamma-ray bursts, kilonovae), and may be a significant source of production of r-process nuclei. A misalignment of the black hole spin with respect to the orbital angular momentum leads to precession of that spin and of the orbital plane, and has a significant effect on the properties of the post-merger remnant and of the material ejected by the merger. We present a first set of simulations of precessing neutron star-black hole mergers using a hot, composition dependent, nuclear-theory based equation of state (DD2). We show that the mass of the remnant and of the dynamical ejecta are broadly consistent with the result of simulations using simpler equations of state, while differences arise when considering the dynamics of the merger and the velocity of the ejecta. We show that the latter can easily be understood from assumptions about the composition of low-density, cold material in the different equations of state, and propose an updated estimate for the ejecta velocity which takes those effects into account. We also present an updated mesh-refinement algorithm which allows us to improve the numerical resolution used to evolve neutron star-black hole mergers. (paper)
Wu, Huai-Ning; Luo, Biao
2012-12-01
It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.
Liu, Jinghua; Zu, Jiyun; Curley, Edward; Carey, Jill
2014-01-01
The purpose of this study is to investigate the impact of discrete anchor items versus passage-based anchor items on observed score equating using empirical data.This study compares an "SAT"® critical reading anchor that contains more discrete items proportionally, compared to the total tests to be equated, to another anchor that…
DEFF Research Database (Denmark)
Pandey, Bishwajeet; Pandey, Sujeet; Sharma, Shivani
2016-01-01
In this paper, we are integrating clock gating in design of energy efficient equation solver circuits based on Vedic mathematics. Clock gating is one of the best energy efficient techniques. The Sutra 'SunyamSamyasamuccaye' says thatif sum of numerator and sum of denominator is same then we can e......, 94.54% for 1800MHz, and 94.02% for 2.2GHz, when we use gated clock instead of un gated one on 40nm FPGA and temperature is 329.85K. Power consumption in 28nm FPGA is less than 40nm FPGA....
Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar
2018-04-01
Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.
Scour depth estimation using an equation based on wind tunnel experiments
Directory of Open Access Journals (Sweden)
Tsutsui Takayuki
2016-01-01
Full Text Available Scour is the result of degradation and aggradation by wind or moving fluid in the front and back of a pole standing in sand, respectively, and is often observed at the bottom of bridge piers in rivers. In this study, we propose a method of estimating the scour depth around a cylindrical structure standing in sand. The relationships among the depth of the scour, the aspect ratio of the structure (= height/diameter, the fluid velocity, and the sand properties (particle size and density were determined experimentally using a wind tunnel. The experiments were carried out under clear-water scour conditions. In the experiments, the aspect ratio of the cylindrical structure, the fluid velocity, and the sand particle size were varied systematically. The diameters of the structure were 20, 40, and 60 mm, and the aspect ratio was varied from 0.25 to 3.0. Sand particles of four sizes (200, 275, 475, and 600 μm were used in the experiment, and the velocity was varied from 4 to 11 m/s. The depth and radius of the scour were measured. As a result, we have developed an equation for estimating the scour depth that uses the aspect ratio, fluid velocity, and sand particle size as parameters.
Zhu, Longji; Zhou, Haixuan; Xie, Xinyu; Li, Xueke; Zhang, Duoying; Jia, Liming; Wei, Qingbin; Zhao, Yue; Wei, Zimin; Ma, Yingying
2018-08-01
Floodgates operation is one of the primary means of flood control in lake development. However, knowledge on the linkages between floodgates operation and nitrogen transformation during the flood season is limited. In this study, water samples from six sampling sites along Lake Xingkai watershed were collected before and after floodgates operation. The causal relationships between environmental factors, bacterioplankton community composition and nitrogen fractions were determined during flood season. We found that concentrations of nitrogen fractions decreased significantly when the floodgates were opened, while the concentrations of total nitrogen (TN) and NO 3 - increased when the floodgates had been shut for a period. Further, we proposed a possible mechanism that the influence of floodgates operation on nitrogen transformation was largely mediated through changes in dissolved organic matter, dissolved oxygen and bacterioplankton community composition as revealed by structural equation modeling (SEM). We conclude that floodgates operation has a high risk for future eutrophication of downstream watershed, although it can reduce nitrogen content temporarily. Therefore, the environmental impacts of floodgates operation should be carefully evaluated before the floodwaters were discharged into downstream watershed. Copyright © 2018. Published by Elsevier B.V.
Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.
Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo
2017-02-01
New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.
Circular economy development phase research based on the IPAT equation: The case Shaanxi
Directory of Open Access Journals (Sweden)
Fang Ying
2015-04-01
Full Text Available In recent years, the worsening of the quality of the air has urged more people to attach great importance to circular economy. Shaanxi, abundant in natural resources, maintained the GDP growth rate of 14.9% during the period of the twelfth five-year plan. However, the fast economic growth under the extensive traditional economic growth mode renders Shaanxi inadequate in resources supply and noticeably worse in ecological environment issues. With the method of the IPAT equation, this paper quantitatively analyzes the developmental stage and the developmental level of the circular economy of Shaanxi to cover the shortage of the previous studies having only been focused on the policy study and the practice mode. The result shows that Shaanxi is in the intermediate stage of circular economy and the advanced stage has an apparent advantage over the intermediate one by comparing their energy consumption and solid pollutant discharge. The development experience of Shaanxi, a typical province of China, has guidance and reference significance to China and other developing countries.
Directory of Open Access Journals (Sweden)
Norman W.H. Mason
2014-02-01
Full Text Available Many studies have quantified uncertainty in forest carbon (C storage estimation, but there is little work examining the degree of uncertainty in shrubland C storage estimates. We used field data to simulate uncertainty in carbon storage estimates from three error sources: (1 allometric biomass equations; (2 measurement errors of shrubs harvested for the allometry; and (3 measurement errors of shrubs in survey plots. We also assessed uncertainty for all possible combinations of these error sources. Allometric uncertainty had the greatest independent effect on C storage estimates for individual plots. The largest error arose when all three error sources were included in simulations (where the 95% confidence interval spanned a range equivalent to 40% of mean C storage. Mean C sequestration (1.73 Mg C ha–1 year–1 exceeded the margin of error produced by the simulated sources of uncertainty. This demonstrates that, even when the major sources of uncertainty were accounted for, we were able to detect relatively modest gains in shrubland C storage.
El Mouden, C; André, J-B; Morin, O; Nettle, D
2014-02-01
Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes. © 2013 The Authors. Journal of Evolutionary Biology © 2013 European Society For Evolutionary Biology.
Okonjo, Kehinde Onwochei
2017-09-01
As a prelude to separating tertiary from quaternary structure contributions to the Bohr effect, we employed the Wyman equation to analyze Bohr data for human hemoglobin to which 2,3-bisphosphoglycerate, 2,3-BPG, is bound. Changes in the pK a s of the histidine Bohr groups result in a net reduction of their contributions to the Bohr effect at pH 7.4 compared to their contributions in stripped hemoglobin. The non-histidine 2,3-BPG binding groups - the β-chain terminal amino group and Lys82β - make negative and positive contributions, respectively, to the Bohr effect. The final result is that the Bohr effect at physiological pH is higher for 2,3-BPG bound compared to stripped hemoglobin. Contributions linked to His2β, His77β and His143β enable us to separate tertiary from quaternary Bohr contributions in stripped and in 2,3-BPG bound hemoglobin. Both contributions serve to make the Bohr effect for 2,3-BPG bound hemoglobin higher than for stripped hemoglobin at physiological pH. Copyright © 2017 Elsevier B.V. All rights reserved.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I
2016-04-01
Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it
Santos, Miguel; Carreira, L Miguel
2016-06-01
The present study was performed in a sample of 33 cats and aimed (1) to characterise the mandible height (Mh), mandibular canal height (MCh) and the distance between the interdental alveolar margin and the mandibular canal (dIAM-MC); and (2) to develop a mathematical model for dimension prediction of MCh using the patient's age, weight (Wg) and canine tooth width at the free gingival margin level (wCGM) that was easily accessible during the oral examination. Age, sex, breed, weight, skull type and the wCGM were the recorded variables for each patient. Right and left lateral view skull radiographs were made followed by measurements of the mandible anatomical structures, taken between the third premolar distal root and the fourth premolar proximal root. Results were considered statistically significant for P values <0.05, and statistical analysis was performed using SPSS software. We observed a strong correlation only between wCGM and MCh, and a prediction mathematical model was developed to calculate the MCh, with a standard error of only 0.4 mm. Our study allows a surgeon to establish relationships between a physical parameter, such as wCGM, evaluated in an oral examination, and the mandibular canal, which is a very important anatomical structure to consider in surgical procedures. Ideally, surgeons should always plan their mandible work only after obtaining a final diagnosis achieved through the use of complementary imaging exams, such as intra- and extra-oral radiographs. Thus, this mathematical equation offers an additional tool, providing more information on the relationships between oral anatomical structures, reducing the risk of iatrogenic lesions and promoting patient safety. © ISFM and AAFP 2015.
A Novel 3D Viscoelastic Acoustic Wave Equation Based Update Method for Reservoir History Matching
Katterbauer, Klemens
2014-12-10
The oil and gas industry has been revolutionized within the last decade, with horizontal drilling and hydraulic fracturing enabling the extraction of huge amounts of shale gas in areas previously considered impossible and the recovering of hydrocarbons in harsh environments like the arctic or in previously unimaginable depths like the off-shore exploration in the South China sea and Gulf of Mexico. With the development of 4D seismic, engineers and scientists have been enabled to map the evolution of fluid fronts within the reservoir and determine the displacement caused by the injected fluids. This in turn has led to enhanced production strategies, cost reduction and increased profits. Conventional approaches to incorporate seismic data into the history matching process have been to invert these data for constraints that are subsequently employed in the history matching process. This approach makes the incorporation computationally expensive and requires a lot of manual processing for obtaining the correct interpretation due to the potential artifacts that are generated by the generally ill-conditioned inversion problems. I have presented here a novel approach via including the time-lapse cross-well seismic survey data directly into the history matching process. The generated time-lapse seismic data are obtained from the full wave 3D viscoelastic acoustic wave equation. Furthermore an extensive analysis has been performed showing the robustness of the method and enhanced forecastability of the critical reservoir parameters, reducing uncertainties and exhibiting the benefits of a full wave 3D seismic approach. Finally, the improved performance has been statistically confirmed. The improvements illustrate the significant improvements in forecasting that are obtained via readily available seismic data without the need for inversion. This further optimizes oil production in addition to increasing return-on-investment on oil & gas field development projects, especially
Equation of teachers primary school course computer with learning method based on imaging
Directory of Open Access Journals (Sweden)
Елена Сергеевна Пучкова
2011-03-01
Full Text Available The paper considers the possibility of training future teachers with the rate of computer methods of teaching through the creation of visual imagery and operate them, еxamples of practice-oriented assignments, formative professional quality based on explicit and implicit use of a visual image, which decision is based on the cognitive function of visibility.
Piatkowski, Marian; Müthing, Steffen; Bastian, Peter
2018-03-01
In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order rotational incremental pressure correction scheme. The major focus of the paper is threefold: i) We propose a modified upwind scheme based on the Vijayasundaram numerical flux that has favourable properties in the context of DG. ii) We present a novel postprocessing technique in the Helmholtz projection step based on H (div) reconstruction of the pressure correction that is computed locally, is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly. As a consequence it also provides local mass conservation of the projected velocity. iii) Numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two-dimensional problems with known solution as well as large-scale three-dimensional problems. In particular we address second-order convergence in time of the splitting scheme as well as its long-time stability.
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Directory of Open Access Journals (Sweden)
Jianping Liu
2016-01-01
Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.
Majeed, Muhammad Usman
2017-01-01
the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time
Directory of Open Access Journals (Sweden)
Donald A. McLaren
2013-04-01
Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.
Kruglyakov, Mikhail; Kuvshinov, Alexey
2018-05-01
3-D interpretation of electromagnetic (EM) data of different origin and scale becomes a common practice worldwide. However, 3-D EM numerical simulations (modeling)—a key part of any 3-D EM data analysis—with realistic levels of complexity, accuracy and spatial detail still remains challenging from the computational point of view. We present a novel, efficient 3-D numerical solver based on a volume integral equation (IE) method. The efficiency is achieved by using a high-order polynomial (HOP) basis instead of the zero-order (piecewise constant) basis that is invoked in all routinely used IE-based solvers. We demonstrate that usage of the HOP basis allows us to decrease substantially the number of unknowns (preserving the same accuracy), with corresponding speed increase and memory saving.
The reactants equation of state for the tri-amino-tri-nitro-benzene (TATB) based explosive PBX 9502
Aslam, Tariq D.
2017-07-01
The response of high explosives (HEs), due to mechanical and/or thermal insults, is of great importance for both safety and performance. A major component of how an HE responds to these stimuli stems from its reactant equation of state (EOS). Here, the tri-amino-tri-nitro-benzene based explosive PBX 9502 is investigated by examining recent experiments. Furthermore, a complete thermal EOS is calibrated based on the functional form devised by Wescott, Stewart, and Davis [J. Appl. Phys. 98, 053514 (2005)]. It is found, by comparing to earlier calibrations, that a variety of thermodynamic data are needed to sufficiently constrain the EOS response over a wide range of thermodynamic state space. Included in the calibration presented here is the specific heat as a function of temperature, isobaric thermal expansion, and shock Hugoniot response. As validation of the resulting model, isothermal compression and isentropic compression are compared with recent experiments.
International Nuclear Information System (INIS)
Kushwah, S.S.; Shrivastava, H.C.; Singh, K.S.
2007-01-01
We have generalized the pressure-volume (P-V) relationships using simple polynomial and logarithmic expansions so as to make them consistent with the infinite pressure extrapolation according to the model of Stacey. The formulations are used to evaluate P-V relationships and pressure derivatives of bulk modulus upto third order (K', K'' and K''') for the earth core material taking input parameters based on the seismological data. The results based on the equations of state (EOS) generalized in the present study are found to yield good agreement with the Stacey EOS. The generalized logarithmic EOS due to Poirier and Tarantola deviates substantially from the seismic values for P, K and K'. The generalized Rydberg EOS gives almost identical results with the Birch-Murnaghan third-order EOS. Both of them yield deviations from the seismic data, which are in opposite direction as compared to those found from the generalized Poirier-Tarantola logarithmic EOS
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Austin, Rickey W.
In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation
International Nuclear Information System (INIS)
Chen Benfu; Guo Xianchun; Zou Zili
2009-01-01
It' s useful to identify the data with errors from the large number of observations during the process of adjustment to decrease the influence of the errors and to improve the quality of the final surveying result. Based on practical conditions of the nuclear power plant's plain control network, it has been given on how to simply calculate the threshold value which used to pre-weight each datum before adjustment calculation; it shows some superiorities in efficiency on data snooping and in quality of the final calculation compared with some traditional methods such as robust estimation, which process data with dynamic weight based the observation' s correction after each iteration. (authors)
The effect of numerical techniques on differential equation based chaotic generators
Zidan, Mohammed A.
2012-07-29
In this paper, we study the effect of the numerical solution accuracy on the digital implementation of differential chaos generators. Four systems are built on a Xilinx Virtex 4 FPGA using Euler, mid-point, and Runge-Kutta fourth order techniques. The twelve implementations are compared based on the FPGA used area, maximum throughput, maximum Lyapunov exponent, and autocorrelation confidence region. Based on circuit performance and the chaotic response of the different implementations, it was found that less complicated numerical solution has better chaotic response and higher throughput.
Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations
DEFF Research Database (Denmark)
Overgaard, Morten; Parner, Erik Thorlund; Pedersen, Jan
2017-01-01
A general asymptotic theory of estimates from estimating functions based on jack-knife pseudo-observations is established by requiring that the underlying estimator can be expressed as a smooth functional of the empirical distribution. Using results in p-variation norms, the theory is applied...
DEFF Research Database (Denmark)
Nadernejad, Ehsan; Nikpour, Mohsen
2012-01-01
In this paper, we have proposed two extensions to pixon-based image modeling. The first one is using bicubic interpolation instead of bilinear interpolation and the second one is using fuzzy filtering method, aiming to improve the quality of the pixonal image. Finally, partial differential...
Energy Technology Data Exchange (ETDEWEB)
Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il [Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Lomakin, V., E-mail: vlomakin@eng.ucsd.edu [Department of Electrical and Computer Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407 (United States)
2016-03-01
Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii) furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.
W. Hasan, W. Z.
2018-01-01
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554
Turcksin, Bruno; Ragusa, Jean C.; Morel, Jim E.
2012-01-01
It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.
Directory of Open Access Journals (Sweden)
A H Sabry
Full Text Available The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S
2018-01-01
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
Guissart, A.; Bernal, L. P.; Dimitriadis, G.; Terrapon, V. E.
2017-05-01
This work presents, compares and discusses results obtained with two indirect methods for the calculation of aerodynamic forces and pitching moment from 2D Particle Image Velocimetry (PIV) measurements. Both methodologies are based on the formulations of the momentum balance: the integral Navier-Stokes equations and the "flux equation" proposed by Noca et al. (J Fluids Struct 13(5):551-578, 1999), which has been extended to the computation of moments. The indirect methods are applied to spatio-temporal data for different separated flows around a plate with a 16:1 chord-to-thickness ratio. Experimental data are obtained in a water channel for both a plate undergoing a large amplitude imposed pitching motion and a static plate at high angle of attack. In addition to PIV data, direct measurements of aerodynamic loads are carried out to assess the quality of the indirect calculations. It is found that indirect methods are able to compute the mean and the temporal evolution of the loads for two-dimensional flows with a reasonable accuracy. Nonetheless, both methodologies are noise sensitive, and the parameters impacting the computation should thus be chosen carefully. It is also shown that results can be improved through the use of dynamic mode decomposition (DMD) as a pre-processing step.
A Structural Equation Model of Knowledge Management Based On Organizational Climate in Universities
F. Nazem; M. Mozaiini; A. Seifi
2014-01-01
The purpose of the present study was to provide a structural model of knowledge management in universities based on organizational climate. The population of the research included all employees of Islamic Azad University (IAU). The sample consisted of 1590 employees selected using stratified and cluster random sampling method. The research instruments were two questionnaires which were administered in 78 IAU branches and education centers: Sallis and Jones’s (2002) Knowledge Management Questi...
Rizzi, F.; Morris, K.; Sargsyan, K.; Mycek, P.; Safta, C.; Le Maî tre, O.; Knio, Omar; Debusschere, B.J.
2017-01-01
We discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ∼ 51K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.
Rizzi, F.
2017-05-25
We discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ∼ 51K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.
Chen, Meixiong; Yuan, Jie; Long, Xingwu; Kang, Zhenglong; Wang, Zhiguo; Li, Yingying
2013-12-01
A general beam position controlling method for 3D optical systems based on the method of solving ray matrix equations has been proposed in this paper. As a typical 3D optical system, nonplanar ring resonator of Zero-Lock Laser Gyroscopes has been chosen as an example to show its application. The total mismatching error induced by Faraday-wedge in nonplanar ring resonator has been defined and eliminated quite accurately with the error less than 1 μm. Compared with the method proposed in Ref. [14], the precision of the beam position controlling has been improved by two orders of magnitude. The novel method can be used to implement automatic beam position controlling in 3D optical systems with servo circuit. All those results have been confirmed by related alignment experiments. The results in this paper are important for beam controlling, ray tracing, cavity design and alignment in 3D optical systems.
A novel method of evaluating the lift force on the bluff body based on Noca’s flux equation
International Nuclear Information System (INIS)
Sui Xiang-Kun; Jiang Nan
2015-01-01
The influence of experimental error on lift force evaluated by Noca’s flux equation is studied based on adding errors into the direct numerical simulation data for flow past cylinder at Re = 100. As Noca suggested using the low-pass filter to get rid of the high-frequency noise in the evaluated lift force, we verify that his method is inapplicable for dealing with the dataset of 1% experimental error, although the precision is acceptable in practice. To overcome this defect, a novel method is proposed in this paper. The average of the lift forces calculated by using multiple control volume is taken as the evaluation before applying the low-pass filter. The method is applied to an experimental data for flow past a cylinder at approximately Re = 900 to verify its validation. The results show that it improves much better on evaluating the lift forces. (paper)
Directory of Open Access Journals (Sweden)
A. Abdullah
2018-04-01
Full Text Available Convection-diffusion problems, due to its fundamental nature, are found in various science and engineering applications. In this research, the importance of the relationship between grid structure and flow parameters in such problems is emphasized. In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two non-dimensional parameters serves as a guideline for more structured decision-making and improves the heuristic process in the determination of the computational domain grid for the numerical solution of convection-diffusion equations especially in the prediction of the concentration of the scalar. Results confirm the effectiveness of the new approach.
Directory of Open Access Journals (Sweden)
S. Ahmadi
2015-09-01
Full Text Available In this paper a multiobjective optimal design method of interior permanent magnet synchronous motor ( IPMSM for traction applications so as to maximize average torque and to minimize torque ripple has been presented. Based on train motion equations and physical properties of train, desired specifications such as steady state speed, rated output power, acceleration time and rated speed of traction motor are related to each other. By considering the same output power, steady state speed, rated voltage, rated current and different acceleration time for a specified train, multiobjective optimal design has been performed by Broyden–Fletcher–Goldfarb–Shanno (BFGS method and finite element method (FEM has been chosen as an analysis tool. BFGS method is one of Quasi Newton methods and is counted in classic approaches. Classic optimization methods are appropriate when FEM is applied as an analysis tool and objective function isn’t expressed in closed form in terms of optimization variables.
Shi, Yifei
2015-10-26
Graphene is a monolayer of carbon atoms structured in the form of a honeycomb lattice. Recent experimental studies have revealed that it can support surface plasmons at Terahertz frequencies thanks to its dispersive conductivity. Additionally, characteristics of these plasmons can be dynamically adjusted via electrostatic gating of the graphene sheet (K. S. Novoselov, et al., Science, 306, 666–669, 2004). These properties suggest that graphene can be a building block for novel electromagnetic and photonic devices for applications in the fields of photovoltaics, bio-chemical sensing, all-optical computing, and flexible electronics. Simulation of electromagnetic interactions on graphene-based devices is not an easy task. The thickness of the graphene sheet is orders of magnitude smaller than any other geometrical dimension of the device. Consequently, discretization of such a device leads to significantly large number of unknowns and/or ill-conditioned matrix systems.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Contact angle adjustment in equation-of-state-based pseudopotential model.
Hu, Anjie; Li, Longjian; Uddin, Rizwan; Liu, Dong
2016-05-01
The single component pseudopotential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many studies, it has been claimed that this model can be stable for density ratios larger than 1000. However, the application of the model is still limited to small density ratios when the contact angle is considered. The reason is that the original contact angle adjustment method influences the stability of the model. Moreover, simulation results in the present work show that, by applying the original contact angle adjustment method, the density distribution near the wall is artificially changed, and the contact angle is dependent on the surface tension. Hence, it is very inconvenient to apply this method with a fixed contact angle, and the accuracy of the model cannot be guaranteed. To solve these problems, a contact angle adjustment method based on the geometry analysis is proposed and numerically compared with the original method. Simulation results show that, with our contact angle adjustment method, the stability of the model is highly improved when the density ratio is relatively large, and it is independent of the surface tension.
International Nuclear Information System (INIS)
Hellums, L.J.; Fine, D.G.; DeCoursey, S.S.; Cronic, K.A.
1984-01-01
The American Petroleum Institute (API) has collected a large tracer data base representing the best field data on atmospheric dispersion performed up to 1982. Twelve of these tracer programs (Hanford 67, Green Glow, Prairie Grass, NRTS, TMI, Ocean Breeze, Dry Gulch, St. Louis, Rancho Seco, Paramount, Karlsruhe, Goodyear) were brought into Phillips Petroleum Company for Gaussian plume formulation using an optimal least squares procedure. The horizontal diffusion and the vertical diffusion were manipulated in an optimal fashion in the Gaussian plume formulation to give a best fit of calculated to experimental (field observations) data important conclusions from the many observations in this work are: 1. Field measured Turner stability when used with Pasquill-Gifford curves does not choose horizontal and vertical dispersion rates representative of true atmospheric turbulence in most cases, 2. Individual stabilities are required rather than assuming one stability for both dispersion rates, and 3. Horizontal diffusion is a function of downwind distance, crosswind distance, and stability for dispersion downwind of building complexes with considerable ground roughness
Yanti, Y. R.; Amin, S. M.; Sulaiman, R.
2018-01-01
This study described representation of students who have musical, logical-mathematic and naturalist intelligence in solving a problem. Subjects were selected on the basis of multiple intelligence tests (TPM) consists of 108 statements, with 102 statements adopted from Chislet and Chapman and 6 statements equal to eksistensial intelligences. Data were analyzed based on problem-solving tests (TPM) and interviewing. See the validity of the data then problem-solving tests (TPM) and interviewing is given twice with an analyzed using the representation indikator and the problem solving step. The results showed that: the stage of presenting information known, stage of devising a plan, and stage of carrying out the plan those three subjects were using same form of representation. While he stage of presenting information asked and stage of looking back, subject of logical-mathematic was using different forms of representation with subjects of musical and naturalist intelligence. From this research is expected to provide input to the teacher in determining the learning strategy that will be used by considering the representation of students with the basis of multiple intelligences.
Patched based methods for adaptive mesh refinement solutions of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Saltzman, J.
1997-09-02
This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.
Constitutive equations for cracked reinforced concrete based on a refined model
International Nuclear Information System (INIS)
Geistefeldt, H.
1977-01-01
Nonlinear numerical methods to calculate structures of reinforced concrete or of prestressed concrete are mostly based on two idealizing assumptions: tension stiffness perpendicular to cracks is equal to the stiffness of reinforcement alone and shear modulus is taken as constant. In real reinforced concrete structures concrete contributes to the tension-stiffness perpendicular to cracks and thus to the global stiffness matrix because of bond action between concrete and reinforcement and shear transfer in cracks is depending on stresses acting in cracks. Only few authors are taking these aspects into account and only with rough semiempirical assumptions. In this paper a refined nonlinear three-dimensional mechanical model for reinforced concrete is presented which can include these effects, hitherto neglected, depending on the given state of stress. The model is composed of three model-elements: component u - uncracked reinforced concrete with perfect bond (stiffness equal to the sum of the stiffnesses of concrete and reinforcement), component r - reinforcement free in surrounding concrete (reinforcement and concrete are having equal normal strains in noncracked directions and equal shear strains), component c - crack-part (shear stiffnesses in cracks is equal to the sum of shear stiffnesses of the reinforcement mesh, interface shear transfer and dowel action in cracks). (Auth.)
A Radiation Chemistry Code Based on the Green's Function of the Diffusion Equation
Plante, Ianik; Wu, Honglu
2014-01-01
Stochastic radiation track structure codes are of great interest for space radiation studies and hadron therapy in medicine. These codes are used for a many purposes, notably for microdosimetry and DNA damage studies. In the last two decades, they were also used with the Independent Reaction Times (IRT) method in the simulation of chemical reactions, to calculate the yield of various radiolytic species produced during the radiolysis of water and in chemical dosimeters. Recently, we have developed a Green's function based code to simulate reversible chemical reactions with an intermediate state, which yielded results in excellent agreement with those obtained by using the IRT method. This code was also used to simulate and the interaction of particles with membrane receptors. We are in the process of including this program for use with the Monte-Carlo track structure code Relativistic Ion Tracks (RITRACKS). This recent addition should greatly expand the capabilities of RITRACKS, notably to simulate DNA damage by both the direct and indirect effect.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Gordon, William J; Polansky, Jesse M; Boscardin, W John; Fung, Kathy Z; Steinman, Michael A
2010-11-01
US cholesterol guidelines use original and simplified versions of the Framingham model to estimate future coronary risk and thereby classify patients into risk groups with different treatment strategies. We sought to compare risk estimates and risk group classification generated by the original, complex Framingham model and the simplified, point-based version. We assessed 2,543 subjects age 20-79 from the 2001-2006 National Health and Nutrition Examination Surveys (NHANES) for whom Adult Treatment Panel III (ATP-III) guidelines recommend formal risk stratification. For each subject, we calculated the 10-year risk of major coronary events using the original and point-based Framingham models, and then compared differences in these risk estimates and whether these differences would place subjects into different ATP-III risk groups (20% risk). Using standard procedures, all analyses were adjusted for survey weights, clustering, and stratification to make our results nationally representative. Among 39 million eligible adults, the original Framingham model categorized 71% of subjects as having "moderate" risk (20%) risk. Estimates of coronary risk by the original and point-based models often differed substantially. The point-based system classified 15% of adults (5.7 million) into different risk groups than the original model, with 10% (3.9 million) misclassified into higher risk groups and 5% (1.8 million) into lower risk groups, for a net impact of classifying 2.1 million adults into higher risk groups. These risk group misclassifications would impact guideline-recommended drug treatment strategies for 25-46% of affected subjects. Patterns of misclassifications varied significantly by gender, age, and underlying CHD risk. Compared to the original Framingham model, the point-based version misclassifies millions of Americans into risk groups for which guidelines recommend different treatment strategies.
Henriques, David; Rocha, Miguel; Saez-Rodriguez, Julio; Banga, Julio R
2015-09-15
Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters. In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two-component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cells. Supplementary data are available at Bioinformatics online. julio@iim.csic.es or saezrodriguez@ebi.ac.uk. © The Author 2015. Published by Oxford University Press.
International Nuclear Information System (INIS)
Dang Xuanju; Tan Yonghong
2005-01-01
A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated
Iterative Splitting Methods for Differential Equations
Geiser, Juergen
2011-01-01
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential
Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D; Macdougall, Iain C; Ponikowski, Piotr; Lainscak, Mitja
2015-12-01
To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P=0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P=0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number: NCT01829880.
Cvan Trobec, Katja; Kerec Kos, Mojca; von Haehling, Stephan; Anker, Stefan D.; Macdougall, Iain C.; Ponikowski, Piotr; Lainscak, Mitja
2015-01-01
Aim To compare the performance of iohexol plasma clearance and creatinine-based renal function estimating equations in monitoring longitudinal renal function changes in chronic heart failure (CHF) patients, and to assess the effects of body composition on the equation performance. Methods Iohexol plasma clearance was measured in 43 CHF patients at baseline and after at least 6 months. Simultaneously, renal function was estimated with five creatinine-based equations (four- and six-variable Modification of Diet in Renal Disease, Cockcroft-Gault, Cockcroft-Gault adjusted for lean body mass, Chronic Kidney Disease Epidemiology Collaboration equation) and body composition was assessed using bioimpedance and dual-energy x-ray absorptiometry. Results Over a median follow-up of 7.5 months (range 6-17 months), iohexol clearance significantly declined (52.8 vs 44.4 mL/[min ×1.73 m2], P = 0.001). This decline was significantly higher in patients receiving mineralocorticoid receptor antagonists at baseline (mean decline -22% of baseline value vs -3%, P = 0.037). Mean serum creatinine concentration did not change significantly during follow-up and no creatinine-based renal function estimating equation was able to detect the significant longitudinal decline of renal function determined by iohexol clearance. After accounting for body composition, the accuracy of the equations improved, but not their ability to detect renal function decline. Conclusions Renal function measured with iohexol plasma clearance showed relevant decline in CHF patients, particularly in those treated with mineralocorticoid receptor antagonists. None of the equations for renal function estimation was able to detect these changes. ClinicalTrials.gov registration number NCT01829880 PMID:26718759
International Nuclear Information System (INIS)
Li Liyong; Tchelepi, Hamdi A.; Zhang Dongxiao
2003-01-01
We present detailed comparisons between high-resolution Monte Carlo simulation (MCS) and low-order numerical solutions of stochastic moment equations (SMEs) for the first and second statistical moments of pressure. The objective is to quantify the difference between the predictions obtained from MCS and SME. Natural formations with high permeability variability and large spatial correlation scales are of special interest for underground resources (e.g. oil and water). Consequently, we focus on such formations. We investigated fields with variance of log-permeability, σ Y 2 , from 0.1 to 3.0 and correlation scales (normalized by domain length) of 0.05 to 0.5. In order to avoid issues related to statistical convergence and resolution level, we used 9000 highly resolved realizations of permeability for MCS. We derive exact discrete forms of the statistical moment equations. Formulations based on equations written explicitly in terms of permeability (K-based) and log-transformed permeability (Y-based) are considered. The discrete forms are applicable to systems of arbitrary variance and correlation scales. However, equations governing a particular statistical moment depend on higher moments. Thus, while the moment equations are exact, they are not closed. In particular, the discrete form of the second moment of pressure includes two triplet terms that involve log-permeability (or permeability) and pressure. We combined MCS computations with full discrete SME equations to quantify the importance of the various terms that make up the moment equations. We show that second-moment solutions obtained using a low-order Y-based SME formulation are significantly better than those from K-based formulations, especially when σ Y 2 >1. As a result, Y-based formulations are preferred. The two triplet terms are complex functions of the variance level and correlation length. The importance (contribution) of these triplet terms increases dramatically as σ Y 2 increases above one. We
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
International Nuclear Information System (INIS)
Qamar, A.; Ahmad, T.M.; Hayat, A.; Khan, M.A.; Rehman, S. Z.
2017-01-01
To compare e-GFR estimated by creatinine or cystatin C based and combined creatinine and cystatin C based equations in type 2 diabetics in different stages of albuminuria. Study Design: Comparative cross-sectional study. Place and Duration of Study: Department of Chemical Pathology, Army Medical College Rawalpindi in collaboration with endocrinology outpatient department Military Hospital Rawalpindi, from Nov 2015 to Nov 2016. Material and Methods: A total of 119 type 2 diabetic subjects of either gender, aged 30- 60 years were enrolled in the study with duration of diabetes less than 15 years and were divided into further sub groups on the basis of degree of albuminuria determined by spot urine albumin to creatinine ratio (uACR). Fifty age matched disease free controls with no history of any systemic disease were also included in the study. Known patients of type 1 diabetes, chronic inflammatory disorders, uncontrolled hypertension, thyroid disease, chronic kidney disease, on lipid lowering drugs, steroids, ACE inhibitors and pregnant ladies were excluded from the study. Serum creatinine serum cystatin C were assessed on fully automated chemistry analyzer selectra. E-GFR was calculated by online GFR calculator by National Kidney Foundation. Comparison of means of e-GFR calculated by various equations was carried out by one way ANOVA and post-hoc Tukey tests. Degree of agreement between various equations for the estimation of GFR was assessed by kappa statistics. A p-value less than 0.05 were considered statistically significant. Results: Mean e-GFR (ml/min/1.73m2) was lowest in cystatin C based CKD-EPI equation (89.56 +- 39.84) followed by combined cystatin C and creatinine based CKD-EPI (92.34 +- 37.88). Values of e-GFR by creatinine based CKD-EPI equation (95.84 +- 27.24), and by creatinine based MDRD equation (105.37 +- 64.98) were both higher. In creatinine based MDRD, equation normo albuminuria and micro albuminuria groups did not show statistically
Fach, S; Sitzenfrei, R; Rauch, W
2009-01-01
It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.
Directory of Open Access Journals (Sweden)
Amir R. Ali
2017-01-01
Full Text Available This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM. The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.
Kim, Miji; Ryu, Eunjung
2015-12-01
The purpose of this study was to construct and test a structural equation model of quality of work life for clinical nurses based on Peterson and Wilson's Culture-Work-Health model (CWHM). A structured questionnaire was completed by 523 clinical nurses to analyze the relationships between concepts of CWHM-organizational culture, social support, employee health, organizational health, and quality of work life. Among these conceptual variables of CWHM, employee health was measured by perceived health status, and organizational health was measured by presenteeism. SPSS21.0 and AMOS 21.0 programs were used to analyze the efficiency of the hypothesized model and calculate the direct and indirect effects of factors affecting quality of work life among clinical nurses. The goodness-of-fit statistics of the final modified hypothetical model are as follows: χ²=586.03, χ²/df=4.19, GFI=.89, AGFI=.85, CFI=.91, TLI=.90, NFI=.89, and RMSEA=.08. The results revealed that organizational culture, social support, organizational health, and employee health accounted for 69% of clinical nurses' quality of work life. The major findings of this study indicate that it is essential to create a positive organizational culture and provide adequate organizational support to maintain a balance between the health of clinical nurses and the organization. Further repeated and expanded studies are needed to explore the multidimensional aspects of clinical nurses' quality of work life in Korea, including various factors, such as work environment, work stress, and burnout.
International Nuclear Information System (INIS)
Kim, Hyun Keol; Charette, Andre
2007-01-01
The Sensitivity Function-based Conjugate Gradient Method (SFCGM) is described. This method is used to solve the inverse problems of function estimation, such as the local maps of absorption and scattering coefficients, as applied to optical tomography for biomedical imaging. A highly scattering, absorbing, non-reflecting, non-emitting medium is considered here and simultaneous reconstructions of absorption and scattering coefficients inside the test medium are achieved with the proposed optimization technique, by using the exit intensity measured at boundary surfaces. The forward problem is solved with a discrete-ordinates finite-difference method on the framework of the frequency-domain full equation of radiative transfer. The modulation frequency is set to 600 MHz and the frequency data, obtained with the source modulation, is used as the input data. The inversion results demonstrate that the SFCGM can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by significantly reducing a cross-talk between inter-parameters. It is also observed that the closer-to-detector objects are better retrieved
International Nuclear Information System (INIS)
Kim, Hyun Keol; Hielscher, Andreas H
2009-01-01
It is well acknowledged that transport-theory-based reconstruction algorithm can provide the most accurate reconstruction results especially when small tissue volumes or high absorbing media are considered. However, these codes have a high computational burden and are often only slowly converging. Therefore, methods that accelerate the computation are highly desirable. To this end, we introduce in this work a partial-differential-equation (PDE) constrained approach to optical tomography that makes use of an all-at-once reduced Hessian sequential quadratic programming (rSQP) scheme. The proposed scheme treats the forward and inverse variables independently, which makes it possible to update the radiation intensities and the optical coefficients simultaneously by solving the forward and inverse problems, all at once. We evaluate the performance of the proposed scheme with numerical and experimental data, and find that the rSQP scheme can reduce the computation time by a factor of 10–25, as compared to the commonly employed limited memory BFGS method. At the same time accuracy and robustness even in the presence of noise are not compromised
Huang, Xingguo; Sun, Hui
2018-05-01
Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.
Feki, Saber
2013-07-01
An explicit marching-on-in-time (MOT)-based time-domain volume integral equation (TDVIE) solver has recently been developed for characterizing transient electromagnetic wave interactions on arbitrarily shaped dielectric bodies (A. Al-Jarro et al., IEEE Trans. Antennas Propag., vol. 60, no. 11, 2012). The solver discretizes the spatio-temporal convolutions of the source fields with the background medium\\'s Green function using nodal discretization in space and linear interpolation in time. The Green tensor, which involves second order spatial and temporal derivatives, is computed using finite differences on the temporal and spatial grid. A predictor-corrector algorithm is used to maintain the stability of the MOT scheme. The simplicity of the discretization scheme permits the computation of the discretized spatio-temporal convolutions on the fly during time marching; no \\'interaction\\' matrices are pre-computed or stored resulting in a memory efficient scheme. As a result, most often the applicability of this solver to the characterization of wave interactions on electrically large structures is limited by the computation time but not the memory. © 2013 IEEE.
Boomer, Kathleen B; Weller, Donald E; Jordan, Thomas E
2008-01-01
The Universal Soil Loss Equation (USLE) and its derivatives are widely used for identifying watersheds with a high potential for degrading stream water quality. We compared sediment yields estimated from regional application of the USLE, the automated revised RUSLE2, and five sediment delivery ratio algorithms to measured annual average sediment delivery in 78 catchments of the Chesapeake Bay watershed. We did the same comparisons for another 23 catchments monitored by the USGS. Predictions exceeded observed sediment yields by more than 100% and were highly correlated with USLE erosion predictions (Pearson r range, 0.73-0.92; p USLE estimates (r = 0.87; p USLE model did not change the results. In ranked comparisons between observed and predicted sediment yields, the models failed to identify catchments with higher yields (r range, -0.28-0.00; p > 0.14). In a multiple regression analysis, soil erodibility, log (stream flow), basin shape (topographic relief ratio), the square-root transformed proportion of forest, and occurrence in the Appalachian Plateau province explained 55% of the observed variance in measured suspended sediment loads, but the model performed poorly (r(2) = 0.06) at predicting loads in the 23 USGS watersheds not used in fitting the model. The use of USLE or multiple regression models to predict sediment yields is not advisable despite their present widespread application. Integrated watershed models based on the USLE may also be unsuitable for making management decisions.
Imanidis, Georgios; Luetolf, Peter
2006-07-01
An extended model for iontophoretic enhancement of transdermal drug permeation under constant voltage is described based on the previously modified Nernst-Planck equation, which included the effect of convective solvent flow. This model resulted in an analytical expression for the enhancement factor as a function of applied voltage, convective flow velocity due to electroosmosis, ratio of lipid to aqueous pathway passive permeability, and weighted average net ionic valence of the permeant in the aqueous epidermis domain. The shift of pH in the epidermis compared to bulk caused by the electrical double layer at the lipid-aqueous domain interface was evaluated using the Poisson-Boltzmann equation. This was solved numerically for representative surface charge densities and yielded pH differences between bulk and epidermal aqueous domain between 0.05 and 0.4 pH units. The developed model was used to analyze the experimental enhancement of an amphoteric weak electrolyte measured in vitro using human cadaver epidermis and a voltage of 250 mV at different pH values. Parameter values characterizing the involved factors were determined that yielded the experimental enhancement factors and passive permeability coefficients at all pH values. The model provided a very good agreement between experimental and calculated enhancement and passive permeability. The deduced parameters showed (i) that the pH shift in the aqueous permeation pathway had a notable effect on the ionic valence and the partitioning of the drug in this domain for a high surface charge density and depending on the pK(a) and pI of the drug in relation to the bulk pH; (ii) the magnitude and the direction of convective transport due to electroosmosis typically reflected the density and sign, respectively, of surface charge of the tissue and its effect on enhancement was substantial for bulk pH values differing from the pI of epidermal tissue; (iii) the aqueous pathway predominantly determined passive
Parand, K.; Nikarya, M.
2017-11-01
In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.
Salama, Amgad; Sun, Shuyu; Amin, Mohamed F. El
2015-01-01
In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.
Directory of Open Access Journals (Sweden)
M.H.T. Alshbool
2017-01-01
Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Salama, Amgad
2015-06-01
In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.
DEFF Research Database (Denmark)
Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode
2009-01-01
are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...
1982-12-01
1Muter.Te Motions Based on Ana lyzed Winds and wind-driven December 1982 Currents from. a Primitive Squat ion General a.OW -love"*..* Oean Circulation...mew se"$ (comeS.... do oISN..u am ae~ 00do OWaor NUN Fourier and Rotary Spc , Analysis Modeled Inertial and Subinrtial Motion 4 Primitive Equation
Directory of Open Access Journals (Sweden)
Eun Young Lee
2013-01-01
Full Text Available Aim. To compare two creatinine-based estimated glomerular filtration rate (eGFR equations, the chronic kidney disease epidemiology collaboration (CKD-EPI and the modification of diet in renal disease (MDRD, for predicting the risk of CKD progression in type 2 diabetic patients with nephropathy. Methods. A total of 707 type 2 diabetic patients with 24 hr urinary albumin excretion of more than 30 mg/day were retrospectively recruited and traced until doubling of baseline serum creatinine (SCr levels was noted. Results. During the follow-up period (median, 2.4 years, the CKD-EPI equation reclassified 10.9% of all MDRD-estimated subjects: 9.1% to an earlier stage of CKD and 1.8% to a later stage of CKD. Overall, the prevalence of CKD (eGFR < 60 mL/min/1.73 m2 was lowered from 54% to 51.6% by applying the CKD-EPI equation. On Cox-regression analysis, both equations exhibited significant associations with an increased risk for doubling of SCr. However, only the CKD-EPI equation maintained a significant hazard ratio for doubling of SCr in earlier-stage CKD (eGFR ≥ 45 mL/min/1.73 m2, when compared to stage 1 CKD (eGFR ≥ 90 mL/min/1.73 m2. Conclusion. In regard to CKD progression, these results suggest that the CKD-EPI equation might more accurately stratify earlier-stage CKD among type 2 diabetic patients with nephropathy than the MDRD study equation.
Yates, Christian A; Flegg, Mark B
2015-05-06
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of
Aldoghaither, Abeer
2015-12-01
In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton\\'s iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.
Aldoghaither, Abeer; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem
2015-01-01
In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.
Chen, Huei-Yen Winnie; Donmez, Birsen
2016-06-01
With the proliferation of new mobile and in-vehicle technologies, understanding the motivations behind a driver's voluntary engagement with such technologies is crucial from a safety perspective, yet is complex. Previous literature either surveyed a large number of distractions that may be diverse, or too focuses on one particular activity, such as cell phone use. Further, earlier studies about social-psychological factors underlying driver distraction tend to focus on one or two factors in-depth, and those that examine a more comprehensive set of factors are often limited in their analyses methods. The present work considers a wide array of social-psychological factors within a structural equation model to predict their influence on a focused set of technology-based distractions. A better understanding of these facilitators can enhance the design of distraction mitigation strategies. We analysed survey responses about three technology-based driver distractions: holding phone conversations, manually interacting with cell phones, and adjusting the settings of in-vehicle technology, as well as responses on five social-psychological factors: attitude, descriptive norm, injunctive norm, technology inclination, and a risk/sensation seeking personality. Using data collected from 525 drivers (ages: 18-80), a structural equation model was built to analyse these social-psychological factors as latent variables influencing self-reported engagement in these three technology-based distractions. Self-reported engagement in technology-based distractions was found to be largely influenced by attitudes about the distractions. Personality and social norms also played a significant role, but technology inclination did not. A closer look at two age groups (18-30 and 30+) showed that the effect of social norms, especially of injunctive norm (i.e., perceived approvals), was less prominent in the 30+ age group, while personality remained a significant predictor for the 30+ age group but
Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin
2018-01-01
In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.
Directory of Open Access Journals (Sweden)
Maisarah Jalalonmuhali
2017-01-01
Full Text Available Aim. To validate the accuracy of estimated glomerular filtration rate (eGFR equations in Malay population attending our hospital in comparison with radiolabeled measured GFR. Methods. A cross-sectional study recruiting volunteered patients in the outpatient setting. Chromium EDTA (51Cr-EDTA was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA, four-variable Modification of Diet in Renal Disease (4-MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations were calculated. Results. A total of 51 subjects were recruited with mean measured GFR 42.04 (17.70–111.10 ml/min/1.73 m2. Estimated GFR based on CGBSA, 4-MDRD, and CKD-EPI were 40.47 (16.52–115.52, 35.90 (14.00–98.00, and 37.24 (14.00–121.00, respectively. Higher accuracy was noted in 4-MDRD equations throughout all GFR groups except for subgroup of GFR ≥ 60 ml/min/1.73 m2 where CGBSA was better. Conclusions. The 4-MDRD equation seems to perform better in estimating GFR in Malay CKD patients generally and specifically in the subgroup of GFR < 60 ml/min/1.73 m2 and both BMI subgroups.
Karimzadeh, Iman; Khalili, Hossein
2016-06-06
Serum cystatin C (Cys C) has a number of advantages over serum creatinine in the evaluation of kidney function. Apart from Cys C level itself, several formulas have also been introduced in different clinical settings for the estimation of glomerular filtration rate (GFR) based upon serum Cys C level. The aim of the present study was to compare a serum Cys C-based equation with Cockcroft-Gault serum creatinine-based formula, both used in the calculation of GFR, in patients receiving amphotericin B. Fifty four adult patients with no history of acute or chronic kidney injury having been planned to receive conventional amphotericin B for an anticipated duration of at least 1 week for any indication were recruited. At three time points during amphotericin B treatment, including days 0, 7, and 14, serum cystatin C as well as creatinine levels were measured. GFR at the above time points was estimated by both creatinine (Cockcroft-Gault) and serum Cys C based equations. There was significant correlation between creatinine-based and Cys C-based GFR values at days 0 (R = 0.606, P = 0.001) and 7 (R = 0.714, P creatinine-and a cystatin C-based glomerular filtration rate equation in patients receiving amphotericin B.
Directory of Open Access Journals (Sweden)
Md Shamsul Arefin
2012-12-01
Full Text Available This work presents a technique for the chirality (n, m assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n, m with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot.
Arefin, Md Shamsul
2012-01-01
This work presents a technique for the chirality (n, m) assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n− m) with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m) of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot. PMID:28348319
International Nuclear Information System (INIS)
Erselcan, Taner; Turgut, Bulent; Dogan, Derya; Ozdemir, Semra
2002-01-01
The standardized uptake value (SUV) has gained recognition in recent years as a semiquantitative evaluation parameter in positron emission tomography (PET) studies. However, there is as yet no consensus on the way in which this index should be determined. One of the confusing factors is the normalisation procedure. Among the proposed anthropometric parameters for normalisation is lean body mass (LBM); LBM has been determined by using a predictive equation in most if not all of the studies. In the present study, we assessed the degree of agreement of various LBM predictive equations with a reference method. Secondly, we evaluated the impact of predicted LBM values on a hypothetical value of 2.5 SUV, normalised to LBM (SUV LBM ), by using various equations. The study population consisted of 153 women, aged 32.3±11.8 years (mean±SD), with a height of 1.61±0.06 m, a weight of 71.1±17.5 kg, a body surface area of 1.77±0.22 m 2 and a body mass index of 27.6±6.9 kg/m 2 . LBM (44.2±6.6 kg) was measured by a dual-energy X-ray absorptiometry (DEXA) method. A total of nine equations from the literature were evaluated, four of them from recent PET studies. Although there was significant correlation between predicted and measured LBM values, 95% limits of agreement determined by the Bland and Altman method showed a wide range of variation in predicted LBM values as compared with DEXA, no matter which predictive equation was used. Moreover, only one predictive equation was not statistically different in the comparison of means (DEXA and predicted LBM values). It was also shown that the predictive equations used in this study yield a wide range of SUV LBM values from 1.78 to 5.16 (29% less or 107% more) for an SUV of 2.5. In conclusion, this study suggests that estimation of LBM by use of a predictive equation may cause substantial error for an individual, and that if LBM is chosen for the SUV normalisation procedure, it should be measured, not predicted. (orig.)
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs
DEFF Research Database (Denmark)
Brunskog, Jonas; Richard, Antoine Philippe André
2016-01-01
Problems such as sound insulation and absorption of plane structures in laboratory conditions can theoretically be described as an integral or integral-differential equation. This equation contains the Green’s function integrated over the surface, which describes the radiation from the surface....... A variational technique, well described by Morse and Ingard, has successfully been used for both absorption and sound insulation for a plane incident wave. The resulting formulas are surprisingly simple, accurate and robust. Moreover, they capture the physics of sound radiation of a finite surface well. However...
Quantum linear Boltzmann equation
International Nuclear Information System (INIS)
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Energy Technology Data Exchange (ETDEWEB)
Chen, Xueli, E-mail: xlchen@xidian.edu.cn, E-mail: jimleung@mail.xidian.edu.cn; Zhang, Qitan; Yang, Defu; Liang, Jimin, E-mail: xlchen@xidian.edu.cn, E-mail: jimleung@mail.xidian.edu.cn [School of Life Science and Technology, Xidian University, Xi' an, Shaanxi 710071 (China)
2014-01-14
To provide an ideal solution for a specific problem of gastric cancer detection in which low-scattering regions simultaneously existed with both the non- and high-scattering regions, a novel hybrid radiosity-SP{sub 3} equation based reconstruction algorithm for bioluminescence tomography was proposed in this paper. In the algorithm, the third-order simplified spherical harmonics approximation (SP{sub 3}) was combined with the radiosity equation to describe the bioluminescent light propagation in tissues, which provided acceptable accuracy for the turbid medium with both low- and non-scattering regions. The performance of the algorithm was evaluated with digital mouse based simulations and a gastric cancer-bearing mouse based in situ experiment. Primary results demonstrated the feasibility and superiority of the proposed algorithm for the turbid medium with low- and non-scattering regions.
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.
Czech Academy of Sciences Publication Activity Database
Skalák, Zdeněk
2016-01-01
Roč. 437, č. 1 (2016), s. 474-484 ISSN 0022-247X R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985874 Keywords : Navier - Stokes equations * regularity of solutions * regularity criteria Subject RIV: BK - Fluid Dynamics Impact factor: 1.064, year: 2016
Given a time series of potential evapotranspiration and rainfall data, there are at least two approaches for estimating vertical percolation rates. One approach involves solving Richards' equation (RE) with a plant uptake model. An alternative approach involves applying a simple soil moisture accoun...
International Nuclear Information System (INIS)
Rajagopalan, S.; Jethra, A.; Khare, A.N.; Ghodgaonkar, M.D.; Srivenkateshan, R.; Menon, S.V.G.
1990-01-01
Issues relating to implementing iterative procedures, for numerical solution of elliptic partial differential equations, on a distributed parallel computing system are discussed. Preliminary investigations show that a speed-up of about 3.85 is achievable on a four transputer pipeline network. (author). 2 figs., 3 a ppendixes., 7 refs
Hao, Tian
2015-02-28
The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).
EunYoung Kim, PhD; Inhyo Cho, PhD; Eun Joo Kim, PhD
2017-01-01
Purpose: This study investigated the mediating effects of loneliness and depression on the relationship between adult attachment and smartphone addiction in university students. Methods: A total of 200 university students participated in this study. The data was analysed using descriptive statistics, correlation analysis, and structural equation modeling. Results: There were significant positive relationships between attachment anxiety, loneliness, depression, and smartphone addiction. ...
International Nuclear Information System (INIS)
Ma, J; Qi, H; Wu, S; Xu, Y; Zhou, L; Yan, H
2016-01-01
Purpose: In transmitted X-ray tomography imaging, projections are sometimes incomplete due to a variety of reasons, such as geometry inaccuracy, defective detector cells, etc. To address this issue, we have derived a direct consistency condition based on John’s Equation, and proposed a method to effectively restore incomplete projections based on this consistency condition. Methods: Through parameter substitutions, we have derived a direct consistency condition equation from John’s equation, in which the left side is only projection derivative of view and the right side is projection derivative of other geometrical parameters. Based on this consistency condition, a projection restoration method is proposed, which includes five steps: 1) Forward projecting reconstructed image and using linear interpolation to estimate the incomplete projections as the initial result; 2) Performing Fourier transform on the projections; 3) Restoring the incomplete frequency data using the consistency condition equation; 4) Performing inverse Fourier transform; 5) Repeat step 2)∼4) until our criteria is met to terminate the iteration. Results: A beam-blocking-based scatter correction case and a bad-pixel correction case were used to demonstrate the efficacy and robustness of our restoration method. The mean absolute error (MAE), signal noise ratio (SNR) and mean square error (MSE) were employed as our evaluation metrics of the reconstructed images. For the scatter correction case, the MAE is reduced from 63.3% to 71.7% with 4 iterations. Compared with the existing Patch’s method, the MAE of our method is further reduced by 8.72%. For the bad-pixel case, the SNR of the reconstructed image by our method is increased from 13.49% to 21.48%, with the MSE being decreased by 45.95%, compared with linear interpolation method. Conclusion: Our studies have demonstrated that our restoration method based on the new consistency condition could effectively restore the incomplete projections
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Directory of Open Access Journals (Sweden)
Jia-fu Feng
Full Text Available OBJECTIVE: To establish equations for the estimation of glomerular filtration rates (eGFRs based on serum creatinine (SCr and/or serum cystatin C (SCysC in Chinese patients with chronic kidney disease (CKD, and to compare the new equations with both the reference GFR (rGFR and the literature equations to evaluate their applicability. METHODS: The 788 Chinese CKD patients were randomly divided into two groups, the training group and the testing group, to establish new eGFR-formulas based on serum CysC and to validate the established formulas, respectively. (99mTc-DTPA clearance (as the rGFR, serum Cr, and serum CysC were determined for all patients, and GFR was calculated using the Cockcroft-Gault equation (eGFR1, the MDRD formula (eGFR2, the CKD-EPI formulas (eGFR3, eGFR4, and the Chinese eGFR Investigation Collaboration formulas (eGFR5, eGFR6. The accuracy of each eGFR was compared with the rGFR. RESULTS: The training and testing groups' mean GFRs were 50.84±31.36 mL/min/1.73 m(2 and 54.16±29.45 mL/min/1.73 m(2, respectively. The two newly developed eGFR formulas were fitted using iterative computation: [Formula: see text] and [Formula: see text]. Significant correlation was observed between each eGFR and the rGFR. However, proportional errors and constant errors were observed between rGFR and eGFR1, eGFR2, eGFR4, eGFR5 or eGFR6, and constant errors were observed between eGFR3 and rGFR, as revealed by the Passing & Bablok plot analysis. The Bland-Altman analysis illustrated that the 95% limits of agreement of all equations exceeded the previously accepted limits of <60 mL/min •1.73 m(2, except the equations of eGFR7 and eGFR8. CONCLUSION: The newly developed formulas, eGFR7 and eGFR8, provide precise and accurate GFR estimation using serum CysC detection alone or in combination with serum Cr detection. Differences in detection methods should be carefully considered when choosing literature eGFR equations to avoid misdiagnosis and
Marsden, O; Bogey, C; Bailly, C
2014-03-01
The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described.
Khodarahmi, Iman; Shakeri, Mostafa; Sharp, M; Amini, Amir A
2010-01-01
Pressure gradient across a Gaussian-shaped 87% area stenosis phantom was estimated by solving the pressure Poisson equation (PPE) for a steady flow mimicking the blood flow through the human iliac artery. The velocity field needed to solve the pressure equation was obtained using particle image velocimetry (PIV). A steady flow rate of 46.9 ml/s was used, which corresponds to a Reynolds number of 188 and 595 at the inlet and stenosis throat, respectively (in the range of mean Reynolds number encountered in-vivo). In addition, computational fluid dynamics (CFD) simulation of the same flow was performed. Pressure drops across the stenosis predicted by PPE/PIV and CFD were compared with those measured by a pressure catheter transducer. RMS errors relative to the measurements were 17% and 10% for PPE/PIV and CFD, respectively.
Zheng, Xiang
2015-03-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors. © 2015 Elsevier Inc.
International Nuclear Information System (INIS)
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-01-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors
Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David
2015-03-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.
Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan
2016-10-01
A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.
Thamareerat, N; Luadsong, A; Aschariyaphotha, N
2016-01-01
In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.
Czech Academy of Sciences Publication Activity Database
Guo, Z.; Kučera, P.; Skalák, Zdeněk
2018-01-01
Roč. 458, č. 1 (2018), s. 755-766 ISSN 0022-247X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985874 Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition Subject RIV: BA - General Mathematics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.064, year: 2016
Energy Technology Data Exchange (ETDEWEB)
Park, Kyung Seok; Kim, Hyun Dae; Yeom, Choong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1995-07-01
A computer code for solving the three-dimensional reactor neutronic transient problems utilizing multi-point reactor kinetics equations recently developed has been developed. For evaluating its applicability, the code has been tested with typical 3-D LWR and CANDU reactor transient problems. The performance of the method and code has been compared with the results by fine and coarse meshes computer codes employing the direct methods.
International Nuclear Information System (INIS)
Benoist, P.
1990-06-01
The migration area, which relates the buckling to the multiplication factor, can be calculated by means of the Deniz formula. This formula involves the direct and adjoint angular fluxes. It is shown in this note that it is possible, using the integral form of the transport equation, to establish an equivalent formula in which only angle-integrated quantities appear. This formulation is more suitable for the calculation by the collision probably method [fr
Malik, G P
2016-01-01
Given the Debye temperature of an elemental superconductor (SC) and its Tc, BCS theory enables one to predict the value of its gap 0 at T = 0, or vice versa. This monograph shows that non-elemental SCs can be similarly dealt with via the generalized BCS equations (GBCSEs) which, given any two parameters of the set {Tc, 10, 20 > 10}, enable one to predict the third. Also given herein are new equations for the critical magnetic field and critical current density of an elemental and a non-elemental SC — equations that are derived directly from those that govern pairing in them. The monograph includes topics that are usually not covered in any one text on superconductivity, e.g., BCS-BEC crossover physics, the long-standing puzzle posed by SrTiO3, and heavy-fermion superconductors — all of which are still imperfectly understood and therefore continue to avidly engage theoreticians. It suggests that addressing the Tcs, s and other properties (e.g., number densities of charge carriers) of high-Tc SCs via GBCSE...
Energy Technology Data Exchange (ETDEWEB)
Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre ' Kurchatov Institute,' (Russian Federation)
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
International Nuclear Information System (INIS)
Basharov, A. M.
2012-01-01
It is shown that the effective Hamiltonian representation, as it is formulated in author’s papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are “locked” inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
International Nuclear Information System (INIS)
Calif, Rudy
2012-01-01
Highlights: ► Probability Density Functions are proposed to fit the wind speed fluctuations distributions for three representative classes. ► Stochastic simulations are performed using a Langevin equation for each class. ► The properties of simulated and measured wind speed sequences are close. -- Abstract: Wind energy production is very sensitive to turbulent wind speed. Thus rapid variation of wind speed due to changes in the local meteorological conditions can lead to electrical power variations of the order of the nominal power output, in particular when wind power variations on very short time scales, range at few seconds to 1 h, are considered. In small grid as they exist on islands (Guadeloupean Archipelago: French West Indies) such fluctuations can cause instabilities in case of intermediate power shortages. The developed analysis in reveals three main classes of time series for the wind speed fluctuations. In this work, Probability Density Functions (PDFs) are proposed to fit the wind speed fluctuations distributions in each class. After, to simulate wind speed fluctuations sequences, we use a stochastic differential equation, the Langevin equation considering Gaussian turbulence PDF (class I), Gram–Charlier PDF (class II) and a mixture of gaussian PDF (class III). The statistical and dynamical properties of simulated wind sequences are close to those of measured wind sequences, for each class.
International Nuclear Information System (INIS)
Palev, T.D.; Stoilova, N.I.
1995-07-01
New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra U q [osp(1/2)], which were found recently. Representations of the braid group B N are defined within any N th tensorial power of root of 1 U q [osp(1/2)] modules. (author). 40 refs
Puig Cayuela, Vicenç; Blesa Izquierdo, Joaquim
2013-01-01
In this paper, a methodology for limnimeter and rain-gauge fault detection and isolation (FDI) in sewer networks is presented. The proposed model based FDI approach uses interval parity equations for fault detection in order to enhance robustness against modelling errors and noise. They both are assumed unknown but bounded, following the so-called interval (or set-membership) approach. On the other hand, fault isolation relies on an algorithm that reasons using several fault signature matrice...
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Wetterich, C.
2018-06-01
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.
Li, Xu; Yang, Chuanlei; Wang, Yinyan; Wang, Hechun
2018-01-01
To achieve a much more extensive intake air flow range of the diesel engine, a variable-geometry compressor (VGC) is introduced into a turbocharged diesel engine. However, due to the variable diffuser vane angle (DVA), the prediction for the performance of the VGC becomes more difficult than for a normal compressor. In the present study, a prediction model comprising an elliptical equation and a PLS (partial least-squares) model was proposed to predict the performance of the VGC. The speed lines of the pressure ratio map and the efficiency map were fitted with the elliptical equation, and the coefficients of the elliptical equation were introduced into the PLS model to build the polynomial relationship between the coefficients and the relative speed, the DVA. Further, the maximal order of the polynomial was investigated in detail to reduce the number of sub-coefficients and achieve acceptable fit accuracy simultaneously. The prediction model was validated with sample data and in order to present the superiority of compressor performance prediction, the prediction results of this model were compared with those of the look-up table and back-propagation neural networks (BPNNs). The validation and comparison results show that the prediction accuracy of the new developed model is acceptable, and this model is much more suitable than the look-up table and the BPNN methods under the same condition in VGC performance prediction. Moreover, the new developed prediction model provides a novel and effective prediction solution for the VGC and can be used to improve the accuracy of the thermodynamic model for turbocharged diesel engines in the future.
Directory of Open Access Journals (Sweden)
Wenwan Ding
2016-01-01
Full Text Available An improved fractal sea surface model, which can describe the capillary waves very well, is introduced to simulate the one-dimension rough sea surface. In this model, the propagation of electromagnetic waves (EWs is computed by the parabolic equation (PE method using the finite-difference (FD algorithm. The numerical simulation results of the introduced model are compared with those of the Miller-Brown model and the Elfouhaily spectrum inversion model. It has been shown that the effects of the fine structure of the sea surface on the EWs propagation in the introduced model are more apparent than those in the other two models.
Directory of Open Access Journals (Sweden)
José Manuel Serrano
2008-11-01
Full Text Available The present study is focused on the design of the assessment of programs for teacher training. The authors emphasize the relevance of the assessment of this kind of programs and its development by models of structural equations. There are specifically postulated four exogenous variables, which coincide with four segments of a program, and an endogenous variable, which refers to the results, expressed these in terms of adequacy, productivity, efficacy, efficiency, and effectiveness. Both the structural and the measurement aspects are totally developed in the corresponding causal model.
International Nuclear Information System (INIS)
Webb, J F; Yong, K S C; Haldar, M K
2015-01-01
Using results that come out of a simplified rate equation model, the suppression of residual amplitude modulation in injection locked quantum cascade lasers with the master laser modulated by its drive current is investigated. Quasi-static and dynamic expressions for intensity modulation are used. The suppression peaks at a specific value of the injection ratio for a given detuning and linewidth enhancement factor. The intensity modulation suppression remains constant over a range of frequencies. The effects of injection ratio, detuning, coupling efficiency and linewidth enhancement factor are considered. (paper)
International Nuclear Information System (INIS)
Monte, Luigi
2009-01-01
The present work describes a model for predicting the population dynamics of the main components (resources and consumers) of terrestrial ecosystems exposed to ionising radiation. The ecosystem is modelled by the Lotka-Volterra equations with consumer competition. Linear dose-response relationships without threshold are assumed to relate the values of the model parameters to the dose rates. The model accounts for the migration of consumers from areas characterised by different levels of radionuclide contamination. The criteria to select the model parameter values are motivated by accounting for the results of the empirical studies of past decades. Examples of predictions for long-term chronic exposure are reported and discussed.
Zheng, Xiang; Yang, Chao; Cai, Xiaochuan; Keyes, David E.
2015-01-01
We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation
International Nuclear Information System (INIS)
Zhang, H.; Rizwan-uddin; Dorning, J.J.
1995-01-01
A diffusion equation-based systematic homogenization theory and a self-consistent dehomogenization theory for fuel assemblies have been developed for use with coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is based on a multiple-scales asymptotic expansion carried out through second order in a small parameter, the ratio of the average diffusion length to the reactor characteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spatial scales, the development systematically yields an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The rector eigenvalue 1/k eff is shown to be obtained to the second order in the small parameter, and the heterogeneous diffusion theory flux is shown to be obtained to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local fluxes and the determination of pin powers, even though homogenized assemblies are used in the global nodal diffusion calculation
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
The Dirac equation for accountants
International Nuclear Information System (INIS)
Ord, G.N.
2006-01-01
In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)
2016-02-20
We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.
On matrix fractional differential equations
Directory of Open Access Journals (Sweden)
Adem Kılıçman
2017-01-01
Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.
Reduced kinetic equations: An influence functional approach
International Nuclear Information System (INIS)
Wio, H.S.
1985-01-01
The author discusses a scheme for obtaining reduced descriptions of multivariate kinetic equations based on the 'influence functional' method of Feynmann. It is applied to the case of Fokker-Planck equations showing the form that results for the reduced equation. The possibility of Markovian or non-Markovian reduced description is discussed. As a particular example, the reduction of the Kramers equation to the Smoluchwski equation in the limit of high friction is also discussed
Energy Technology Data Exchange (ETDEWEB)
Marc O Delchini; Jean E. Ragusa; Ray A. Berry
2015-07-01
We present a new version of the entropy viscosity method, a viscous regularization technique for hyperbolic conservation laws, that is well-suited for low-Mach flows. By means of a low-Mach asymptotic study, new expressions for the entropy viscosity coefficients are derived. These definitions are valid for a wide range of Mach numbers, from subsonic flows (with very low Mach numbers) to supersonic flows, and no longer depend on an analytical expression for the entropy function. In addition, the entropy viscosity method is extended to Euler equations with variable area for nozzle flow problems. The effectiveness of the method is demonstrated using various 1-D and 2-D benchmark tests: flow in a converging–diverging nozzle; Leblanc shock tube; slow moving shock; strong shock for liquid phase; low-Mach flows around a cylinder and over a circular hump; and supersonic flow in a compression corner. Convergence studies are performed for smooth solutions and solutions with shocks present.
Directory of Open Access Journals (Sweden)
Ti Hu
2016-01-01
Full Text Available We introduce a new perspective to systematically investigate the cause-and-effect relationships among competition, innovation, risk-taking, and profitability in the Chinese banking industry. Our hypotheses are tested by the structural equation modeling (SEM, and the empirical results show that (i risk-taking is positively related to profitability; (ii innovation positively affects both risk-taking and profitability, and the effect of innovation on profitability works both directly and indirectly; (iii competition negatively affects risk-taking but positively affects both innovation and profitability, and the effects of competition on risk-taking and profitability work both directly and indirectly; (iv there is a cascading relationship among market competition and bank innovation, risk-taking, and profitability.
Directory of Open Access Journals (Sweden)
Liudan Jiao
2016-09-01
Full Text Available The rapid urbanization process has brought problems to China, such as traffic congestion, air pollution, water pollution and resources scarcity. Sustainable urbanization is commonly appreciated as an effective way to promote the sustainable development. The proper understanding of the sustainable urbanization performance is critical to provide governments with support in making urban development strategies and policies for guiding the sustainable development. This paper utilizes the method of Structural equation modeling (SEM to establish an assessment model for measuring sustainable urbanization performance. Four unobserved endogenous variables, economic variable, social variable, environment variable and resource variable, and 21 observed endogenous variables comprise the SEM model. A case study of the 31 provinces in China demonstrates the validity of the SEM model and the analysis results indicated that the assessment model could help make more effective policies and strategies for improving urban sustainability by recognizing the statue of sustainable urbanization.
Kim, EunYoung; Cho, Inhyo; Kim, Eun Joo
2017-06-01
This study investigated the mediating effects of loneliness and depression on the relationship between adult attachment and smartphone addiction in university students. A total of 200 university students participated in this study. The data was analysed using descriptive statistics, correlation analysis, and structural equation modeling. There were significant positive relationships between attachment anxiety, loneliness, depression, and smartphone addiction. However, attachment anxiety was not significantly correlated with smartphone addiction. The results also showed that loneliness did not directly mediate between attachment anxiety and smartphone addiction. In addition, loneliness and depression serially mediated between attachment anxiety and smartphone addiction. The results suggest there are mediating effects of loneliness and depression in the relationship between attachment anxiety and smartphone addiction. The hypothesized model was found to be a suitable model for predicting smartphone addiction among university students. Future study is required to find a causal path to prevent smartphone addiction among university students. Copyright © 2017. Published by Elsevier B.V.
Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame
Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.
2010-01-01
Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.
Bhrawy, A. H.; Zaky, M. A.
2015-01-01
In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.
Energy Technology Data Exchange (ETDEWEB)
Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan); Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering
1996-10-01
The effect of initial models on full-wave inversion (FWI) analysis based on acoustic wave-equation was studied for elastic wave tomography of underground structures. At present, travel time inversion using initial motion travel time is generally used, and inverse analysis is conducted using the concept `ray,` assuming very high wave frequency. Although this method can derive stable solutions relatively unaffected by initial model, it uses only the data of initial motion travel time. FWI calculates theoretical waveform at each receiver using all of observed waveforms as data by wave equation modeling where 2-D underground structure is calculated by difference calculus under the assumption that wave propagation is described by wave equation of P wave. Although it is a weak point that FWI is easily affected by noises in an initial model and data, it is featured by high resolution of solutions. This method offers very excellent convergence as a proper initial model is used, resulting in sufficient performance, however, it is strongly affected by initial model. 2 refs., 7 figs., 1 tab.
International Nuclear Information System (INIS)
Chen, Qianghua; Zhang, Mengce; Liu, Shuaijie; He, Yongxi; Luo, Huifu; Luo, Jun; Lv, Weiwei
2016-01-01
At present the formulae proposed by G Boensch and E Potulski in 1998 (Boensch and Potulski 1998 Metrologia 35 133–9) are mostly used to calculate the air refractive index. However, the humidity correction equation in the formulae is derived by using the light source of a Cd lamp whose light frequency stability is poor and at a narrow temperature range, around 20 °C. So it is no longer suitable in present optical precision measurements. To solve this problem, we propose a refractive index measurement system based on phase step interferometer with three frequency stabilized lasers (532 nm, 633 nm, 780 nm), corrected coefficients of the humidity are measured and a corresponding revised humidity correction equation is acquired. Meanwhile, the application temperature range is extended from 14.6 °C to 25.0 °C. The experiment comparison results at the temperature of 22.2–23.2 °C show the accuracy by the presented equation is better than that of Boensch and Potulski. (paper)
Chavez, Gustavo Ivan
2017-07-10
This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.
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Guozheng Zhao
2013-01-01
Full Text Available The B3LYP/6-31G (d density functional theory (DFT method was used to study molecular geometry, electronic structure, infrared spectrum (IR and thermodynamic properties. Heat of formation (HOF and calculated density were estimated to evaluate detonation properties using Kamlet-Jacobs equations. Thermal stability of 3,6,7,8-tetranitro-3,6,7,8-tetraaza-tricyclo [3.1.1.1(2,4]octane (TTTO was investigated by calculating bond dissociation energy (BDE at the unrestricted B3LYP/6-31G(d level. Results showed the N-NO2 bond is a trigger bond during the thermolysis initiation process. The crystal structure obtained by molecular mechanics (MM methods belongs to P2(1/C space group, with cell parameters a = 8.239 Å, b = 8.079 Å, c = 16.860 Å, Z = 4 and r = 1.922 g cm-3. Both detonation velocity of 9.79 km s-1 and detonation pressure of 44.22 GPa performed similarly to CL-20. According to the quantitative standards of energetics and stability, TTTO essentially satisfies this requirement as a high energy density compound (HEDC.
International Nuclear Information System (INIS)
Reuter, W.G.; Place, T.A.
1981-01-01
An accurate assessment of the influence of defects on structural component integrity is needed. Generally accepted analytical techniques are not available for the very ductile materials used in many nuclear reactor components. Some results are presented from a test programme to obtain data by which to evaluate proposed models. Plate and pipe specimens containing surface flaws were fabricated from annealed Type 304 stainless steel and tested at room temperature. An evaluation of an empirical equation based on flow stress is presented. In essentially all instances the flow stress is not a constant but varies as a function of the size of the surface flaw. (author)
Chien, Hui-Min; Kao, Chia-Pin; Yeh, I-Jan; Lin, Kuen-Yi
2012-01-01
This study was conducted to investigate elementary school teachers' attitudes and motivation toward web-based professional development. The relationship between teachers' attitudes and motivation was explored using the AWPD (Attitudes toward Web-based Professional Development) and MWPD (Motivation toward Web-based Professional Development)…
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Engelhardt, Benjamin; Kschischo, Maik; Fröhlich, Holger
2017-06-01
Ordinary differential equations (ODEs) are a popular approach to quantitatively model molecular networks based on biological knowledge. However, such knowledge is typically restricted. Wrongly modelled biological mechanisms as well as relevant external influence factors that are not included into the model are likely to manifest in major discrepancies between model predictions and experimental data. Finding the exact reasons for such observed discrepancies can be quite challenging in practice. In order to address this issue, we suggest a Bayesian approach to estimate hidden influences in ODE-based models. The method can distinguish between exogenous and endogenous hidden influences. Thus, we can detect wrongly specified as well as missed molecular interactions in the model. We demonstrate the performance of our Bayesian dynamic elastic-net with several ordinary differential equation models from the literature, such as human JAK-STAT signalling, information processing at the erythropoietin receptor, isomerization of liquid α -Pinene, G protein cycling in yeast and UV-B triggered signalling in plants. Moreover, we investigate a set of commonly known network motifs and a gene-regulatory network. Altogether our method supports the modeller in an algorithmic manner to identify possible sources of errors in ODE-based models on the basis of experimental data. © 2017 The Author(s).
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Analytic equation of state for FCC C60 solid based on analytic mean-field potential approach
International Nuclear Information System (INIS)
Sun Jiuxun
2006-01-01
The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized self-consistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320 K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature
International Nuclear Information System (INIS)
Lee, Jin Pyo; Joo, Han Gyu
2010-01-01
In the thermo-fluid analysis code named CUPID, the linear system of pressure equations must be solved in each iteration step. The time for repeatedly solving the linear system can be quite significant because large sparse matrices of Rank more than 50,000 are involved and the diagonal dominance of the system is hardly hold. Therefore parallelization of the linear system solver is essential to reduce the computing time. Meanwhile, Graphics Processing Units (GPU) have been developed as highly parallel, multi-core processors for the global demand of high quality 3D graphics. If a suitable interface is provided, parallelization using GPU can be available to engineering computing. NVIDIA provides a Software Development Kit(SDK) named CUDA(Compute Unified Device Architecture) to code developers so that they can manage GPUs for parallelization using the C language. In this research, we implement parallel routines for the linear system solver using CUDA, and examine the performance of the parallelization. In the next section, we will describe the method of CUDA parallelization for the CUPID code, and then the performance of the CUDA parallelization will be discussed
International Nuclear Information System (INIS)
Zeng Zhenzhong; Piao Shilong; Yin Guodong; Peng Shushi; Lin Xin; Ciais, Philippe; Myneni, Ranga B
2012-01-01
We applied a land water mass balance equation over 59 major river basins during 2003–9 to estimate evapotranspiration (ET), using as input terrestrial water storage anomaly (TWSA) data from the GRACE satellites, precipitation and in situ runoff measurements. We found that the terrestrial water storage change cannot be neglected in the estimation of ET on an annual time step, especially in areas with relatively low ET values. We developed a spatial regression model of ET by integrating precipitation, temperature and satellite-derived normalized difference vegetation index (NDVI) data, and used this model to extrapolate the spatio-temporal patterns of changes in ET from 1982 to 2009. We found that the globally averaged land ET is about 604 mm yr −1 with a range of 558–650 mm yr −1 . From 1982 to 2009, global land ET was found to increase at a rate of 1.10 mm yr −2 , with the Amazon regions and Southeast Asia showing the highest ET increasing trend. Further analyses, however, show that the increase in global land ET mainly occurred between the 1980s and the 1990s. The trend over the 2000s, its magnitude or even the sign of change substantially depended on the choice of the beginning year. This suggests a non-significant trend in global land ET over the last decade. (letter)
Scalco, Andrea; Noventa, Stefano; Sartori, Riccardo; Ceschi, Andrea
2017-05-01
During the last decade, the purchase of organic food within a sustainable consumption context has gained momentum. Consequently, the amount of research in the field has increased, leading in some cases to discrepancies regarding both methods and results. The present review examines those works that applied the theory of planned behavior (TPB; Ajzen, 1991) as a theoretical framework in order to understand and predict consumers' motivation to buy organic food. A meta-analysis has been conducted to assess the strength of the relationships between attitude, subjective norms, perceived behavioral control, and intention, as well as between intention and behavior. Results confirm the major role played by individual attitude in shaping buying intention, followed by subjective norms and perceived behavioral control. Intention-behavior shows a large effect size, few studies however explicitly reported such an association. Furthermore, starting from a pooled correlation matrix, a meta-analytic structural equation model has been applied to jointly evaluate the strength of the relationships among the factors of the original model. Results suggest the robustness of the TPB model. In addition, mediation analysis indicates a potential direct effect from subjective norms to individual attitude in the present context. Finally, some issues regarding methodological aspects of the application of the TPB within the context of organic food are discussed for further research developments. Copyright © 2017 Elsevier Ltd. All rights reserved.
Lee, Eunjung
2013-01-01
The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…
Huen, Jenny My; Lai, Eliza Sy; Shum, Angie Ky; So, Sam Wk; Chan, Melissa Ky; Wong, Paul Wc; Law, Y W; Yip, Paul Sf
2016-10-07
Digital game-based learning (DGBL) makes use of the entertaining power of digital games for educational purposes. Effectiveness assessment of DGBL programs has been underexplored and no attempt has been made to simultaneously model both important components of DGBL: learning attainment (ie, educational purposes of DGBL) and engagement of users (ie, entertaining power of DGBL) in evaluating program effectiveness. This study aimed to describe and evaluate an Internet-based DGBL program, Professor Gooley and the Flame of Mind, which promotes mental health to adolescents in a positive youth development approach. In particular, we investigated whether user engagement in the DGBL program could enhance their attainment on each of the learning constructs per DGBL module and subsequently enhance their mental health as measured by psychological well-being. Users were assessed on their attainment on each learning construct, psychological well-being, and engagement in each of the modules. One structural equation model was constructed for each DGBL module to model the effect of users' engagement and attainment on the learning construct on their psychological well-being. Of the 498 secondary school students that registered and participated from the first module of the DGBL program, 192 completed all 8 modules of the program. Results from structural equation modeling suggested that a higher extent of engagement in the program activities facilitated users' attainment on the learning constructs on most of the modules and in turn enhanced their psychological well-being after controlling for users' initial psychological well-being and initial attainment on the constructs. This study provided evidence that Internet intervention for mental health, implemented with the technologies and digital innovations of DGBL, could enhance youth mental health. Structural equation modeling is a promising approach in evaluating the effectiveness of DGBL programs.
Directory of Open Access Journals (Sweden)
Yun Wang
2017-10-01
Full Text Available Understanding the public transportation users’ preferences to long-distance travel modes would contribute to reasonable developing policies and resource allocation. This paper aims to explore the influencing mechanism of potential factors on the long-distance travel mode choice. A survey was conducted to collect the data. The analysis of variance (ANOVA approach was applied to analyze the correlation relationship between potential factors and travel mode choice behavior. The results showed that, except gender, service demand for safety and departure time, all of the other factors significantly influenced the travel mode choice behavior. Specifically, passengers with higher education level and income level were more likely to choose high-speed railway (HSR and plane; passengers caring about travel expense were more likely to choose ordinary train, whereas plane and HSR may be chosen more by passengers caring more about comfort, punctuality and efficiency; the more passengers were satisfied with travel modes’ service performance, the more they would be likely to choose them; the most competitive distance ranges for coach, ordinary train, HSR and plane were below 500 km, 500–1000 km, 500–1500 km and over 1500 km, respectively. Besides, the structural equation modeling (SEM technique was applied to investigate the influencing mechanism of factors on the long-distance travel mode choice. The results revealed that travel distance was the most significant variable directly influencing passengers’ mode choices, followed by the service demand, performance evaluation, and personal attributes. Furthermore, personal attributes were verified to have an indirect effect on travel mode choice behavior by significantly affecting the service demand and performance evaluation.
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe
2013-08-01
Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
International Nuclear Information System (INIS)
Ma, Weiwu; Fang, Song; Su, Bo; Xue, Xinpei; Li, Min
2017-01-01
Highlights: • Second-law analysis leads to analytical COP formulas for refrigeration cycles. • Relative errors of the analytical equations are smaller than ±5.0%. • The analytical expressions characterize the influence of refrigerants. • Global entropy analysis elucidates the impact of cycle processes on COP. - Abstract: This article reports a second-law-based analysis of the vapor-compression refrigeration cycle, which leads to a set of explicit theoretical formulas for the coefficient of performance (COP). These analytical expressions provide a fast and accurate approach to computer simulations of the vapor-compression cycle without recourse to thermodynamic diagrams or equations of state. The second-law-based analysis yields specific expressions for the entropy generations of irreversible processes, enabling us to evaluate the thermodynamic features of the refrigerant and to elucidate the thermodynamic mechanisms behind the effects of the cycle processes, including superheat, subcooling, and throttling processes. In particular, these processes can interact, therefore this paper presents a global entropy generation analysis for evaluating the impact of the interacted processes on COP.
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal; Suh, Kune Y.
2011-01-01
This paper considers the concept of analog computing based on a cellular neural network (CNN) paradigm to simulate nuclear reactor dynamics using a time-dependent second order form of the neutron transport equation. Instead of solving nuclear reactor dynamic equations numerically, which is time-consuming and suffers from such weaknesses as vulnerability to transient phenomena, accumulation of round-off errors and floating-point overflows, use is made of a new method based on a cellular neural network. The state-of-the-art shows the CNN as being an alternative solution to the conventional numerical computation method. Indeed CNN is an analog computing paradigm that performs ultra-fast calculations and provides accurate results. In this study use is made of the CNN model to simulate the space-time response of scalar flux distribution in steady state and transient conditions. The CNN model also is used to simulate step perturbation in the core. The accuracy and capability of the CNN model are examined in 2D Cartesian geometry for two fixed source problems, a mini-BWR assembly, and a TWIGL Seed/Blanket problem. We also use the CNN model concurrently for a typical small PWR assembly to simulate the effect of temperature feedback, poisons, and control rods on the scalar flux distribution
Polygons of differential equations for finding exact solutions
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.; Demina, Maria V.
2007-01-01
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given
Tsujimura, Kazuma; Ota, Morihito; Chinen, Kiyoshi; Adachi, Takayuki; Nagayama, Kiyomitsu; Oroku, Masato; Nishihira, Morikuni; Shiohira, Yoshiki; Iseki, Kunitoshi; Ishida, Hideki; Tanabe, Kazunari
2017-06-23
BACKGROUND Precise evaluation of a living donor's renal function is necessary to ensure adequate residual kidney function after donor nephrectomy. Our aim was to evaluate the feasibility of estimating glomerular filtration rate (GFR) using serum cystatin-C prior to kidney transplantation. MATERIAL AND METHODS Using the equations of the Japanese Society of Nephrology, we calculated the GFR using serum creatinine (eGFRcre) and cystatin C levels (eGFRcys) for 83 living kidney donors evaluated between March 2010 and March 2016. We compared eGFRcys and eGFRcre values against the creatinine clearance rate (CCr). RESULTS The study population included 27 males and 56 females. The mean eGFRcys, eGFRcre, and CCr were, 91.4±16.3 mL/min/1.73 m² (range, 59.9-128.9 mL/min/1.73 m²), 81.5±14.2 mL/min/1.73 m² (range, 55.4-117.5 mL/min/1.73 m²) and 108.4±21.6 mL/min/1.73 m² (range, 63.7-168.7 mL/min/1.73 m²), respectively. eGFRcys was significantly lower than CCr (p<0.001). The correlation coefficient between eGFRcys and CCr values was 0.466, and the mean difference between the two values was -17.0 (15.7%), with a root mean square error of 19.2. Thus, eGFRcre was significantly lower than CCr (p<0.001). The correlation coefficient between eGFRcre and CCr values was 0.445, and the mean difference between the two values was -26.9 (24.8%), with a root mean square error of 19.5. CONCLUSIONS Although eGFRcys provided a better estimation of GFR than eGFRcre, eGFRcys still did not provide an accurate measure of kidney function in Japanese living kidney donors.
Directory of Open Access Journals (Sweden)
Ahmed Yehia Ebeid
2014-09-01
Full Text Available There is a shortage in the research which addresses the relationship between negative word of mouth (WOM communication and customer-based brand equity dilution. This research utilizes attribution theory to demonstrate the negative word-of-mouth impact on the customer-based brand equity. Structural equation modeling was used to investigate the proposed effect of negative WOM on brand equity. The study sample consists of 71 post-graduate students, the object of negative WOM was laptops which considered a highly involvement product. Experimental investigation results reveal that customer exposure to negative word-of-mouth increases the brand equity dilution. Results were discussed in the light of casual attribution theory, and practical implications were provided.
Carichino, Lucia; Guidoboni, Giovanna; Szopos, Marcela
2018-07-01
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived.
Liu, Gaisheng; Lu, Zhiming; Zhang, Dongxiao
2007-01-01
A new approach has been developed for solving solute transport problems in randomly heterogeneous media using the Karhunen‐Loève‐based moment equation (KLME) technique proposed by Zhang and Lu (2004). The KLME approach combines the Karhunen‐Loève decomposition of the underlying random conductivity field and the perturbative and polynomial expansions of dependent variables including the hydraulic head, flow velocity, dispersion coefficient, and solute concentration. The equations obtained in this approach are sequential, and their structure is formulated in the same form as the original governing equations such that any existing simulator, such as Modular Three‐Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3DMS), can be directly applied as the solver. Through a series of two‐dimensional examples, the validity of the KLME approach is evaluated against the classical Monte Carlo simulations. Results indicate that under the flow and transport conditions examined in this work, the KLME approach provides an accurate representation of the mean concentration. For the concentration variance, the accuracy of the KLME approach is good when the conductivity variance is 0.5. As the conductivity variance increases up to 1.0, the mismatch on the concentration variance becomes large, although the mean concentration can still be accurately reproduced by the KLME approach. Our results also indicate that when the conductivity variance is relatively large, neglecting the effects of the cross terms between velocity fluctuations and local dispersivities, as done in some previous studies, can produce noticeable errors, and a rigorous treatment of the dispersion terms becomes more appropriate.
International Nuclear Information System (INIS)
Bourdon, A; Pasko, V P; Liu, N Y; Celestin, S; Segur, P; Marode, E
2007-01-01
This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP 3 ) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by Segur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 O 2 O 2 is the partial pressure of molecular oxygen in air in units of Torr ( p O 2 = 150 Torr) at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP 3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Acid-base titrations for polyacids: Significance of the pK sub a and parameters in the Kern equation
Meites, L.
1978-01-01
A new method is suggested for calculating the dissociation constants of polyvalent acids, especially polymeric acids. In qualitative form the most significant characteristics of the titration curves are demonstrated and identified which are obtained when titrating the solutions of such acids with a standard base potentiometrically.
Hwang, Gwo-Jen; Kuo, Fan-Ray
2015-01-01
Web-based problem-solving, a compound ability of critical thinking, creative thinking, reasoning thinking and information-searching abilities, has been recognised as an important competence for elementary school students. Some researchers have reported the possible correlations between problem-solving competence and information searching ability;…
Zhao, Ying; Schillinger, Dominik; Xu, Bai-Xiang
2017-07-01
The primal variational formulation of the fourth-order Cahn-Hilliard equation requires C1-continuous finite element discretizations, e.g., in the context of isogeometric analysis. In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn-Hilliard equation in primal variables. Our formulation is based on the symmetric variant of Nitsche's method, does not introduce additional degrees of freedom and is shown to be variationally consistent. In contrast to strong enforcement, the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree. In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions. Unfitted Cartesian B-spline meshes constitute an effective alternative to boundary-fitted isogeometric parametrizations for constructing C1-continuous discretizations, in particular for complex geometries. We combine our variational boundary condition formulation with unfitted Cartesian B-spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode. This example, involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces, demonstrates the flexibility of variational boundary conditions in the context of higher-order unfitted isogeometric discretizations.
Cheng, Xuemin; Yang, Yikang; Hao, Qun
2016-10-17
The thermal environment is an important factor in the design of optical systems. This study investigated the thermal analysis technology of optical systems for navigation guidance and control in supersonic aircraft by developing empirical equations for the front temperature gradient and rear thermal diffusion distance, and for basic factors such as flying parameters and the structure of the optical system. Finite element analysis (FEA) was used to study the relationship between flying and front dome parameters and the system temperature field. Systematic deduction was then conducted based on the effects of the temperature field on the physical geometry and ray tracing performance of the front dome and rear optical lenses, by deriving the relational expressions between the system temperature field and the spot size and positioning precision of the rear optical lens. The optical systems used for navigation guidance and control in supersonic aircraft when the flight speed is in the range of 1-5 Ma were analysed using the derived equations. Using this new method it was possible to control the precision within 10% when considering the light spot received by the four-quadrant detector, and computation time was reduced compared with the traditional method of separately analysing the temperature field of the front dome and rear optical lens using FEA. Thus, the method can effectively increase the efficiency of parameter analysis and computation in an airborne optical system, facilitating the systematic, effective and integrated thermal analysis of airborne optical systems for navigation guidance and control.
Directory of Open Access Journals (Sweden)
Xuemin Cheng
2016-10-01
Full Text Available The thermal environment is an important factor in the design of optical systems. This study investigated the thermal analysis technology of optical systems for navigation guidance and control in supersonic aircraft by developing empirical equations for the front temperature gradient and rear thermal diffusion distance, and for basic factors such as flying parameters and the structure of the optical system. Finite element analysis (FEA was used to study the relationship between flying and front dome parameters and the system temperature field. Systematic deduction was then conducted based on the effects of the temperature field on the physical geometry and ray tracing performance of the front dome and rear optical lenses, by deriving the relational expressions between the system temperature field and the spot size and positioning precision of the rear optical lens. The optical systems used for navigation guidance and control in supersonic aircraft when the flight speed is in the range of 1–5 Ma were analysed using the derived equations. Using this new method it was possible to control the precision within 10% when considering the light spot received by the four-quadrant detector, and computation time was reduced compared with the traditional method of separately analysing the temperature field of the front dome and rear optical lens using FEA. Thus, the method can effectively increase the efficiency of parameter analysis and computation in an airborne optical system, facilitating the systematic, effective and integrated thermal analysis of airborne optical systems for navigation guidance and control.
Yue, C.; Bortnik, J.; Thorne, R. M.; Ma, Q.; An, X.; Chappell, C. R.; Gerrard, A. J.; Lanzerotti, L. J.; Shi, Q.
2017-12-01
Understanding the source and loss processes of various plasma populations is greatly aided by having accurate knowledge of their pitch angle distributions (PADs). Here, we statistically analyze 1 eV to 600 keV hydrogen (H+) PADs near the geomagnetic equator in the inner magnetosphere based on Van Allen Probes measurements, to comprehensively investigate how the H+ PADs vary with different energies, magnetic local times (MLTs), L-shells, and geomagnetic conditions. Our survey clearly indicates four distinct populations with different PADs: (1) a pancake distribution of the plasmaspheric H+ at low L-shells except for dawn sector; (2) a bi-directional field-aligned distribution of the warm plasma cloak; (3) pancake or isotropic distributions of ring current H+; (4) radiation belt particles show pancake, butterfly and isotropic distributions depending on their energy, MLT and L-shell. Meanwhile, the pancake distribution of ring current H+ moves to lower energies as L-shell increases which is primarily caused by adiabatic transport. Furthermore, energetic H+ (> 10 keV) PADs become more isotropic following the substorm injections, indicating wave-particle interactions. The radiation belt H+ butterfly distributions are identified in a narrow energy range of 100 5), which are less significant during quiet times and extend from dusk to dawn sector through midnight during substorms. The different PADs near the equator provide clues of the underlying physical processes that produce the dynamics of these different populations.
International Nuclear Information System (INIS)
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B sol (rvec x) is developed. The analysis is carried out for a thin beam with characteristic beam radius r b much-lt S, and directed axial momentum γ b mβ b c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f b (rvec x,rvec p,t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B z (z) = B 0 = const. and for the case of a periodic solenoidal focusing field B z (z + S) = B z (z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field rvec B sol (rvec x) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria
Equations of state for light water
International Nuclear Information System (INIS)
Rubin, G.A.; Granziera, M.R.
1983-01-01
The equations of state for light water were developed, based on the tables of Keenan and Keyes. Equations are presented, describing the specific volume, internal energy, enthalpy and entropy of saturated steam, superheated vapor and subcooled liquid as a function of pressure and temperature. For each property, several equations are shown, with different precisions and different degress of complexity. (Author) [pt
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Notes on the infinity Laplace equation
Lindqvist, Peter
2016-01-01
This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY
Enrique Gonzalo Reyes Garcia
2004-01-01
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...
Yadav, Ram Bharos; Srivastava, Subodh; Srivastava, Rajeev
2016-01-01
The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.
Weil, Joyce; Hutchinson, Susan R; Traxler, Karen
2014-11-01
Data from the Women's Health and Aging Study were used to test a model of factors explaining depressive symptomology. The primary purpose of the study was to explore the association between performance-based measures of functional ability and depression and to examine the role of self-rated physical difficulties and perceived instrumental support in mediating the relationship between performance-based functioning and depression. The inclusion of performance-based measures allows for the testing of functional ability as a clinical precursor to disability and depression: a critical, but rarely examined, association in the disablement process. Structural equation modeling supported the overall fit of the model and found an indirect relationship between performance-based functioning and depression, with perceived physical difficulties serving as a significant mediator. Our results highlight the complementary nature of performance-based and self-rated measures and the importance of including perception of self-rated physical difficulties when examining depression in older persons. © The Author(s) 2014.
Arteaga, Lionel; Haëntjens, Nils; Boss, Emmanuel; Johnson, Kenneth S.; Sarmiento, Jorge L.
2018-04-01
Carbon export efficiency (e-ratio) is defined as the fraction of organic carbon fixed through net primary production (NPP) that is exported out of the surface productive layer of the ocean. Recent observations for the Southern Ocean suggest a negative e-ratio versus NPP relationship, and a reduced dependency of export efficiency on temperature, different than in the global domain. In this study, we complement information from a passive satellite sensor with novel space-based lidar observations of ocean particulate backscattering to infer NPP over the entire annual cycle, and estimate Southern Ocean export rates from five different empirical models of export efficiency. Inferred Southern Ocean NPP falls within the range of previous studies, with a mean estimate of 15.8 (± 3.9) Pg C yr-1 for the region south of 30°S during the 2005-2016 period. We find that an export efficiency model that accounts for silica(Si)-ballasting, which is constrained by observations with a negative e-ratio versus NPP relationship, shows the best agreement with in situ-based estimates of annual net community production (annual export of 2.7 ± 0.6 Pg C yr-1 south of 30°S). By contrast, models based on the analysis of global observations with a positive e-ratio versus NPP relationship predict annually integrated export rates that are ˜ 33% higher than the Si-dependent model. Our results suggest that accounting for Si-induced ballasting is important for the estimation of carbon export in the Southern Ocean.
International Nuclear Information System (INIS)
Barik, N.; Das, M.
1983-01-01
The effect of confinement on the magnetic moment of a quark has been studied in a simple independent-quark model based on the Dirac equation with a power-law potential. The magnetic moments so obtained for the constituent quarks, which are found to be significantly different from their corresponding Dirac moments, are used in predicting the magnetic moments of baryons in the nucleon octet as well as those in the charmed and b-flavored sectors. We not only get an improved result for the proton magnetic moment, but the calculation for the rest of the nucleon octet also turns out to be in reasonable agreement with experiment. The overall predictions for the charmed and b-flavored baryons are also comparable with other model predictions
Lin, Pei-Chun; Yu, Chun-Chang; Chen, Charlie Chung-Ping
2015-01-01
As one of the critical stages of a very large scale integration fabrication process, postexposure bake (PEB) plays a crucial role in determining the final three-dimensional (3-D) profiles and lessening the standing wave effects. However, the full 3-D chemically amplified resist simulation is not widely adopted during the postlayout optimization due to the long run-time and huge memory usage. An efficient simulation method is proposed to simulate the PEB while considering standing wave effects and resolution enhancement techniques, such as source mask optimization and subresolution assist features based on the Sylvester equation and Abbe-principal component analysis method. Simulation results show that our algorithm is 20× faster than the conventional Gaussian convolution method.
Mohammadfam, Iraj; Soltanzadeh, Ahmad; Moghimbeigi, Abbas; Akbarzadeh, Mehdi
2016-09-01
Individual and organizational factors are the factors influencing traumatic occupational injuries. The aim of the present study was the short path analysis of the severity of occupational injuries based on individual and organizational factors. The present cross-sectional analytical study was implemented on traumatic occupational injuries within a ten-year timeframe in 13 large Iranian construction industries. Modeling and data analysis were done using the structural equation modeling (SEM) approach and the IBM SPSS AMOS statistical software version 22.0, respectively. The mean age and working experience of the injured workers were 28.03 ± 5.33 and 4.53 ± 3.82 years, respectively. The portions of construction and installation activities of traumatic occupational injuries were 64.4% and 18.1%, respectively. The SEM findings showed that the individual, organizational and accident type factors significantly were considered as effective factors on occupational injuries' severity (P accidents' severity in large construction industries.
Energy Technology Data Exchange (ETDEWEB)
Koshelev, A. S., E-mail: alexsander.coshelev@yandex.ru; Arapov, A. V.; Ovchinnikov, M. A. [Russian Federal Nuclear Center–All-Russian Research Institute of Experimental Physics (Russian Federation)
2016-12-15
The file-evaluation results of a reactimeter based on the inverse solution to the kinetics equation (ISKE) are presented, which were obtained using an operating hardware-measuring complex with a KNK-4 neutron detector working in the current mode. The processing of power-recording files of the BR-1M, BR-K1, and VIR-2M reactors of the Russian Federal Nuclear Center—All-Russian Research Institute of Experimental Physics, which was performed with the use of Excel simulation of the ISKE formalism, demonstrated the feasibility of implementation of the reactivity monitoring (during the operation of these reactors at stationary power) beginning from the level of ~5 × 10{sup –4}β{sub eff}.
Lorin, E.; Yang, X.; Antoine, X.
2016-06-01
The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.
Keddis, Mira T; Amer, Hatem; Voskoboev, Nikolay; Kremers, Walter K; Rule, Andrew D; Lieske, John C
2016-09-07
eGFR equations have been evaluated in kidney transplant recipients with variable performance. We assessed the performance of the Modification of Diet in Renal Disease equation and the Chronic Kidney Disease Epidemiology Collaboration equations on the basis of creatinine, cystatin C, and both (eGFR creatinine-cystatin C) compared with measured GFR by iothalamate clearance and evaluated their non-GFR determinants and associations across 15 cardiovascular risk factors. A cross-sectional cohort of 1139 kidney transplant recipients >1 year after transplant was analyzed. eGFR bias, precision, and accuracy (percentage of estimates within 30% of measured GFR) were assessed. Interaction of each cardiovascular risk factor with eGFR relative to measured GFR was determined. Median measured GFR was 55.0 ml/min per 1.73 m(2). eGFR creatinine overestimated measured GFR by 3.1% (percentage of estimates within 30% of measured GFR of 80.4%), and eGFR Modification of Diet in Renal Disease underestimated measured GFR by 2.2% (percentage of estimates within 30% of measured GFR of 80.4%). eGFR cystatin C underestimated measured GFR by -13.7% (percentage of estimates within 30% of measured GFR of 77.1%), and eGFR creatinine-cystatin C underestimated measured GFR by -8.1% (percentage of estimates within 30% of measured GFR of 86.5%). Lower measured GFR associated with older age, women, obesity, longer time after transplant, lower HDL, lower hemoglobin, lower albumin, higher triglycerides, higher proteinuria, and an elevated cardiac troponin T level but did not associate with diabetes, smoking, cardiovascular events, pretransplant dialysis, or hemoglobin A1c. These risk factor associations differed for five risk factors with eGFR creatinine, six risk factors for eGFR Modification of Diet in Renal Disease, ten risk factors for eGFR cystatin C, and four risk factors for eGFR creatinine-cystatin C. Thus, eGFR creatinine and eGFR creatinine-cystatin C are preferred over eGFR cystatin C in
Cheng, Jian; Yue, Huiqiang; Yu, Shengjiao; Liu, Tiegang
2018-06-01
In this paper, an adjoint-based high-order h-adaptive direct discontinuous Galerkin method is developed and analyzed for the two dimensional steady state compressible Navier-Stokes equations. Particular emphasis is devoted to the analysis of the adjoint consistency for three different direct discontinuous Galerkin discretizations: including the original direct discontinuous Galerkin method (DDG), the direct discontinuous Galerkin method with interface correction (DDG(IC)) and the symmetric direct discontinuous Galerkin method (SDDG). Theoretical analysis shows the extra interface correction term adopted in the DDG(IC) method and the SDDG method plays a key role in preserving the adjoint consistency. To be specific, for the model problem considered in this work, we prove that the original DDG method is not adjoint consistent, while the DDG(IC) method and the SDDG method can be adjoint consistent with appropriate treatment of boundary conditions and correct modifications towards the underlying output functionals. The performance of those three DDG methods is carefully investigated and evaluated through typical test cases. Based on the theoretical analysis, an adjoint-based h-adaptive DDG(IC) method is further developed and evaluated, numerical experiment shows its potential in the applications of adjoint-based adaptation for simulating compressible flows.
Leion, Felicia; Hegbrant, Josefine; den Bakker, Emil; Jonsson, Magnus; Abrahamson, Magnus; Nyman, Ulf; Björk, Jonas; Lindström, Veronica; Larsson, Anders; Bökenkamp, Arend; Grubb, Anders
2017-09-01
Estimating glomerular filtration rate (GFR) in adults by using the average of values obtained by a cystatin C- (eGFR cystatin C ) and a creatinine-based (eGFR creatinine ) equation shows at least the same diagnostic performance as GFR estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparison of eGFR cystatin C and eGFR creatinine plays a pivotal role in the diagnosis of Shrunken Pore Syndrome, where low eGFR cystatin C compared to eGFR creatinine has been associated with higher mortality in adults. The present study was undertaken to elucidate if this concept can also be applied in children. Using iohexol and inulin clearance as gold standard in 702 children, we studied the diagnostic performance of 10 creatinine-based, 5 cystatin C-based and 3 combined cystatin C-creatinine eGFR equations and compared them to the result of the average of 9 pairs of a eGFR cystatin C and a eGFR creatinine estimate. While creatinine-based GFR estimations are unsuitable in children unless calibrated in a pediatric or mixed pediatric-adult population, cystatin C-based estimations in general performed well in children. The average of a suitable creatinine-based and a cystatin C-based equation generally displayed a better diagnostic performance than estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparing eGFR cystatin and eGFR creatinine may help identify pediatric patients with Shrunken Pore Syndrome.
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
He, Xueqin; Han, Lujia; Ge, Jinyi; Huang, Guangqun
2018-04-01
This study establishes an optimal mathematical modelling to rationally describe the dynamic changes and spatial distribution of temperature and oxygen concentration in the aerobic composting process using coupling mass-heat-momentum transfer based on the microbial mechanism. Two different conditional composting experiments, namely continuous aeration and intermittent aeration, were performed to verify the proposed model. The results show that the model accurately predicted the dynamic changes in temperature (case I: R 2 = 0.93, RMSE = 1.95 K; case II: R 2 = 0.86, RMSE = 4.69 K) and oxygen concentration (case I: R 2 = 0.90, RMSE = 1.26%; case II: R 2 = 0.75, RMSE = 2.93%) in the central point of compost substrates. It also systematically simulated fluctuations in oxygen concentration caused by boundary conditions and the spatial distribution of the actual temperature and oxygen concentration. The proposed model exhibits good applicability in simulating the actual working conditions of aerobic composting process. Copyright © 2018 Elsevier Ltd. All rights reserved.
Integrable discretizations of the short pulse equation
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.
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.
Directory of Open Access Journals (Sweden)
Deimel Christian
2014-03-01
Full Text Available The most common method for simulating cavitating flows is using the governing flow equations in a form with a variable density and treats both phases as incompressible in combination with a transport equation for the vapour volume fraction. This approach is commonly referred to as volume of fluid method (VoF. To determine the transition of the liquid phase to vapour and vice versa, a relation for the mass transfer is needed. Several models exist, based on slightly differing physical assumptions, for example derivation from the dynamics of single bubbles or large bubble clusters. In our simulation, we use the model of Sauer and Schnerr which is based on the Rayleigh equation. One common problem of all mass transfer models is the use of model constants which often need to be tuned with regard to the examined problem. Furthermore, these models often overpredict the turbulent dynamic viscosity in the two-phase region which counteracts the development of transient shedding behaviour and is compensated by the modification proposed by Reboud. In the presented study, we vary the parameters of the Sauer-Schnerr model with Reboud modification that we implemented into an OpenFOAM solver to match numerical to experimental data.
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Oki, Kensuke; Ma, Bei; Ishitani, Yoshihiro
2017-11-01
Population distributions and transition fluxes of the A exciton in bulk GaN are theoretically analyzed using rate equations of states of the principal quantum number n up to 5 and the continuum. These rate equations consist of the terms of radiative, electron-collisional, and phononic processes. The dependence of the rate coefficients on temperature is revealed on the basis of the collisional-radiative model of hydrogen plasma for the electron-collisional processes and theoretical formulation using Fermi's "golden rule" for the phononic processes. The respective effects of the variations in electron, exciton, and lattice temperatures are exhibited. This analysis is a base of the discussion on nonthermal equilibrium states of carrier-exciton-phonon dynamics. It is found that the exciton dissociation is enhanced even below 150 K mainly by the increase in the lattice temperature. When the thermal-equilibrium temperature increases, the population fluxes between the states of n >1 and the continuum become more dominant. Below 20 K, the severe deviation from the Saha-Boltzmann distribution occurs owing to the interband excitation flux being higher than the excitation flux from the 1 S state. The population decay time of the 1 S state at 300 K is more than ten times longer than the recombination lifetime of excitons with kinetic energy but without the upper levels (n >1 and the continuum). This phenomenon is caused by a shift of population distribution to the upper levels. This phonon-exciton-radiation model gives insights into the limitations of conventional analyses such as the ABC model, the Arrhenius plot, the two-level model (n =1 and the continuum), and the neglect of the upper levels.
Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue
2018-01-01
An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.
International Nuclear Information System (INIS)
Kipriyanov, A.A.; Doktorov, A.B.
2005-01-01
We have considered two many-particle models of the irreversible reaction A + B → Product for which closed kinetic equations for the mean concentration N A (t) of A species can be exactly obtained. These equations are identically recast into a unified form of integro-differential equation of general kinetic theory. It is shown that the memory functions for both models under consideration can be represented as a sum of the Markovian and non-Markovian parts. It is essential that the Markovian part of the Laplace transform of any kernel can be obtained using the Laplace transform of the kernel itself, and is the root of the non-Markovian part of the Laplace transform of the kernel. The properties established allowed us to perform correct approximation of the memory functions at small concentrations [B] of B species and derive the binary non-Markovian integro-differential equation. Within the binary theory accuracy this equation has been rewritten in a regular frame of a familiar rate equation satisfying general principles of binary kinetic equations. Thus using particular exactly solvable many-particle models, we have reproduced the most essential steps of the known general way for the derivation of the binary kinetic equation avoiding the sophisticated many-particle technique and the corresponding approximations. Besides, the results obtained can serve as an additional evidence of the approximations made in a general many-particle approach to the derivation of the binary kinetic equation
Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation
Wang, D.
2017-12-01
The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Sparse dynamics for partial differential equations.
Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley
2013-04-23
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Directory of Open Access Journals (Sweden)
Alexey Solovyev
Full Text Available Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI. People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation.
Chen, Haiwen
2012-01-01
In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…
International Nuclear Information System (INIS)
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Numerical optimization using flow equations
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
Energy Technology Data Exchange (ETDEWEB)
Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics
1990-03-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).
International Nuclear Information System (INIS)
Zhou Xin
1990-01-01
For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)
Generalization of Einstein's gravitational field equations
Moulin, Frédéric
2017-12-01
The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.
Gomez, Humberto
2016-06-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Zhang, Yanxiang; Chen, Yu; Yan, Mufu
2017-07-01
The open circuit voltage (OCV) of solid oxide fuel cells is generally overestimated by the Nernst equation and the Wagner equation, due to the polarization losses at electrodes. Considering both the electronic conduction of electrolyte and the electrode polarization losses, we express the OCV as an implicit function of the characteristic oxygen pressure of electrolyte (p* [atm], at which the electronic and ionic conductivities are the same), and the relative polarization resistance of electrodes (rc = Rc/Ri and ra = Ra/Ri, where Ri/c/a [Ωcm2] denotes the ionic resistance of electrolyte, and the polarization resistances of cathode and anode, respectively). This equation approaches to the Wagner equation when the electrodes are highly active (rc and ra → 0), and approaches to the Nernst equation when the electrolyte is a purely ionic conductor (p* → 0). For the fuel cells whose OCV is well below the prediction of the Wagner equation, for example with thin doped ceria electrolyte, it is demonstrated that the combination of OCV and impedance spectroscopy measurements allows the determination of p*, Rc and Ra. This equation can serve as a simple yet powerful tool to study the internal losses in the cell under open circuit condition.
Critical spaces for quasilinear parabolic evolution equations and applications
Prüss, Jan; Simonett, Gieri; Wilke, Mathias
2018-02-01
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.
International Conference on Differential and Difference Equations with Applications
Došlá, Zuzana; Došlý, Ondrej; Kloeden, Peter
2016-01-01
Aimed at the community of mathematicians working on ordinary and partial differential equations, difference equations, and functional equations, this book contains selected papers based on the presentations at the International Conference on Differential and Difference Equations and Applications (ICDDEA) 2015, dedicated to the memory of Professor Georg Sell. Contributions include new trends in the field of differential and difference equations, applications of differential and difference equations, as well as high-level survey results. The main aim of this recurring conference series is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with special emphasis on applications.
Bry, X; Verron, T; Cazes, P
2009-05-29
In this work, we consider chemical and physical variable groups describing a common set of observations (cigarettes). One of the groups, minor smoke compounds (minSC), is assumed to depend on the others (minSC predictors). PLS regression (PLSR) of m inSC on the set of all predictors appears not to lead to a satisfactory analytic model, because it does not take into account the expert's knowledge. PLS path modeling (PLSPM) does not use the multidimensional structure of predictor groups. Indeed, the expert needs to separate the influence of several pre-designed predictor groups on minSC, in order to see what dimensions this influence involves. To meet these needs, we consider a multi-group component-regression model, and propose a method to extract from each group several strong uncorrelated components that fit the model. Estimation is based on a global multiple covariance criterion, used in combination with an appropriate nesting approach. Compared to PLSR and PLSPM, the structural equation exploratory regression (SEER) we propose fully uses predictor group complementarity, both conceptually and statistically, to predict the dependent group.
Energy Technology Data Exchange (ETDEWEB)
Furusawa, Shun; Yamada, Shoichi [Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan); Sumiyoshi, Kohsuke [Numazu College of Technology, Ooka 3600, Numazu, Shizuoka 410-8501 (Japan); Suzuki, Hideyuki, E-mail: furusawa@heap.phys.waseda.ac.jp [Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510 (Japan)
2013-08-01
We construct new equations of state for baryons at subnuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with thermodynamic quantities. A model free energy is constructed, based on the relativistic mean field theory for nucleons and the mass formula for nuclei with the proton number up to {approx}1000. The formulation is an extension of the previous model, in which we adopted the liquid drop model to all nuclei under the nuclear statistical equilibrium. We reformulate the new liquid drop model so that the temperature dependences of bulk energies could be taken into account. Furthermore, we extend the region in the nuclear chart, in which shell effects are included, by using theoretical mass data in addition to experimental ones. We also adopt a quantum-theoretical mass evaluation of light nuclei, which incorporates the Pauli- and self-energy shifts that are not included in the ordinary liquid drop model. The pasta phases for heavy nuclei are taken into account in the same way as in the previous model. We find that the abundances of heavy nuclei are modified by the shell effects of nuclei and temperature dependence of bulk energies. These changes may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The abundances of light nuclei are also modified by the new mass evaluation, which may affect the heating and cooling rates of supernova cores and shocked envelopes.
Gregory, Gerald L.; Scott, A. Donald, Jr.
1995-01-01
This compendium describes aircraft data that are available from NASA's Transport and Atmospheric Chemistry near the Equator - Atlantic (TRACE-A) conducted in September/October 1992. The broad objectives of TRACE-A were to study chemical processes and long-range transport associated with South American and African continental outflow during periods of widespread vegetation burning, and to understand the ozone enhancements observed from satellite data measured over the southern tropical Atlantic Ocean during the September/October time period. Flight experiments were conducted from Brazil, South Africa, Namibia, and the Ascension Island. This document provides a representation of aircraft data that are available from NASA Langley's Distributed Active Archive Center (DAAC). The data format of time series and altitude profile plots is not intended to support original analyses, but to assist the reader in identifying data that are of interest. This compendium is for only the NASA aircraft data. The DAAC data base includes numerous supporting data-meteorological products, results from surface studies, satellite observations, and data from sonde releases.
Directory of Open Access Journals (Sweden)
Niki eDe Bondt
2015-12-01
Full Text Available The Overexcitability Questionnaire-Two (OEQ-II measures the degree and nature of overexcitability, which assists in determining the developmental potential of an individual according to Dabrowski’s Theory of Positive Disintegration. Previous validation studies using frequentist confirmatory factor analysis, which postulates exact parameter constraints, led to model rejection and a long series of model modifications. Bayesian structural equation modeling (BSEM allows the application of zero-mean, small-variance priors for cross-loadings, residual covariances, and differences in measurement parameters across groups, better reflecting substantive theory and leading to better model fit and less overestimation of factor correlations. Our BSEM analysis with a sample of 516 students in higher education yields positive results regarding the factorial validity of the OEQ-II. Likewise, applying BSEM-based alignment with approximate measurement invariance, the absence of non-invariant factor loadings and intercepts across gender is supportive of the psychometric quality of the OEQ-II. Compared to males, females scored significantly higher on emotional and sensual overexcitability, and significantly lower on psychomotor overexcitability.
International Nuclear Information System (INIS)
Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki
2013-01-01
We construct new equations of state for baryons at subnuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with thermodynamic quantities. A model free energy is constructed, based on the relativistic mean field theory for nucleons and the mass formula for nuclei with the proton number up to ∼1000. The formulation is an extension of the previous model, in which we adopted the liquid drop model to all nuclei under the nuclear statistical equilibrium. We reformulate the new liquid drop model so that the temperature dependences of bulk energies could be taken into account. Furthermore, we extend the region in the nuclear chart, in which shell effects are included, by using theoretical mass data in addition to experimental ones. We also adopt a quantum-theoretical mass evaluation of light nuclei, which incorporates the Pauli- and self-energy shifts that are not included in the ordinary liquid drop model. The pasta phases for heavy nuclei are taken into account in the same way as in the previous model. We find that the abundances of heavy nuclei are modified by the shell effects of nuclei and temperature dependence of bulk energies. These changes may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The abundances of light nuclei are also modified by the new mass evaluation, which may affect the heating and cooling rates of supernova cores and shocked envelopes
Furusawa, Shun; Sumiyoshi, Kohsuke; Yamada, Shoichi; Suzuki, Hideyuki
2013-08-01
We construct new equations of state for baryons at subnuclear densities for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with thermodynamic quantities. A model free energy is constructed, based on the relativistic mean field theory for nucleons and the mass formula for nuclei with the proton number up to ~1000. The formulation is an extension of the previous model, in which we adopted the liquid drop model to all nuclei under the nuclear statistical equilibrium. We reformulate the new liquid drop model so that the temperature dependences of bulk energies could be taken into account. Furthermore, we extend the region in the nuclear chart, in which shell effects are included, by using theoretical mass data in addition to experimental ones. We also adopt a quantum-theoretical mass evaluation of light nuclei, which incorporates the Pauli- and self-energy shifts that are not included in the ordinary liquid drop model. The pasta phases for heavy nuclei are taken into account in the same way as in the previous model. We find that the abundances of heavy nuclei are modified by the shell effects of nuclei and temperature dependence of bulk energies. These changes may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. The abundances of light nuclei are also modified by the new mass evaluation, which may affect the heating and cooling rates of supernova cores and shocked envelopes.
Richardson, Andrea S.; Meyer, Katie A.; Howard, Annie Green; Boone-Heinonen, Janne; Popkin, Barry M.; Evenson, Kelly R.; Shikany, James M.; Lewis, Cora E.; Gordon-Larsen, Penny
2016-01-01
Objectives To examine longitudinal pathways from multiple types of neighborhood restaurants and food stores to BMI, through dietary behaviors. Methods We used data from participants (n=5114) in the United States-based Coronary Artery Risk Development in Young Adults study and a structural equation model to estimate longitudinal (1985–86 to 2005–06) pathways simultaneously from neighborhood fast food restaurants, sit-down restaurants, supermarkets, and convenience stores to BMI through dietary behaviors, controlling for socioeconomic status (SES) and physical activity. Results Higher numbers of neighborhood fast food restaurants and lower numbers of sit-down restaurants were associated with higher consumption of an obesogenic fast food-type diet. The pathways from food stores to BMI through diet were inconsistent in magnitude and statistical significance. Conclusions Efforts to decrease the numbers of neighborhood fast food restaurants and to increase the numbers of sit-down restaurant options could influence diet behaviors. Availability of neighborhood fast food and sit-down restaurants may play comparatively stronger roles than food stores in shaping dietary behaviors and BMI. PMID:26454248
Kim, Peter S; Lee, Peter P
2012-01-01
A next generation approach to cancer envisions developing preventative vaccinations to stimulate a person's immune cells, particularly cytotoxic T lymphocytes (CTLs), to eliminate incipient tumors before clinical detection. The purpose of our study is to quantitatively assess whether such an approach would be feasible, and if so, how many anti-cancer CTLs would have to be primed against tumor antigen to provide significant protection. To understand the relevant dynamics, we develop a two-compartment model of tumor-immune interactions at the tumor site and the draining lymph node. We model interactions at the tumor site using an agent-based model (ABM) and dynamics in the lymph node using a system of delay differential equations (DDEs). We combine the models into a hybrid ABM-DDE system and investigate dynamics over a wide range of parameters, including cell proliferation rates, tumor antigenicity, CTL recruitment times, and initial memory CTL populations. Our results indicate that an anti-cancer memory CTL pool of 3% or less can successfully eradicate a tumor population over a wide range of model parameters, implying that a vaccination approach is feasible. In addition, sensitivity analysis of our model reveals conditions that will result in rapid tumor destruction, oscillation, and polynomial rather than exponential decline in the tumor population due to tumor geometry.
Kishi, Ryohei; Nakano, Masayoshi
2011-04-21
A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.
Directory of Open Access Journals (Sweden)
S. Dehghani
2014-06-01
Full Text Available Early maladaptive schema is assumed to be a disrupting factor for quality of life. Yet, the mechanism of this vulnerability is not well known. The purpose of this study was to investigate the characteristic of emotional intelligence and coping strategy with stress as a mediator between early maladaptive defectiveness/ shame and mental quality of life. Participants were 245 men and women in Isfahan who were selected as the sample by availability sampling method. They completed the Petrides and Furnham's Trait Emotional Intelligence Questionnaire-Short Form (TEIQue-SF, Coping Inventory for stressful situation (CISS and WHO Quality of Life-BREF (WHOQOL-BREF and Young Schema Questionnaire-Short Form (YSQ-SF. Data was analyzed by means of structural equation modeling. The results indicated that the suggested model of study needs modification and only emotional intelligence was the mediator. Standard path coefficient of defectiveness/shame schema to emotional intelligence was -0.55 and emotional intelligence to problem focused coping, emotion focused coping and mental quality of life were 0.49, -0.59 and 0.78 (p<0.05. Based on results, emotional intelligence training can improve mental quality of life and coping strategies in people who have early defectiveness/shame maladaptive schema.
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
International Nuclear Information System (INIS)
Dyshekov, A.A.; Khapachev, Yu.P.
1997-01-01
It is proposed to use qualitative investigation methods of the differential Takagi equation solutions for the analysis of general properties of wave fields in deformed crystals. The physical interpretation of possible types of the Takagi equation solutions is considered briefly from the viewpoint of the stability theory. The type of solutions are defined by ratios between parameters involved in the equations set. For the Takagi equation these parameters are prescribed by the angular tuning from the precise Bragg angle as well as structural characteristics of the crystal and the deformation profile. The qualitative analysis for the problem of the dynamic X-ray diffraction is carried out for films with the variable deformation gradient and superlattices [ru
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
Schulze, J.; Donkó, Z.; Lafleur, T.; Wilczek, S.; Brinkmann, R. P.
2018-05-01
Power absorption by electrons from the space- and time-dependent electric field represents the basic sustaining mechanism of all radio-frequency driven plasmas. This complex phenomenon has attracted significant attention. However, most theories and models are, so far, only able to account for part of the relevant mechanisms. The aim of this work is to present an in-depth analysis of the power absorption by electrons, via the use of a moment analysis of the Boltzmann equation without any ad-hoc assumptions. This analysis, for which the input quantities are taken from kinetic, particle based simulations, allows the identification of all physical mechanisms involved and an accurate quantification of their contributions. The perfect agreement between the sum of these contributions and the simulation results verifies the completeness of the model. We study the relative importance of these mechanisms as a function of pressure, with high spatial and temporal resolution, in an electropositive argon discharge. In contrast to some widely accepted previous models we find that high space- and time-dependent ambipolar electric fields outside the sheaths play a key role for electron power absorption. This ambipolar field is time-dependent within the RF period and temporally asymmetric, i.e., the sheath expansion is not a ‘mirror image’ of the sheath collapse. We demonstrate that this time-dependence is mainly caused by a time modulation of the electron temperature resulting from the energy transfer to electrons by the ambipolar field itself during sheath expansion. We provide a theoretical proof that this ambipolar electron power absorption would vanish completely, if the electron temperature was constant in time. This mechanism of electron power absorption is based on a time modulated electron temperature, markedly different from the Hard Wall Model, of key importance for energy transfer to electrons on time average and, thus, essential for the generation of capacitively
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Explicit solutions of two nonlinear dispersive equations with variable coefficients
International Nuclear Information System (INIS)
Lai Shaoyong; Lv Xiumei; Wu Yonghong
2008-01-01
A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa-Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions