expansion method and travelling wave solutions for the perturbed ...
Indian Academy of Sciences (India)
Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...
The extended (G/G)-expansion method and travelling wave ...
Indian Academy of Sciences (India)
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters.
The extended (G/G)-expansion method and travelling wave ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 82; Issue 6. The extended (′/)-expansion method and travelling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity. Zaiyun Zhang Jianhua Huang Juan Zhong Sha-Sha Dou Jiao Liu Dan Peng Ting Gao. Research Articles ...
DEFF Research Database (Denmark)
Alvarez, Yuri; Cappellin, Cecilia; Las-Heras, Fernando
2008-01-01
A comparison between two recently developed methods for antenna diagnostics is presented. On one hand, the Spherical Wave Expansion-to-Plane Wave Expansion (SWE-PWE), based on the relationship between spherical and planar wave modes. On the other hand, the Sources Reconstruction Method (SRM), based...
The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation
Directory of Open Access Journals (Sweden)
Hasibun Naher
2011-01-01
Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.
Expansion and compression shock wave calculation in pipes with the C.V.M. numerical method
International Nuclear Information System (INIS)
Raymond, P.; Caumette, P.; Le Coq, G.; Libmann, M.
1983-03-01
The Control Variables Method for fluid transients computations has been used to compute expansion and compression shock waves propagations. In this paper, first analytical solutions for shock wave and rarefaction wave propagation are detailed. Then after a rapid description of the C.V.M. technique and its stability and monotonicity properties, we will present some results about standard shock tube problem, reflection of shock wave, finally a comparison between experimental results obtained on the ELF facility and calculations is given
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.; Stoffa, Paul L.
2010-01-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.
2010-07-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2013-01-01
Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.
Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method
International Nuclear Information System (INIS)
Saddique, I.; Nazar, K.
2009-01-01
In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)
Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method
Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan
2018-01-01
Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.
Expansions for Coulomb wave functions
Boersma, J.
1969-01-01
In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are
Akbar, M Ali; Hj Mohd Ali, Norhashidah
2014-01-01
The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.
Indian Academy of Sciences (India)
of a system under investigation is to model the system in terms of some ... The organization of the paper is as follows: In §2, a brief account of the (G /G)- expansion ...... It is interesting to note that from the general results, one can easily recover.
International Nuclear Information System (INIS)
Song Lina; Zhang Hongqing
2007-01-01
In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.
Directory of Open Access Journals (Sweden)
Ziyang Lian
2016-01-01
Full Text Available An enhanced plane wave expansion (PWE method is proposed to solve piezoelectric phononic crystal (PPC connected with resonant shunting circuits (PPC-C, which is named as PWE-PPC-C. The resonant shunting circuits can not only bring about the locally resonant (LR band gap for the PPC-C but also conveniently tune frequency and bandwidth of band gaps through adjusting circuit parameters. However, thus far, more than one-dimensional PPC-C has been studied just by Finite Element method. Compared with other methods, the PWE has great advantages in solving more than one-dimensional PC as well as various lattice types. Nevertheless, the conventional PWE cannot accurately solve coupling between the structure and resonant shunting circuits of the PPC-C since only taking one-way coupling from displacements to electrical parameters into consideration. A two-dimensional PPC-C model of orthorhombic lattice is established to demonstrate the whole solving process of PWE-PPC-C. The PWE-PPC-C method is validated by Transfer Matrix method as well as Finite Element method. The dependence of band gaps on circuit parameters has been investigated in detail by PWE-PPC-C. Its advantage in solving various lattice types is further illustrated by calculating the PPC-C of triangular and hexagonal lattices, respectively.
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Shahnam Javadi
2013-07-01
Full Text Available In this paper, the $(G'/G$-expansion method is applied to solve a biological reaction-convection-diffusion model arising in mathematical biology. Exact traveling wave solutions are obtained by this method. This scheme can be applied to a wide class of nonlinear partial differential equations.
International Nuclear Information System (INIS)
Zhou Yubin; Li Chao
2009-01-01
A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. (general)
Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-
2014-01-01
Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.
International Nuclear Information System (INIS)
Wang Qi; Chen Yong; Zhang Hongqing
2005-01-01
With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition
Directory of Open Access Journals (Sweden)
Tarikul Islam
2018-03-01
Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.
Discrete expansions of continuum wave functions
International Nuclear Information System (INIS)
Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.
1980-01-01
Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)
Faria, Luiz; Rosales, Rodolfo
2017-11-01
We introduce an alternative to the method of matched asymptotic expansions. In the ``traditional'' implementation, approximate solutions, valid in different (but overlapping) regions are matched by using ``intermediate'' variables. Here we propose to match at the level of the equations involved, via a ``uniform expansion'' whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the ``simplest'' set of equations that capture the behavior. Ruben Rosales work was partially supported by NSF Grants DMS-1614043 and DMS-1719637.
Alam, Md Nur; Akbar, M Ali
2013-01-01
The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.
Batool, Fiza; Akram, Ghazala
2018-05-01
An improved (G'/G)-expansion method is proposed for extracting more general solitary wave solutions of the nonlinear fractional Cahn-Allen equation. The temporal fractional derivative is taken in the sense of Jumarie's fractional derivative. The results of this article are generalized and extended version of previously reported solutions.
Directory of Open Access Journals (Sweden)
Rashida Hussain
2017-04-01
Full Text Available In this paper, Novel (Gʹ/G-expansion method is used to find new generalized exact travelling wave solutions of fractional order coupled Burger’s equations in terms of trigonometric functions, rational functions and hyperbolic functions with arbitrary parameters. For the conversion of the partial differential equation to the ordinary differential equation, complex transformation method is used. Novel (Gʹ/G-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear equations. Moreover, for the representation of these exact solutions we have plotted graphs for different values of parameters which were in travelling waveform.
Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar
2014-01-01
In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.
Instability of a planar expansion wave
International Nuclear Information System (INIS)
Velikovich, A.L.; Zalesak, S.T.; Metzler, N.; Wouchuk, J.G.
2005-01-01
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent γ. At γ>3, the mass modulation amplitude δm in a rippled expansion wave exhibits a power-law growth with time ∝t β , where β=(γ-3)/(γ-1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme γ-1 -1/2 , and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low γ. Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results
Instability of a planar expansion wave.
Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G
2005-10-01
An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.
Directory of Open Access Journals (Sweden)
Jesús García
2012-01-01
Full Text Available The application of a 3D domain decomposition finite-element and spherical mode expansion for the design of planar ESPAR (electronically steerable passive array radiator made with probe-fed circular microstrip patches is presented in this work. A global generalized scattering matrix (GSM in terms of spherical modes is obtained analytically from the GSM of the isolated patches by using rotation and translation properties of spherical waves. The whole behaviour of the array is characterized including all the mutual coupling effects between its elements. This procedure has been firstly validated by analyzing an array of monopoles on a ground plane, and then it has been applied to synthesize a prescribed radiation pattern optimizing the reactive loads connected to the feeding ports of the array of circular patches by means of a genetic algorithm.
Directory of Open Access Journals (Sweden)
M.G. Hafez
2016-06-01
Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.
Expansion of continuum functions on resonance wave functions and amplitudes
International Nuclear Information System (INIS)
Bang, J.; Gareev, F.A.; Gizzatkulov, M.H.; Goncharov, S.A.
1978-01-01
To overcome difficulties encountered with wave functions of continuum spectrum (for example, in a shell model with continuum) the pole expansion (by the Mittag-Leffler theorem) of wave functions, scattering amplitudes and the Green functions with positive energies are considered. It is shown that resonance functions (the Gamov functions) form a complete set over which the continuum functions could be expanded. The general view of these expansions for final potentials and for the Coulomb repulsion potential are obtained and discussed. It is shown that the application of the method to nuclear structure calculations leads to simple algebraic equations
Critical point anomalies include expansion shock waves
Energy Technology Data Exchange (ETDEWEB)
Nannan, N. R., E-mail: ryan.nannan@uvs.edu [Mechanical Engineering Discipline, Anton de Kom University of Suriname, Leysweg 86, PO Box 9212, Paramaribo, Suriname and Process and Energy Department, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft (Netherlands); Guardone, A., E-mail: alberto.guardone@polimi.it [Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano (Italy); Colonna, P., E-mail: p.colonna@tudelft.nl [Propulsion and Power, Delft University of Technology, Kluyverweg 1, 2629 HS Delft (Netherlands)
2014-02-15
From first-principle fluid dynamics, complemented by a rigorous state equation accounting for critical anomalies, we discovered that expansion shock waves may occur in the vicinity of the liquid-vapor critical point in the two-phase region. Due to universality of near-critical thermodynamics, the result is valid for any common pure fluid in which molecular interactions are only short-range, namely, for so-called 3-dimensional Ising-like systems, and under the assumption of thermodynamic equilibrium. In addition to rarefaction shock waves, diverse non-classical effects are admissible, including composite compressive shock-fan-shock waves, due to the change of sign of the fundamental derivative of gasdynamics.
On WKB expansions for Alfven waves in the solar wind
International Nuclear Information System (INIS)
Hollweg, J.V.
1990-01-01
The author reexamines the WKB expansion for toroidal Alfven waves in the solar wind, as described by equations (9) of Heinemann and Olbert (1980). His principal conclusions are as follows: (1) The WKB expansion used by Belcher (1971) and Hollweg (1973) is nonuniformly convergent. (2) Using the method of multiple scales (Nayfeh, 1981), he obtains an expansion which is uniform. (3) The uniform expansion takes into account the small modification to the Alfven wave phase speed due to spatial gradients of the background. (4) Both the uniform and nonuniform expansions reveal that each normal mode has both Elsaesser variables δz + ≠ 0 and δz - ≠ 0. Thus if δz - corresponds to the outgoing mode in a homogeneous background, an observation of δz + ≠ 0 does not necessarily imply the presence of the inward propagating mode, as is commonly assumed. (5) Even at the Alfven critical point (where V = υ A ) he finds that δz + ≠ 0. Thus incompressible MHD turbulence, which requires both δz + ≠ 0 and δz - ≠ 0, can proceed at the Alfven critical point (cf. Roberts, 1989). (6) With very few exceptions, the predictions of these calculations do not agree with recent observations (Marsch and Tu, 1990) of the power spectra of δz + and δz - in the solar wind. Thus the evolution of Alfven waves in the solar wind is governed by dynamics not included in the Heinemann and Olbert equations
Spherical-wave expansions of piston-radiator fields.
Wittmann, R C; Yaghjian, A D
1991-09-01
Simple spherical-wave expansions of the continuous-wave fields of a circular piston radiator in a rigid baffle are derived. These expansions are valid throughout the illuminated half-space and are useful for efficient numerical computation in the near-field region. Multipole coefficients are given by closed-form expressions which can be evaluated recursively.
The optimizied expansion method for wavefield extrapolation
Wu, Zedong
2013-01-01
Spectral methods are fast becoming an indispensable tool for wave-field extrapolation, especially in anisotropic media, because of its dispersion and artifact free, as well as highly accurate, solutions of the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number of inverse FFT required per time extrapolation step, and thus, a lower rank admits faster extrapolations. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its low rank representation.Thus,we obtain more accurate wave-fields using lower rank representation, and thus cheaper extrapolations. The optimization operation to define the low rank representation depends only on the velocity model, and this is done only once, and valid for a full reverse time migration (many shots) or one iteration of full waveform inversion. Applications on the BP model yielded superior results than those obtained using the decomposition approach. For transversely isotopic media, the solutions were free of the shear wave artifacts, and does not require that eta>0.
Acoustic waves in shock tunnels and expansion tubes
Paull, A.; Stalker, R. J.
1992-01-01
It is shown that disturbances in shock and expansion tubes can be modelled as lateral acoustic waves. The ratio of sound speed across the driver-test gas interface is shown to govern the quantity of noise in the test gas. Frequency 'focusing' which is fundamental to centered unsteady expansions is discussed and displayed in centerline pitot pressure measurements.
Improved wave functions for large-N expansions
International Nuclear Information System (INIS)
Imbo, T.; Sukhatme, U.
1985-01-01
Existing large-N expansions of radial wave functions phi/sub n/,l(r) are only accurate near the minimum of the effective potential. Within the framework of the shifted 1/N expansion, we use known analytic results to motivate a simple modification so that the improved wave functions are accurate over a wide range of r and any choice of quantum numbers n and l. It is shown that these wave functions yield simple and accurate analytic expressions for certain quantities of interest in quarkonium physics
Asymptotic Expansions - Methods and Applications
International Nuclear Information System (INIS)
Harlander, R.
1999-01-01
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed. (author)
Disjoint sum expansion method in FTA
International Nuclear Information System (INIS)
Ruan Keqiang
1987-01-01
An expansion formula for transforming boolean algebraic expressions into disjoint form was proved. Based on this expansion formula, a method for transforming system failure function into disjoint form was devised. The fact that the expansion can be done for several elements simulatneously makes the method flexible and fast. Some examples from fault tree analysis (FTA) and network analysis were examined by the new method to show its algorithm and its merit. Besides, by means of the proved expansion formula some boolean algebraic relations can proved very easily
Gabor Wave Packet Method to Solve Plasma Wave Equations
International Nuclear Information System (INIS)
Pletzer, A.; Phillips, C.K.; Smithe, D.N.
2003-01-01
A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach
The linear potential propagator via wave function expansion
International Nuclear Information System (INIS)
Nassar, Antonio B.; Cattani, Mauro S.D.
2002-01-01
We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developed formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities. (author)
Potential harmonic expansion for atomic wave functions
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.; Larsen, S.Y.
1991-01-01
One way to reduce the large degeneracy of the Hyperspherical Harmonic basis for solving few- and many-body bound state problems is to introduce an optimal basis truncation called the Potential Harmonic (PH) basis. Various PH truncation schemes are introduced, and their accuracies are evaluated in predicting the energies of the Helium and H - ground states , and the excited 2 1 S level of the Helium atom. It was found that the part of the PH basis that accounts for one-body correlations gives a better ground state energy for He than the Hartree-Fock approximation. When an orthogonal complement is introduced to the basis to account for e-e correlations, the error in the binding energy is found to be .00025 au and .00015 au for ground and excited helium, resp., and .00035 au for H - . Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the Hyperspherical Harmonic method useful for systems with N>3. (R.P.) 14 refs., 4 tabs
Trinucleon wave functions from separable expansions of the N-N interaction
International Nuclear Information System (INIS)
Birrell, N.D.
1976-09-01
This work is intended to determine whether a separable expansion for the N-N interaction can be used to obtain trinucleon wave functions of high quality. The expansions used in the study are the Unitary Pole expansion of Harms, Afnan and Read, and the expansion of Adhikari and Sloan. We first compare the calculation of the RSC potential Triton binding energy with the two methods, and find that the results agree quite closely. However, while it is found necessary to use t-matrix perturbation theory to obtain the UPE result, such is not the case with the ASE, thus offering a considerable improvement on the previously used method. We then proceed to calculate the L-S coupling probabilities for the wave function, and in so doing, discover a source of inaccuracy in the work of other authors. We also find that the UPE and ASE give probabilities in good agreement with one another. The calculation of the He 3 charge form factor turns out to be the most critical judge of the accuracy of the wave function. Although both expansions give quite satisfactory results for the charge form factor, those obtained with the ASE are exceptionally pleasing. We finally apply both methods to the OBEP of Holinde and Machleidt, and find that the UPE is quite unsuitable for such application. The ASE, however, once again gives very good results, indicating the high quality of the trinucleon wave function obtained with it. (author)
Fully resolved simulations of expansion waves propagating into particle beds
Marjanovic, Goran; Hackl, Jason; Annamalai, Subramanian; Jackson, Thomas; Balachandar, S.
2017-11-01
There is a tremendous amount of research that has been done on compression waves and shock waves moving over particles but very little concerning expansion waves. Using 3-D direct numerical simulations, this study will explore expansion waves propagating into fully resolved particle beds of varying volume fractions and geometric arrangements. The objectives of these simulations are as follows: 1) To fully resolve all (1-way coupled) forces on the particles in a time varying flow and 2) to verify state-of-the-art drag models for such complex flows. We will explore a range of volume fractions, from very low ones that are similar to single particle flows, to higher ones where nozzling effects are observed between neighboring particles. Further, we will explore two geometric arrangements: body centered cubic and face centered cubic. We will quantify the effects that volume fraction and geometric arrangement plays on the drag forces and flow fields experienced by the particles. These results will then be compared to theoretical predictions from a model based on the generalized Faxen's theorem. This work was supported in part by the U.S. Department of Energy under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.
Experimental methods of shock wave research
Seiler, Friedrich
2016-01-01
This comprehensive and carefully edited volume presents a variety of experimental methods used in Shock Waves research. In 14 self contained chapters this 9th volume of the “Shock Wave Science and Technology Reference Library” presents the experimental methods used in Shock Tubes, Shock Tunnels and Expansion Tubes facilities. Also described is their set-up and operation. The uses of an arc heated wind tunnel and a gun tunnel are also contained in this volume. Whenever possible, in addition to the technical description some typical scientific results obtained using such facilities are described. Additionally, this authoritative book includes techniques for measuring physical properties of blast waves and laser generated shock waves. Information about active shock wave laboratories at different locations around the world that are not described in the chapters herein is given in the Appendix, making this book useful for every researcher involved in shock/blast wave phenomena.
Temporal quadratic expansion nodal Green's function method
International Nuclear Information System (INIS)
Liu Cong; Jing Xingqing; Xu Xiaolin
2000-01-01
A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method
The asymptotic expansion method via symbolic computation
Navarro, Juan F.
2012-01-01
This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
The Asymptotic Expansion Method via Symbolic Computation
Directory of Open Access Journals (Sweden)
Juan F. Navarro
2012-01-01
Full Text Available This paper describes an algorithm for implementing a perturbation method based on an asymptotic expansion of the solution to a second-order differential equation. We also introduce a new symbolic computation system which works with the so-called modified quasipolynomials, as well as an implementation of the algorithm on it.
The optimizied expansion method for wavefield extrapolation
Wu, Zedong; Alkhalifah, Tariq Ali
2013-01-01
, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain operator.In this abstract, we propose an optimized expansion method that can approximate this operator with its low rank representation. The rank defines the number
Treatment of Ion-Atom Collisions Using a Partial-Wave Expansion of the Projectile Wavefunction
Wong, T. G.; Foster, M.; Colgan, J.; Madison, D. H.
2009-01-01
We present calculations of ion-atom collisions using a partial-wave expansion of the projectile wavefunction. Most calculations of ion-atom collisions have typically used classical or plane-wave approximations for the projectile wavefunction, since partial-wave expansions are expected to require prohibitively large numbers of terms to converge…
Interactions of solitary waves and compression/expansion waves in core-annular flows
Maiden, Michelle; Anderson, Dalton; El, Gennady; Franco, Nevil; Hoefer, Mark
2017-11-01
The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been well-studied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible core-annular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are well-described by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).
A polynomial expansion method and its application in the coupled Zakharov-Kuznetsov equations
International Nuclear Information System (INIS)
Huang Wenhua
2006-01-01
A polynomial expansion method is presented to solve nonlinear evolution equations. Applying this method, the coupled Zakharov-Kuznetsov equations in fluid system are studied and many exact travelling wave solutions are obtained. These solutions include solitary wave solutions, periodic solutions and rational type solutions
International Nuclear Information System (INIS)
Chen Yong; Wang Qi; Li Biao
2005-01-01
Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally
A double expansion method for the frequency response of finite-length beams with periodic parameters
Ying, Z. G.; Ni, Y. Q.
2017-03-01
A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response
Density-functional expansion methods: Grand challenges.
Giese, Timothy J; York, Darrin M
2012-03-01
We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.
International Nuclear Information System (INIS)
Naserpour, Mahin; Zapata-Rodríguez, Carlos J.
2018-01-01
Highlights: • Paraxial beams are represented in a series expansion in terms of Bessel wave functions. • The coefficients of the series expansion can be analytically determined by using the pattern in the focal plane. • In particular, Gaussian beams and apertured wave fields have been critically examined. • This representation of the wave field is adequate for scattering problems with shaped beams. - Abstract: The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.
International Nuclear Information System (INIS)
Wang Qi; Chen Yong; Zhang Hongqing
2005-01-01
In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation
Gravity waves as a probe of the Hubble expansion rate during an electroweak scale phase transition
International Nuclear Information System (INIS)
Chung, Daniel J. H.; Zhou Peng
2010-01-01
Just as big bang nucleosynthesis allows us to probe the expansion rate when the temperature of the Universe was around 1 MeV, the measurement of gravity waves from electroweak scale first order phase transitions may allow us to probe the expansion rate when the temperature of the Universe was at the electroweak scale. We compute the simple transformation rule for the gravity wave spectrum under the scaling transformation of the Hubble expansion rate. We then apply this directly to the scenario of quintessence kination domination and show how gravity wave spectra would shift relative to Laser Interferometer Space Antenna and Big Bang Observer projected sensitivities.
Taylor-series method for four-nucleon wave functions
International Nuclear Information System (INIS)
Sandulescu, A.; Tarnoveanu, I.; Rizea, M.
1977-09-01
Taylor-series method for transforming the infinite or finite well two-nucleon wave functions from individual coordinates to relative and c.m. coordinates, by expanding the single particle shell model wave functions around c.m. of the system, is generalized to four-nucleon wave functions. Also the connections with the Talmi-Moshinsky method for two and four harmonic oscillator wave functions are deduced. For both methods Fortran IV programs for the expansion coefficients have been written and the equivalence of corresponding expressions numerically proved. (author)
Teaching graphical simulations of Fourier series expansion of some periodic waves using spreadsheets
Singh, Iqbal; Kaur, Bikramjeet
2018-05-01
The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave, half wave rectifier and full wave rectifier signals.
Correlation expansion: a powerful alternative multiple scattering calculation method
International Nuclear Information System (INIS)
Zhao Haifeng; Wu Ziyu; Sebilleau, Didier
2008-01-01
We introduce a powerful alternative expansion method to perform multiple scattering calculations. In contrast to standard MS series expansion, where the scattering contributions are grouped in terms of scattering order and may diverge in the low energy region, this expansion, called correlation expansion, partitions the scattering process into contributions from different small atom groups and converges at all energies. It converges faster than MS series expansion when the latter is convergent. Furthermore, it takes less memory than the full MS method so it can be used in the near edge region without any divergence problem, even for large clusters. The correlation expansion framework we derive here is very general and can serve to calculate all the elements of the scattering path operator matrix. Photoelectron diffraction calculations in a cluster containing 23 atoms are presented to test the method and compare it to full MS and standard MS series expansion
Teaching Graphical Simulations of Fourier Series Expansion of Some Periodic Waves Using Spreadsheets
Singh, Iqbal; Kaur, Bikramjeet
2018-01-01
The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…
Gauthier, Robert C.; Alzahrani, Mohammed A.; Jafari, Seyed Hamed
2015-02-01
The plane wave expansion (PWM) technique applied to Maxwell's wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell's wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.
Directory of Open Access Journals (Sweden)
Jiang Ying
2017-01-01
Full Text Available In this work, we study the (2+1-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models
Asymptotic expansions of Mathieu functions in wave mechanics
International Nuclear Information System (INIS)
Hunter, G.; Kuriyan, M.
1976-01-01
Solutions of the radial Schroedinger equation containing a polarization potential r -4 are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states
Application of potential harmonic expansion method to BEC ...
Indian Academy of Sciences (India)
We adopt the potential harmonics expansion method for an ab initio solu- ... commonly adopted mean-field theories, our method is capable of handling ..... potentials in self-consistent mean-field calculation [7] gives wrong results as the.
A ''quadratized'' augmented plane wave method
International Nuclear Information System (INIS)
Smrcka, L.
1982-02-01
The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)
Gandhi, Saurabh; Yurtsev, Eugene; Korolev, Kirill; Gore, Jeff
Range expansions are becoming more frequent due to environmental changes and rare long distance dispersal, often facilitated by anthropogenic activities. Simple models in theoretical ecology explain many emergent properties of range expansions, such as a constant expansion velocity, in terms of organism-level properties such as growth and dispersal rates. Testing these quantitative predictions in natural populations is difficult because of large environmental variability. Here, we used a controlled microbial model system to study range expansions of populations with and without intra-specific cooperativity. For non-cooperative growth, the expansion dynamics were dominated by population growth at the low-density front, which pulled the expansion forward. We found these expansions to be in close quantitative agreement with the classical theory of pulled waves by Fisher and Skellam, suitably adapted to our experimental system. However, as cooperativity increased, the expansions transitioned to being pushed, i.e. controlled by growth in the bulk as well as in the front. Although both pulled and pushed waves expand at a constant velocity and appear otherwise similar, their distinct dynamics leads to very different evolutionary consequences. Given the prevalence of cooperative growth in nature, understanding the effects of cooperativity is essential to managing invading species and understanding their evolution.
expansion method for the Burgers, Burgers–Huxley and modified
Indian Academy of Sciences (India)
expansion method; Burgers equation; Burgers–Huxley equation; modified. Burgers–KdV equation .... Substituting the solution set (12) and the corresponding solutions of (4) into (8), we have ..... During the past several years, many have done.
IRP methods for Environmental Impact Statements of utility expansion plans
International Nuclear Information System (INIS)
Cavallo, J.D.; Hemphill, R.C.; Veselka, T.D.
1992-01-01
Most large electric utilities and a growing number of gas utilities in the United States are using a planning method -- Integrated Resource Planning (IRP) - which incorporates demand-side management (DSM) programs whenever the marginal cost of the DSM programs are lower than the marginal cost of supply-side expansion options. Argonne National Laboratory has applied the IRP method in its socio-economic analysis of an Environmental Impact Statement (EIS) of power marketing for a system of electric utilities in the mountain and western regions of the United States. Applying the IRP methods provides valuable information to the participants in an EIS process involving capacity expansion of an electric or gas utility. The major challenges of applying the IRP method within an EIS are the time consuming and costly task of developing a least cost expansion path for each altemative, the detailed quantification of environmental damages associated with capacity expansion, and the explicit inclusion of societal-impacts to the region
Naserpour, Mahin; Zapata-Rodríguez, Carlos J.
2018-01-01
The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.
Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method
Chu, Chunlei
2012-07-01
Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.
Partial wave expansions for arbitrary spin and the role of non-central forces
International Nuclear Information System (INIS)
Johnson, R.C.
1976-09-01
The partial wave expansion of the amplitudes used by Hooton and Johnson for the scattering of particles of arbitrary spin is derived. A discussion is given of the extent to which effects arising from transition matrix elements that are diagonal and nondiagonal in orbital angular momentum can be distinguished in observables
Partial wave expansions for arbitrary spin and the role of non-central forces
International Nuclear Information System (INIS)
Johnson, R.C.
1977-01-01
The partial wave expansion of the amplitudes used by Hooton and Johnson for the scattering of particles of arbitrary spin is derived. A discussion is given of the extent to which effects arising from transition matrix elements that are diagonal and non-diagonal in orbital angular momentum can be distinguished in observables. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Ren, Baiyang; Lissenden, Cliff J.
2018-04-01
Guided waves have been extensively studied and widely used for structural health monitoring because of their large volumetric coverage and good sensitivity to defects. Effectively and preferentially exciting a desired wave mode having good sensitivity to a certain defect is of great practical importance. Piezoelectric discs and plates are the most common types of surface-mounted transducers for guided wave excitation and reception. Their geometry strongly influences the proportioning between excited modes as well as the total power of the excited modes. It is highly desirable to predominantly excite the selected mode while the total transduction power is maximized. In this work, a fully coupled multi-physics finite element analysis, which incorporates the driving circuit, the piezoelectric element and the wave guide, is combined with the normal mode expansion method to study both the mode tuning and total wave power. The excitation of circular crested waves in an aluminum plate with circular piezoelectric discs is numerically studied for different disc and adhesive thicknesses. Additionally, the excitation of plane waves in an aluminum plate, using a stripe piezoelectric element is studied both numerically and experimentally. It is difficult to achieve predominant single mode excitation as well as maximum power transmission simultaneously, especially for higher order modes. However, guidelines for designing the geometry of piezoelectric elements for optimal mode excitation are recommended.
Application of potential harmonic expansion method to BEC
Indian Academy of Sciences (India)
We adopt the potential harmonics expansion method for an ab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations.
Application of Rational Expansion Method for Differential-Difference Equation
International Nuclear Information System (INIS)
Wang Qi
2011-01-01
In this paper, we applied the rational formal expansion method to construct a series of soliton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions. The efficiency of the method can be demonstrated on Toda Lattice and Ablowitz-Ladik Lattice. (general)
An improved wave rotor refrigerator using an outside gas flow for recycling the expansion work
Zhao, J.; Hu, D.
2017-03-01
To overcome the bottleneck of traditional gas wave refrigeration, an improved wave rotor refrigerator (WRR) cycle has been proposed, in which the expansion work was recycled during the process of refrigeration. Thermodynamic analysis of the two cycles shows that the refrigeration efficiency of the improved WRR cycle has been greatly increased compared with the traditional WRR. The performance of an improved WRR was investigated by adjusting the major operational parameters, such as the rotational speed of the wave rotor, port size, and inflow overpressure. The experimental results show that pressure loss can be reduced by nearly 40 % in this improved refrigeration system. Meanwhile, a two-dimensional numerical simulation was performed to understand the wave interactions that take place inside the rotor channels.
International Nuclear Information System (INIS)
Komatsu, Nobuyoshi; Abe, Takashi
2007-01-01
Why does not an expansion shock wave exist in a gaseous medium in nature? The reason has been widely believed to be the irreversibility in nature, while an obvious demonstration for this belief has not been accomplished yet. In order to resolve the question from a microscopic viewpoint, an implosion process dual to an explosion process was investigated by means of the molecular-dynamics method (MD). To this aim, we employed a ''bit-reversible algorithm (Bit MD)'' that was completely time-reversible in a microscopic viewpoint and was free from any round-off error. Here we show that, through a dual implosion simulation (i.e., a time-reversible simulation of the explosion), a kind of expansion shock wave is successfully formed in the Bit MD simulation. Furthermore, we show that when the controlled noise is intentionally added to the Bit MD, the expansion shock wave disappears dramatically and turns into an isentropic expansion wave, even if the noise is extremely small. Since the controlled noise gives rise to the irreversibility in the Bit MD simulation, it can be concluded that the irreversibility in the system prohibits the expansion shock wave from appearing in the system
The (G′/G-Expansion Method and Its Application for Higher-Order Equations of KdV (III
Directory of Open Access Journals (Sweden)
Huizhang Yang
2014-01-01
Full Text Available New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G′/G-expansion method, where G=G(ξ satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. The property of this method is that it is quite simple and understandable.
Quality of potential harmonics expansion method for dilute Bose ...
Indian Academy of Sciences (India)
Abstract. We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correla- tions for dilute Bose–Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the ...
Optimized t-expansion method for the Rabi Hamiltonian
International Nuclear Information System (INIS)
Travenec, Igor; Samaj, Ladislav
2011-01-01
A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E 0 of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E 0 is assumed to be stationary with respect to the free parameters. A high accuracy of E 0 estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than 10 -4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E 1 , with the relative error smaller than 10 -2 (1%). -- Highlights: → We study the ground state energy of the Rabi Hamiltonian. → We use the t-expansion method with an optimized trial function. → High accuracy of estimates is achieved, the relative error being smaller than 0.01%. → The calculation of the first excited state energy is made. The method has a general applicability.
The method of boson expansions in quantum theory
International Nuclear Information System (INIS)
Garbaczewski, P.
1977-06-01
A review is presented of boson expansion methods applied in quantum theory, e.g. expansions of spin, bifermion and fermion operators in cases of finite and infinite number of degrees of freedom. The basic purpose of the paper is to formulate the most general criterion allowing one to obtain the so-called finite spin approximation of any given Bose field theory and the class of fermion theories associated with it. On the other hand, we also need to be able to reconstruct the primary Bose field theory, when any finite spin or Fermi systems are given
Experiences using DAKOTA stochastic expansion methods in computational simulations.
Energy Technology Data Exchange (ETDEWEB)
Templeton, Jeremy Alan; Ruthruff, Joseph R.
2012-01-01
Uncertainty quantification (UQ) methods bring rigorous statistical connections to the analysis of computational and experiment data, and provide a basis for probabilistically assessing margins associated with safety and reliability. The DAKOTA toolkit developed at Sandia National Laboratories implements a number of UQ methods, which are being increasingly adopted by modeling and simulation teams to facilitate these analyses. This report disseminates results as to the performance of DAKOTA's stochastic expansion methods for UQ on a representative application. Our results provide a number of insights that may be of interest to future users of these methods, including the behavior of the methods in estimating responses at varying probability levels, and the expansion levels for the methodologies that may be needed to achieve convergence.
The rate of beneficial mutations surfing on the wave of a range expansion.
Directory of Open Access Journals (Sweden)
Rémi Lehe
Full Text Available Many theoretical and experimental studies suggest that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly deleterious mutations can reach large frequencies in the newly colonized regions, as if they were surfing the front of the range expansion. These findings raise the question of how frequently beneficial mutations successfully surf at shifting range margins, thereby promoting adaptation towards a range-expansion phenotype. Here, we use individual-based simulations to study the surfing statistics of recurrent beneficial mutations on wave-like range expansions in linear habitats. We show that the rate of surfing depends on two strongly antagonistic factors, the probability of surfing given the spatial location of a novel mutation and the rate of occurrence of mutations at that location. The surfing probability strongly increases towards the tip of the wave. Novel mutations are unlikely to surf unless they enjoy a spatial head start compared to the bulk of the population. The needed head start is shown to be proportional to the inverse fitness of the mutant type, and only weakly dependent on the carrying capacity. The precise location dependence of surfing probabilities is derived from the non-extinction probability of a branching process within a moving field of growth rates. The second factor is the mutation occurrence which strongly decreases towards the tip of the wave. Thus, most successful mutations arise at an intermediate position in the front of the wave. We present an analytic theory for the tradeoff between these factors that allows to predict how frequently substitutions by beneficial mutations occur at invasion fronts. We find that small amounts of genetic drift increase the fixation rate of beneficial mutations at the advancing front, and thus could be important for adaptation during species invasions.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
International Nuclear Information System (INIS)
Garibotti, C.R.; Grinstein, F.F.
1978-01-01
Previous theorems on the convergence of the [n,n+m] punctual Pade approximants to the scattering amplitude are extended. The new proofs include the cases of nonforward and backward scattering corresponding to potentials having 1/r and 1/r 2 long-range behaviors, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long-range potentials of interest in potential scattering
International Nuclear Information System (INIS)
Garibotti, C.R.; Grinstein, F.F.
1978-01-01
Previous theorems on the convergence of the [n, n+m] Punctual Pade Approximants to the scattering amplitude are extended. The new proofs include the cases of non-forward and backward scattering corresponding to potentials having 1/r and 1/r 2 long range behaviours, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long range potentials of interest in potential scattering [pt
Conservative numerical methods for solitary wave interactions
Energy Technology Data Exchange (ETDEWEB)
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
Design of materials with extreme thermal expansion using a three-phase topology optimization method
DEFF Research Database (Denmark)
Sigmund, Ole; Torquato, S.
1997-01-01
Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases...... materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion...
International Franchising as a Method for Business Expansion
Karpushina, Darya Evgenjevna
2009-01-01
The present Master Thesis investigates the concept of international franchising from both business and legal standpoints. The actuality of the topic is obvious: Franchising becomes one of the most perspective and fast-developing method for business expansion, and this Diploma was written as a reflection of such tendency. In the meantime, Franchising is an extremely complex and arguable business issue and still causes a kind of confusion in people's mind. For this reason, my effort in this Wor...
Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)
Pestana, Reynam C.
2009-01-01
We show that the wave equation solution using a conventional finite‐difference scheme, derived commonly by the Taylor series approach, can be derived directly from the rapid expansion method (REM). After some mathematical manipulation we consider an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second order time finite‐difference scheme that is frequently used in more conventional finite‐difference implementations. We then show that if we use more terms from the REM we can obtain a more accurate time integration of the wave field. Consequently, we have demonstrated that the REM is more accurate than the usual finite‐difference schemes and it provides a wave equation solution which allows us to march in large time steps without numerical dispersion and is numerically stable. We illustrate the method with post and pre stack migration results.
Chemical Kinetics in the expansion flow field of a rotating detonation-wave engine
Kailasanath, Kazhikathra; Schwer, Douglas
2014-11-01
Rotating detonation-wave engines (RDE) are a form of continuous detonation-wave engines. They potentially provide further gains in performance than an intermittent or pulsed detonation-wave engine (PDE). The overall flow field in an idealized RDE, primarily consisting of two concentric cylinders, has been discussed in previous meetings. Because of the high pressures involved and the lack of adequate reaction mechanisms for this regime, previous simulations have typically used simplified chemistry models. However, understanding the exhaust species concentrations in propulsion devices is important for both performance considerations as well as estimating pollutant emissions. A key step towards addressing this need will be discussed in this talk. In this approach, an induction parameter model is used for simulating the detonation but a more detailed finite-chemistry model is used in the expansion flow region, where the pressures are lower and the uncertainties in the chemistry model are greatly reduced. Results show that overall radical concentrations in the exhaust flow are substantially lower than from earlier predictions with simplified models. The performance of a baseline hydrogen/air RDE increased from 4940 s to 5000 s with the expansion flow chemistry, due to recombination of radicals and more production of H2O, resulting in additional heat release.
Xiong, Jia-ming; Li, Lee; Dai, Hong-yu; Wu, Hai-bo; Peng, Ming-yang; Lin, Fu-chang
2018-03-01
During the formation of a high current impulse discharge arc, objects near the discharge arc will be strongly impacted. In this paper, a high power, high current gas switch is used as the site of the impulse discharge arc. The explosion wave theory and the arc channel energy balance equation are introduced to analyze the development of the shock wave overpressure driven by the high current impulse discharge arc, and the demarcation point of the arc channel is given, from which the energy of the arc channel is no longer converted into shock waves. Through the analysis and calculation, it is found that the magnitude of the shock wave overpressure caused by impulse discharge arc expansion is closely related to the arc current rising rate. The arc shock wave overpressure will undergo a slow decay process and then decay rapidly. The study of this paper will perform the function of deepening the understanding of the physical nature of the impulse arc discharge, which can be used to explain the damage effect of the high current impulse discharge arc.
Low-Frequency Waves in the Near-Earth Magnetotail before Substorm Expansion Onsets
Miyashita, Y.; Saito, M. H.; Hiraki, Y.; Machida, S.
2013-12-01
Magnetic reconnection and dipolarization, which occur in the near-Earth magnetotail just before substorm expansion onsets, are important processes for the substorm triggering. To understand the triggering of these processes, we have investigated low-frequency waves that were observed in the near-Earth magnetotail before onsets, by performing statistical analysis based on Geotail observations and case studies based on multi-point THEMIS and Geotail observations. Here we focused our examination on ~10 min interval before onsets. We find that small-amplitude Alfven and slow-mode magnetosonic waves with a period of ~1 to 2 min continuously exist for more than 10 min before onsets. Such waves are seen not only in the initial dipolarization region but also midway between the magnetic reconnection and initial dipolarization regions. It seems that the amplitudes of the waves are larger in the off-equator plasma sheet and the plasma sheet boundary layer than at the magnetic equator and in the lobe. After onsets the waves considerably amplify in the plasma sheet. These results may imply that instabilities already begin to grow gradually in a wide region during the substorm growth phase, while their explosive growth begins in localized regions just before onsets.
Monte Carlo methods for flux expansion solutions of transport problems
International Nuclear Information System (INIS)
Spanier, J.
1999-01-01
Adaptive Monte Carlo methods, based on the use of either correlated sampling or importance sampling, to obtain global solutions to certain transport problems have recently been described. The resulting learning algorithms are capable of achieving geometric convergence when applied to the estimation of a finite number of coefficients in a flux expansion representation of the global solution. However, because of the nonphysical nature of the random walk simulations needed to perform importance sampling, conventional transport estimators and source sampling techniques require modification to be used successfully in conjunction with such flux expansion methods. It is shown how these problems can be overcome. First, the traditional path length estimators in wide use in particle transport simulations are generalized to include rather general detector functions (which, in this application, are the individual basis functions chosen for the flus expansion). Second, it is shown how to sample from the signed probabilities that arise as source density functions in these applications, without destroying the zero variance property needed to ensure geometric convergence to zero error
Precision die design by the die expansion method
Ibhadode, A O Akii
2009-01-01
This book presents a new method for the design of the precision dies used in cold-forging, extrusion and drawing processes. The method is based upon die expansion, and attempts to provide a clear-cut theoretical basis for the selection of critical die dimensions for this group of precision dies when the tolerance on product diameter (or thickness) is specified. It also presents a procedure for selecting the minimum-production-cost die from among a set of design alternatives. The mathematical content of the book is relatively simple and will present no difficulty to those who have taken basic c
High-frequency Rayleigh-wave method
Xia, J.; Miller, R.D.; Xu, Y.; Luo, Y.; Chen, C.; Liu, J.; Ivanov, J.; Zeng, C.
2009-01-01
High-frequency (???2 Hz) Rayleigh-wave data acquired with a multichannel recording system have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. This overview article discusses the main research results of high-frequency surface-wave techniques achieved by research groups at the Kansas Geological Survey and China University of Geosciences in the last 15 years. The multichannel analysis of surface wave (MASW) method is a non-invasive acoustic approach to estimate near-surface S-wave velocity. The differences between MASW results and direct borehole measurements are approximately 15% or less and random. Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and an investigation depth. The other important seismic property, quality factor (Q), can also be estimated with the MASW method by inverting attenuation coefficients of Rayleigh waves. An inverted model (S-wave velocity or Q) obtained using a damped least-squares method can be assessed by an optimal damping vector in a vicinity of the inverted model determined by an objective function, which is the trace of a weighted sum of model-resolution and model-covariance matrices. Current developments include modeling high-frequency Rayleigh-waves in near-surface media, which builds a foundation for shallow seismic or Rayleigh-wave inversion in the time-offset domain; imaging dispersive energy with high resolution in the frequency-velocity domain and possibly with data in an arbitrary acquisition geometry, which opens a door for 3D surface-wave techniques; and successfully separating surface-wave modes, which provides a valuable tool to perform S-wave velocity profiling with high-horizontal resolution. ?? China University of Geosciences (Wuhan) and Springer-Verlag GmbH 2009.
Hadronic wave functions at short distances and the operator product expansion
International Nuclear Information System (INIS)
Brodsky, S.J.; Lepage, G.P.
1980-01-01
The operator product expansion, of appropriate products of quark fields, is used to find the anamalous dimensions which control the short distance behavior of hadronic wave functions. This vehavior in turn controls the high-Q 2 limit of hadronic form factors. In particular, we relate each anamalous dimension of the nonsinglet structure functions to a corresponding logarithmic correction factor to the nominal αsub(s)(Q 2 )/Q 2 fall off of meson form factors. Unlike the case of deep inelastic lepton-hadron scattering, the operator product necessary here involves extra terms which do not contribute to forward matrix elements. (orig.)
A multi-stage stochastic transmission expansion planning method
International Nuclear Information System (INIS)
Akbari, Tohid; Rahimikian, Ashkan; Kazemi, Ahad
2011-01-01
Highlights: → We model a multi-stage stochastic transmission expansion planning problem. → We include available transfer capability (ATC) in our model. → Involving this criterion will increase the ATC between source and sink points. → Power system reliability will be increased and more money can be saved. - Abstract: This paper presents a multi-stage stochastic model for short-term transmission expansion planning considering the available transfer capability (ATC). The ATC can have a huge impact on the power market outcomes and the power system reliability. The transmission expansion planning (TEP) studies deal with many uncertainties, such as system load uncertainties that are considered in this paper. The Monte Carlo simulation method has been applied for generating different scenarios. A scenario reduction technique is used for reducing the number of scenarios. The objective is to minimize the sum of investment costs (IC) and the expected operation costs (OC). The solution technique is based on the benders decomposition algorithm. The N-1 contingency analysis is also done for the TEP problem. The proposed model is applied to the IEEE 24 bus reliability test system and the results are efficient and promising.
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.
Analytic function expansion nodal method for nuclear reactor core design
International Nuclear Information System (INIS)
Noh, Hae Man
1995-02-01
In most advanced nodal methods the transverse integration is commonly used to reduce the multi-dimensional diffusion equation into equivalent one- dimensional diffusion equations when derving the nodal coupling equations. But the use of the transverse integration results in some limitations. The first limitation is that the transverse leakage term which appears in the transverse integration procedure must be appropriately approximated. The second limitation is that the one-dimensional flux shapes in each spatial direction resulted from the nodal calculation are not accurate enough to be directly used in reconstructing the pinwise flux distributions. Finally the transverse leakage defined for a non-rectangular node such as a hexagonal node or a triangular node is too complicated to be easily handled and may contain non-physical singular terms of step-function and delta-function types. In this thesis, the Analytic Function Expansion Nodal (AFEN) method and its two variations : the Polynomial Expansion Nodal (PEN) method and the hybrid of the AFEN and PEN methods, have been developed to overcome the limitations of the transverse integration procedure. All of the methods solve the multidimensional diffusion equation without the transverse integration. The AFEN method which we believe is the major contribution of this study to the reactor core analysis expands the homogeneous flux distributions within a node in non-separable analytic basis functions satisfying the neutron diffusion equations at any point of the node and expresses the coefficients of the flux expansion in terms of the nodal unknowns which comprise a node-average flux, node-interface fluxes, and corner-point fluxes. Then, the nodal coupling equations composed of the neutron balance equations, the interface current continuity equations, and the corner-point leakage balance equations are solved iteratively to determine all the nodal unknowns. Since the AFEN method does not use the transverse integration in
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1999-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
Directory of Open Access Journals (Sweden)
Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
Character expansion methods for matrix models of dually weighted graphs
International Nuclear Information System (INIS)
Kazakov, V.A.; Staudacher, M.; Wynter, T.
1996-01-01
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large N limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices. (orig.). With 4 figs
Feasibility of wavelet expansion methods to treat the energy variable
International Nuclear Information System (INIS)
Van Rooijen, W. F. G.
2012-01-01
This paper discusses the use of the Discrete Wavelet Transform (DWT) to implement a functional expansion of the energy variable in neutron transport. The motivation of the work is to investigate the possibility of adapting the expansion level of the neutron flux in a material region to the complexity of the cross section in that region. If such an adaptive treatment is possible, 'simple' material regions (e.g., moderator regions) require little effort, while a detailed treatment is used for 'complex' regions (e.g., fuel regions). Our investigations show that in fact adaptivity cannot be achieved. The most fundamental reason is that in a multi-region system, the energy dependence of the cross section in a material region does not imply that the neutron flux in that region has a similar energy dependence. If it is chosen to sacrifice adaptivity, then the DWT method can be very accurate, but the complexity of such a method is higher than that of an equivalent hyper-fine group calculation. The conclusion is thus that, unfortunately, the DWT approach is not very practical. (authors)
General method for designing wave shape transformers.
Ma, Hua; Qu, Shaobo; Xu, Zhuo; Wang, Jiafu
2008-12-22
An effective method for designing wave shape transformers (WSTs) is investigated by adopting the coordinate transformation theory. Following this method, the devices employed to transform electromagnetic (EM) wave fronts from one style with arbitrary shape and size to another style, can be designed. To verify this method, three examples in 2D spaces are also presented. Compared with the methods proposed in other literatures, this method offers the general procedure in designing WSTs, and thus is of great importance for the potential and practical applications possessed by such kinds of devices.
International Nuclear Information System (INIS)
Workman, R. L.; Tiator, L.; Wunderlich, Y.; Doring, M.; Haberzettl, H.
2017-01-01
Here, we compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).
The optimized expansion based low-rank method for wavefield extrapolation
Wu, Zedong
2014-03-01
Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that n > 0. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.
An alternative solver for the nodal expansion method equations - 106
International Nuclear Information System (INIS)
Carvalho da Silva, F.; Carlos Marques Alvim, A.; Senra Martinez, A.
2010-01-01
An automated procedure for nuclear reactor core design is accomplished by using a quick and accurate 3D nodal code, aiming at solving the diffusion equation, which describes the spatial neutron distribution in the reactor. This paper deals with an alternative solver for nodal expansion method (NEM), with only two inner iterations (mesh sweeps) per outer iteration, thus having the potential to reduce the time required to calculate the power distribution in nuclear reactors, but with accuracy similar to the ones found in conventional NEM. The proposed solver was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of the method for practical purposes. (authors)
Surface wave velocity tracking by bisection method
International Nuclear Information System (INIS)
Maeda, T.
2005-01-01
Calculation of surface wave velocity is a classic problem dating back to the well-known Haskell's transfer matrix method, which contributes to solutions of elastic wave propagation, global subsurface structure evaluation by simulating observed earthquake group velocities, and on-site evaluation of subsurface structure by simulating phase velocity dispersion curves and/or H/V spectra obtained by micro-tremor observation. Recently inversion analysis on micro-tremor observation requires efficient method of generating many model candidates and also stable, accurate, and fast computation of dispersion curves and Raleigh wave trajectory. The original Haskell's transfer matrix method has been improved in terms of its divergence tendency mainly by the generalized transmission and reflection matrix method with formulation available for surface wave velocity; however, root finding algorithm has not been fully discussed except for the one by setting threshold to the absolute value of complex characteristic functions. Since surface wave number (reciprocal to the surface wave velocity multiplied by frequency) is a root of complex valued characteristic function, it is intractable to use general root finding algorithm. We will examine characteristic function in phase plane to construct two dimensional bisection algorithm with consideration on a layer to be evaluated and algorithm for tracking roots down along frequency axis. (author)
International Nuclear Information System (INIS)
Chen Yong; Yan Zhenya
2005-01-01
In this paper (2 + 1)-dimensional Gardner equation is investigated using a sine-Gordon equation expansion method, which was presented via a generalized sine-Gordon reduction equation and a new transformation. As a consequence, it is shown that the method is more powerful to obtain many types of new doubly periodic solutions of (2 + 1)-dimensional Gardner equation. In particular, solitary wave solutions are also given as simple limits of doubly periodic solutions
Wave propagation retrieval method for chiral metamaterials
DEFF Research Database (Denmark)
Andryieuski, Andrei; Malureanu, Radu; Lavrinenko, Andrei
2010-01-01
In this paper we present the wave propagation method for the retrieving of effective properties of media with circularly polarized eigenwaves, in particularly for chiral metamaterials. The method is applied for thick slabs and provides bulk effective parameters. Its strong sides are the absence...
Ledoux, L.A.F.; Berkhoff, Arthur P.; Thijssen, J.M.
The Conjugate Gradient Rayleigh method for the calculation of acoustic reflection and transmission at a rough interface between two media was experimentally verified. The method is based on a continuous version of the conjugate gradient technique and plane-wave expansions. We measured the beam
Smit, Hans Harmen; Meijaard, Erik; van der Laan, Carina; Mantel, Stephan; Budiman, Arif; Verweij, Pita
2013-01-01
Land degradation is a global concern. In tropical areas it primarily concerns the conversion of forest into non-forest lands and the associated losses of environmental services. Defining such degradation is not straightforward hampering effective reduction in degradation and use of already degraded lands for more productive purposes. To facilitate the processes of avoided degradation and land rehabilitation, we have developed a methodology in which we have used international environmental and social sustainability standards to determine the suitability of lands for sustainable agricultural expansion. The method was developed and tested in one of the frontiers of agricultural expansion, West Kalimantan province in Indonesia. The focus was on oil palm expansion, which is considered as a major driver for deforestation in tropical regions globally. The results suggest that substantial changes in current land-use planning are necessary for most new plantations to comply with international sustainability standards. Through visualizing options for sustainable expansion with our methodology, we demonstrate that the link between oil palm expansion and degradation can be broken. Application of the methodology with criteria and thresholds similar to ours could help the Indonesian government and the industry to achieve its pro-growth, pro-job, pro-poor and pro-environment development goals. For sustainable agricultural production, context specific guidance has to be developed in areas suitable for expansion. Our methodology can serve as a template for designing such commodity and country specific tools and deliver such guidance. PMID:24039700
Systems and methods for wave energy conversion
MacDonald, Daniel G.; Cantara, Justin; Nathan, Craig; Lopes, Amy M.; Green, Brandon E.
2017-02-28
Systems for wave energy conversion that have components that can survive the harsh marine environment and that can be attached to fixed structures, such as a pier, and having the ability to naturally adjust for tidal height and methods for their use are presented.
Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef
2013-01-01
Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.
Grinevich, P. G.; Santini, P. M.
2018-04-01
The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.
Heuristic method for determining outgoing waves in many-body wave functions
International Nuclear Information System (INIS)
Redish, E.F.; Tandy, P.C.; L'Huillier, M.
1975-12-01
A new and simple method is proposed for determining the kinds of outgoing waves present in a given many-body wave function. Whether any particular wave function contains ''hidden'' rearrangement components can be determined. 1 figure
Exchange splitting of the interaction energy and the multipole expansion of the wave function
Energy Technology Data Exchange (ETDEWEB)
Gniewek, Piotr, E-mail: pgniewek@tiger.chem.uw.edu.pl; Jeziorski, Bogumił, E-mail: jeziorsk@chem.uw.edu.pl [Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw (Poland)
2015-10-21
The exchange splitting J of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula J{sub surf}[Φ], the volume-integral formula of the symmetry-adapted perturbation theory J{sub SAPT}[Φ], and a variational volume-integral formula J{sub var}[Φ]. The calculations are based on the multipole expansion of the wave function Φ, which is divergent for any internuclear distance R. Nevertheless, the resulting approximations to the leading coefficient j{sub 0} in the large-R asymptotic series J(R) = 2e{sup −R−1}R(j{sub 0} + j{sub 1}R{sup −1} + j{sub 2}R{sup −2} + ⋯) converge with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the J{sub var}[Φ], J{sub surf}[Φ], and J{sub SAPT}[Φ] formulas are used, respectively. Additionally, we observe that also the higher j{sub k} coefficients are predicted correctly when the multipole expansion is used in the J{sub var}[Φ] and J{sub surf}[Φ] formulas. The symmetry adapted perturbation theory formula J{sub SAPT}[Φ] predicts correctly only the first two coefficients, j{sub 0} and j{sub 1}, gives a wrong value of j{sub 2}, and diverges for higher j{sub n}. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.
International Nuclear Information System (INIS)
Olsen, Jeppe
2014-01-01
A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10 6 coefficients in the CSF basis is obtained from the 150 × 10 6 coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require
Photonic band structures solved by a plane-wave-based transfer-matrix method.
Li, Zhi-Yuan; Lin, Lan-Lan
2003-04-01
Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.
Photonic band structures solved by a plane-wave-based transfer-matrix method
International Nuclear Information System (INIS)
Li Zhiyuan; Lin Lanlan
2003-01-01
Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method
Analytical method for estimating the thermal expansion coefficient of metals at high temperature
International Nuclear Information System (INIS)
Takamoto, S; Izumi, S; Nakata, T; Sakai, S; Oinuma, S; Nakatani, Y
2015-01-01
In this paper, we propose an analytical method for estimating the thermal expansion coefficient (TEC) of metals at high-temperature ranges. Although the conventional method based on quasiharmonic approximation (QHA) shows good results at low temperatures, anharmonic effects caused by large-amplitude thermal vibrations reduces its accuracy at high temperatures. Molecular dynamics (MD) naturally includes the anharmonic effect. However, since the computational cost of MD is relatively high, in order to make an interatomic potential capable of reproducing TEC, an analytical method is essential. In our method, analytical formulation of the radial distribution function (RDF) at finite temperature realizes the estimation of the TEC. Each peak of the RDF is approximated by the Gaussian distribution. The average and variance of the Gaussian distribution are formulated by decomposing the fluctuation of interatomic distance into independent elastic waves. We incorporated two significant anharmonic effects into the method. One is the increase in the averaged interatomic distance caused by large amplitude vibration. The second is the variation in the frequency of elastic waves. As a result, the TECs of fcc and bcc crystals estimated by our method show good agreement with those of MD. Our method enables us to make an interatomic potential that reproduces the TEC at high temperature. We developed the GEAM potential for nickel. The TEC of the fitted potential showed good agreement with experimental data from room temperature to 1000 K. As compared with the original potential, it was found that the third derivative of the wide-range curve was modified, while the zeroth, first and second derivatives were unchanged. This result supports the conventional theory of solid state physics. We believe our analytical method and developed interatomic potential will contribute to future high-temperature material development. (paper)
Study on evaluation methods for Rayleigh wave dispersion characteristic
Shi, L.; Tao, X.; Kayen, R.; Shi, H.; Yan, S.
2005-01-01
The evaluation of Rayleigh wave dispersion characteristic is the key step for detecting S-wave velocity structure. By comparing the dispersion curves directly with the spectra analysis of surface waves (SASW) method, rather than comparing the S-wave velocity structure, the validity and precision of microtremor-array method (MAM) can be evaluated more objectively. The results from the China - US joint surface wave investigation in 26 sites in Tangshan, China, show that the MAM has the same precision with SASW method in 83% of the 26 sites. The MAM is valid for Rayleigh wave dispersion characteristic testing and has great application potentiality for site S-wave velocity structure detection.
Elastic wave scattering methods: assessments and suggestions
International Nuclear Information System (INIS)
Gubernatis, J.E.
1985-01-01
The author was asked by the meeting organizers to review and assess the developments over the past ten or so years in elastic wave scattering methods and to suggest areas of future research opportunities. He highlights the developments, focusing on what he feels were distinct steps forward in our theoretical understanding of how elastic waves interact with flaws. For references and illustrative figures, he decided to use as his principal source the proceedings of the various annual Reviews of Progress in Quantitative Nondestructive Evaluation (NDE). These meetings have been the main forum not only for presenting results of theoretical research but also for demonstrating the relevance of the theoretical research for the design and interpretation of experiment. In his opinion a quantitative NDE is possible only if this relevance exists, and his major objective is to discuss and illustrate the degree to which relevance has developed
Three-dimensional static and dynamic reactor calculations by the nodal expansion method
International Nuclear Information System (INIS)
Christensen, B.
1985-05-01
This report reviews various method for the calculation of the neutron-flux- and power distribution in an nuclear reactor. The nodal expansion method (NEM) is especially described in much detail. The nodal expansion method solves the diffusion equation. In this method the reactor core is divided into nodes, typically 10 to 20 cm in each direction, and the average flux in each node is calculated. To obtain the coupling between the nodes the local flux inside each node is expressed by use of a polynomial expansion. The expansion is one-dimensional, so inside each node such three expansions occur. To calculate the expansion coefficients it is necessary that the polynomial expansion is a solution to the one-dimensional diffusion equation. When the one-dimensional diffusion equation is established a term with the transversal leakage occur, and this term is expanded after the same polynomials. The resulting equation system with the expansion coefficients as the unknowns is solved with weigthed residual technique. The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The program and input to it are described. The program is tested on a number of examples extending from small theoretical one up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested. (author)
Genetic traces of east-to-west human expansion waves in Eurasia.
Chaix, Raphaëlle; Austerlitz, Frédéric; Hegay, Tatyana; Quintana-Murci, Lluís; Heyer, Evelyne
2008-07-01
In this study, we describe the landscape of human demographic expansions in Eurasia using a large continental Y chromosome and mitochondrial DNA dataset. Variation at these two uniparentally-inherited genetic systems retraces expansions that occurred in the past 60 ky, and shows a clear decrease of expansion ages from east to west Eurasia. To investigate the demographic events at the origin of this westward decrease of expansion ages, the estimated divergence ages between Eurasian populations are compared with the estimated expansion ages within each population. Both markers suggest that the demographic expansion diffused from east to west in Eurasia in a demic way, i.e., through migrations of individuals (and not just through diffusion of new technologies), highlighting the prominent role of eastern regions within Eurasia during Palaeolithic times. (c) 2008 Wiley-Liss, Inc.
International Nuclear Information System (INIS)
Sabry, R.; Zahran, M.A.; Fan Engui
2004-01-01
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found
International Nuclear Information System (INIS)
Ibrahim, R. S.; El-Kalaawy, O. H.
2006-01-01
The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model
The essential theory of fast wave current drive with full wave method
International Nuclear Information System (INIS)
Liu Yan; Gong Xueyu; Yang Lei; Yin Chenyan; Yin Lan
2007-01-01
The full wave numerical method is developed for analyzing fast wave current drive in the range of ion cyclotron waves in tokamak plasmas, taking into account finite larmor radius effects and parallel dispersion. the physical model, the dispersion relation on the assumption of Finite Larmor Radius (FLR) effects and the form of full wave be used for computer simulation are developed. All of the work will contribute to further study of fast wave current drive. (authors)
The resonance expansion for the Green's function of the Schroedinger and wave equations
International Nuclear Information System (INIS)
Albeverio, S.; Aix-Marseille-2 Univ., 13 - Marseille; Hoeegh-Krohn, R.; Oslo Univ.
1984-01-01
We give a survey of some recent mathematical work on resonances, in particular on perturbation series, low energy expansions and on resonances for point interactions. Expansions of the kernels of esup(-it)√sup(H+) and esup(-itH) in terms of resonances are also given (where Hsub(+) is the positive part of the Hamiltonian). (orig.)
International Nuclear Information System (INIS)
Oda, Ryuichi; Ishida, Shin; Wada, Hiroaki; Yamada, Kenji; Sekiguchi, Motoo
1999-01-01
We examine mass spectra and wave functions of the nn-bar, cc-bar and bb-bar meson systems within the framework of the covariant oscillator quark model with the boosted LS-coupling scheme. We solve nonperturbatively an eigenvalue problem for the squared-mass operator, which incorporates the four-dimensional color-Coulomb-type interaction, by taking a set of covariant oscillator wave functions as an expansion basis. We obtain mass spectra of these meson systems, which reproduce quite well their experimental behavior. The resultant manifestly covariant wave functions, which are applicable to analyses of various reaction phenomena, are given. Our results seem to suggest that the present model may be considered effectively as a covariant version of the nonrelativistic linear-plus-Coulomb potential quark model. (author)
Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions
International Nuclear Information System (INIS)
Ablowitz, M J; Haut, T S
2010-01-01
High-order asymptotic series are obtained for gravity-capillary solitary waves, where the first term in the series is the well-known sech 2 solution of the KdV equation. The asymptotic series is used, with nine terms included, to investigate the effects of surface tension on the height and energy of large amplitude waves, and waves close to the solitary version of Stokes' extreme wave. In particular, for surface tension below a critical value, the solitary wave with the maximum energy is obtained. For large surface tension, the series is also used to study the energy related to the solitary waves of depression. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. Comparisons are also made with recent experiments.
Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.
2018-06-01
In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.
Projector augmented wave method: ab initio molecular dynamics ...
Indian Academy of Sciences (India)
Unknown
kinetic energy is small and the wave function is smooth. However, the wave ... and various strategies have been developed. ... methods let us briefly review the history of augmented ..... alleviated by adding an intelligent zero: If an operator B.
Non-Gaussian wave packet dynamics in anharmonic potential: Cumulant expansion treatment
International Nuclear Information System (INIS)
Toutounji, Mohamad
2015-01-01
This manuscript utilizes cumulant expansion as an alternative algebraic approach to evaluating integrals and solving a system of nonlinear differential equations for probing anharmonic dynamics in condensed phase systems using Morse oscillator. These integrals and differential equations become harder to solve as the anharmonicity of the system goes beyond that of Morse oscillator description. This algebraic approach becomes critically important in case of Morse oscillator as it tends to exhibit divergent dynamics and numerical uncertainties at low temperatures. The autocorrelation function is calculated algebraically and compared to the exact one for they match perfectly. It is also compared to the approximate autocorrelation function using the differential equations technique reported in Toutounji (2014) for weak and strong electron–phonon coupling cases. It is found that the present cumulant method is more efficient, and easier to use, than the exact expression. Deviation between the approximate autocorrelation function and the exact autocorrelation function starts to arise as the electron–phonon coupling strength increases. The autocorrelation function obtained using cumulants identically matches the exact autocorrelation function, thereby surpassing the approach presented in Toutounji (2014). The advantage of the present methodology is its applicability to various types of electron–phonon coupling cases. Additionally, the herein approach only uses algebraic techniques, thereby avoiding both the divergence integral and solving a set of linear first- and second-order partial differential equations as was done in previous work. Model calculations are presented to demonstrate the accuracy of the herein work
Directory of Open Access Journals (Sweden)
Guo Zheng-Hong
2016-01-01
Full Text Available In this article, the Sumudu transform series expansion method is used to handle the local fractional Laplace equation arising in the steady fractal heat-transfer problem via local fractional calculus.
Numerical simulation of stratified shear flow using a higher order Taylor series expansion method
Energy Technology Data Exchange (ETDEWEB)
Iwashige, Kengo; Ikeda, Takashi [Hitachi, Ltd. (Japan)
1995-09-01
A higher order Taylor series expansion method is applied to two-dimensional numerical simulation of stratified shear flow. In the present study, central difference scheme-like method is adopted for an even expansion order, and upwind difference scheme-like method is adopted for an odd order, and the expansion order is variable. To evaluate the effects of expansion order upon the numerical results, a stratified shear flow test in a rectangular channel (Reynolds number = 1.7x10{sup 4}) is carried out, and the numerical velocity and temperature fields are compared with experimental results measured by laser Doppler velocimetry thermocouples. The results confirm that the higher and odd order methods can simulate mean velocity distributions, root-mean-square velocity fluctuations, Reynolds stress, temperature distributions, and root-mean-square temperature fluctuations.
Modeling laser beam diffraction and propagation by the mode-expansion method.
Snyder, James J
2007-08-01
In the mode-expansion method for modeling propagation of a diffracted beam, the beam at the aperture can be expanded as a weighted set of orthogonal modes. The parameters of the expansion modes are chosen to maximize the weighting coefficient of the lowest-order mode. As the beam propagates, its field distribution can be reconstructed from the set of weighting coefficients and the Gouy phase of the lowest-order mode. We have developed a simple procedure to implement the mode-expansion method for propagation through an arbitrary ABCD matrix, and we have demonstrated that it is accurate in comparison with direct calculations of diffraction integrals and much faster.
Ground penetrating radar antenna measurements based on plane-wave expansions
DEFF Research Database (Denmark)
Lenler-Eriksen, Hans-Rudolph; Meincke, Peter
2005-01-01
The plane-wave transmitting spectrum of the system consisting of the ground penetrating radar (GPR) antenna and the air-soil interface is measured using a loop buried in the soil. The plane-wave spectrum is used to determine various parameters characterizing the radiation of the GPR antenna...
Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum
2014-01-01
In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.
Traveling wave tube and method of manufacture
Vancil, Bernard K. (Inventor)
2004-01-01
A traveling wave tube includes a glass or other insulating envelope having a plurality of substantially parallel glass rods supported therewithin which in turn support an electron gun, a collector and an intermediate slow wave structure. The slow wave structure itself provides electrostatic focussing of a central electron beam thereby eliminating the need for focussing magnetics and materially decreasing the cost of construction as well as enabling miniaturization. The slow wave structure advantageously includes cavities along the electron beam through which the r.f. energy is propagated, or a double, interleaved ring loop structure supported by dielectric fins within a ground plane cylinder disposed coaxially within the glass envelope.
A nodal expansion method using conformal mapping for hexagonal geometry
International Nuclear Information System (INIS)
Chao, Y.A.; Shatilla, Y.A.
1993-01-01
Hexagonal nodal methods adopting the same transverse integration process used for square nodal methods face the subtle theoretical problem that this process leads to highly singular nonphysical terms in the diffusion equation. Lawrence, in developing the DIF3D-N code, tried to approximate the singular terms with relatively simple polynomials. In the HEX-NOD code, Wagner ignored the singularities to simplify the diffusion equation and introduced compensating terms in the nodal equations to restore the nodal balance relation. More recently developed hexagonal nodal codes, such as HEXPE-DITE and the hexagonal version of PANTHER, used methods similar to Wagner's. It will be shown that for light water reactor applications, these two different approximations significantly degraded the accuracy of the respective method as compared to the established square nodal methods. Alternatively, the method of conformal mapping was suggested to map a hexagon to a rectangle, with the unique feature of leaving the diffusion operator invariant, thereby fundamentally resolving the problems associated with transverse integration. This method is now implemented in the Westinghouse hexagonal nodal code ANC-H. In this paper we report on the results of comparing the three methods for a variety of problems via benchmarking against the fine-mesh finite difference code
Adaptive Laguerre-Gaussian variant of the Gaussian beam expansion method.
Cagniot, Emmanuel; Fromager, Michael; Ait-Ameur, Kamel
2009-11-01
A variant of the Gaussian beam expansion method consists in expanding the Bessel function J0 appearing in the Fresnel-Kirchhoff integral into a finite sum of complex Gaussian functions to derive an analytical expression for a Laguerre-Gaussian beam diffracted through a hard-edge aperture. However, the validity range of the approximation depends on the number of expansion coefficients that are obtained by optimization-computation directly. We propose another solution consisting in expanding J0 onto a set of collimated Laguerre-Gaussian functions whose waist depends on their number and then, depending on its argument, predicting the suitable number of expansion functions to calculate the integral recursively.
An Expansion Method to Unfold Proton Recoil Spectra
Energy Technology Data Exchange (ETDEWEB)
Kockum, J
1970-07-01
A method is given to obtain a good estimate of the input neutron spectrum from a pulse-height distribution measured with proportional counters filled with a hydrogenous gas. The method consists of expanding the sought estimate as a product of two functions where one is obtained by differentiating the pulse-height distribution and the other is a power series of the neutron energy. The coefficients of this series are determined by a least-squares fit of the calculated pulse-height distribution to the measured one. The method has been tested on pulse-height distributions obtained by calculations from a realistic neutron spectrum and response functions for a spherical counter 3. 94 cm in diameter and filled with 7 atm. of methane and 1 atm. of hydrogen, respectively. In the former case it is possible with the method described, to unfold pulse-height distributions up to a neutron energy of about 3 MeV to within 10 % of the input spectrum. The differentiating procedure included in the method ensures that all spectral details not smoothed out by the finite resolution of the counter, are kept in the spectrum estimate. A realistic estimate of the statistical uncertainty of each neutron spectrum value is given. Some of the possible systematical errors caused by uncertainties in input data have been investigated.
Nguyen, Thao T. P.; Tanabe, Rie; Ito, Yoshiro
2018-03-01
We compared the expansion characteristics of the plasma plumes and shock waves generated in laser-induced shock process between the two ablation regimes: in air and under water. The observation was made from the initial moment when the laser pulse hit the target until 1.5 μs. The shock processes were driven by focusing a single laser pulse (1064 nm, FWHM = 13 ns) onto the surface of epoxy-resin blocks using a 40-mm focal length lens. The estimated laser intensity at the target plane is approximate to 9 ×109Wcm-2 . We used the fast-imaging technique to observe the expansion of the plasma plume and a custom-designed time-resolved photoelasticity imaging technique to observe the propagation of shock waves with the time resolution of nanoseconds. We found that at the same intensity of the laser beam, the plasma expansion during the laser pulse follows different mechanisms: the plasma plume that grows in air follows a radiation-wave model while a detonation-wave model can explain the expansion of the plasma plume induced in water. The ideal blast wave theory can be used to predict the decay of the shock wave in air but is not appropriate to describe the decay of the shock wave induced under water.
The Sturmian expansion: A well-depth-method for orbitals in a deformed potential
International Nuclear Information System (INIS)
Bang, J.M.; Vaagen, J.S.
1980-01-01
The Sturmian expansion method has over the years successfully been used to generate orbitals in a deformed potential. In this paper we review the method in detail including more recent extentions. The convergence properties are discussed in terms of examples of current interest for nucleon-transfer reactions. Comparisons with other methods are also made. (orig.)
Mountain Wave Analysis Using Fourier Methods
National Research Council Canada - National Science Library
Roadcap, John R
2007-01-01
...) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms...
Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation
International Nuclear Information System (INIS)
Wang Dengshan; Zhang Hongqing
2005-01-01
In this paper, with the aid of the symbolic computation we improve the extended F-expansion method in [Chaos, Solitons and Fractals 2004; 22:111] and propose the further improved F-expansion method. Using this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. In addition,the solutions we get are more general than the solutions that the extended F-expansion method gets.The solutions we get include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on. Our method can also apply to other partial differential equations and can also get many new exact solutions
A wave propagation matrix method in semiclassical theory
International Nuclear Information System (INIS)
Lee, S.Y.; Takigawa, N.
1977-05-01
A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied
Multimodal method for scattering of sound at a sudden area expansion in a duct with subsonic flow
Kooijman, G.; Testud, P.; Aurégan, Y.; Hirschberg, A.
2008-03-01
The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both two-dimensional (2D) rectangular and 2D cylindrical geometry and uniform mean flow as well as non-uniform mean flow profiles are considered. Model results for the scattering of plane waves in case of uniform flow, in which case an infinitely thin shear layer is formed downstream of the area expansion, are compared to results obtained by other models in literature. Generally good agreement is found. Furthermore, model results for the scattering are compared to experimental data found in literature. Also here fairly good correspondence is observed. When employing a turbulent pipe flow profile in the model, instead of a uniform flow profile, the prediction for the downstream transmission- and upstream reflection coefficient is improved. However, worse agreement is observed for the upstream transmission and downstream reflection coefficient. On the contrary, employing a non-uniform jet flow profile, which represents a typical shear layer flow downstream of the expansion, gives worse agreement for the downstream transmission- and the upstream reflection coefficient, whereas prediction for the upstream transmission and downstream reflection coefficient improves.
Higher order polynomial expansion nodal method for hexagonal core neutronics analysis
International Nuclear Information System (INIS)
Jin, Young Cho; Chang, Hyo Kim
1998-01-01
A higher-order polynomial expansion nodal(PEN) method is newly formulated as a means to improve the accuracy of the conventional PEN method solutions to multi-group diffusion equations in hexagonal core geometry. The new method is applied to solving various hexagonal core neutronics benchmark problems. The computational accuracy of the higher order PEN method is then compared with that of the conventional PEN method, the analytic function expansion nodal (AFEN) method, and the ANC-H method. It is demonstrated that the higher order PEN method improves the accuracy of the conventional PEN method and that it compares very well with the other nodal methods like the AFEN and ANC-H methods in accuracy
DEFF Research Database (Denmark)
Karamehmedovic, Mirza; Breinbjerg, Olav
2002-01-01
The Method of Auxiliary Sources (MAS) is applied to 3D scattering problems involving spherical impedance scatterers. The MAS results are compared with the reference spherical wave expansion (SWE) solution. It is demonstrated that good agreement is achieved between the MAS and SWE results....
DEFF Research Database (Denmark)
Nour, Baqer; Breinbjerg, Olav
2010-01-01
This article addresses the problem of communication in near field region. The proposed example is the communication between two small antennas, which are modelled as an electric dipole antenna (transmitter) and a small box (receiver), near a sphere that models a head. Spherical vector wave...
A second-order shock-expansion method applicable to bodies of revolution near zero lift
1957-01-01
A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.
Using nodal expansion method in calculation of reactor core with square fuel assemblies
International Nuclear Information System (INIS)
Abdollahzadeh, M. Y.; Boroushaki, M.
2009-01-01
A polynomial nodal method is developed to solve few-group neutron diffusion equations in cartesian geometry. In this article, the effective multiplication factor, group flux and power distribution based on the nodal polynomial expansion procedure is presented. In addition, by comparison of the results the superiority of nodal expansion method on finite-difference and finite-element are fully demonstrated. The comparison of the results obtained by these method with those of the well known benchmark problems have shown that they are in very good agreement.
Directory of Open Access Journals (Sweden)
Xingjun Lv
2011-11-01
Full Text Available In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping
2011-01-01
In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
Method and apparatus for generating acoustic waves
International Nuclear Information System (INIS)
Rao, G.V.; Gopal, R.
1982-01-01
A portable source of acoustic waves comprises a sample of iron-nickel alloy including an austenite phase cooled to become martensite, and a wave guide to transmit the acoustic waves. The source is applied to the pressure boundary region of a pressurized water reactor to simulate an actual metal flaw and test the calibration of the monitoring and surveillance system. With at most 29.7% nickel in the sample, the source provides acoustic emission due to ductile deformation, and with at least 30% nickel the acoustic emission is characteristic of a brittle deformation. Thus, the monitoring and surveillance system can be tested in either or both situations. In the prior art, synthetic waveform signals were used for such calibration but found not suitable for on-line simulation of the surveillance system. This invention provides an improved system in that it generates true acoustic signals. (author)
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks
International Nuclear Information System (INIS)
Phillips, C.K.; Perkins, F.W.; Hwang, D.Q.
1985-07-01
Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are ignored by ray tracing mthods, are included self-consistently using the parabolic method since continuous representations for the wave electromagnetic fields are computed directly. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters
Problems of the orthogonalized plane wave method. 1
International Nuclear Information System (INIS)
Farberovich, O.V.; Kurganskii, S.I.; Domashevskaya, E.P.
1979-01-01
The main problems of the orthogonalized plane wave method are discussed including (a) consideration of core states; (b) effect of overlap of wave functions of external core states upon the band structure; (c) calculation of d-type states. The modified orthogonal plane wave method (MOPW method) of Deegan and Twose is applied in a general form to solve the problems of the usual OPW method. For the first time the influence on the spectrum of the main parameters of the MOPW method is studied systematically by calculating the electronic energy spectrum in the transition metals Nb and V. (author)
Design of materials with extreme thermal expansion using a three-phase topology optimization method
DEFF Research Database (Denmark)
Sigmund, Ole; Torquato, S.
1997-01-01
We show how composites with extremal or unusual thermal expansion coefficients can be designed using a numerical topology optimization method. The composites are composed of two different material phases and void. The optimization method is illustrated by designing materials having maximum therma...
New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method
International Nuclear Information System (INIS)
Pandir, Yusuf; Duzgun, Hasan Huseyin
2017-01-01
In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)
Engineered high expansion glass-ceramics having near linear thermal strain and methods thereof
Energy Technology Data Exchange (ETDEWEB)
Dai, Steve Xunhu; Rodriguez, Mark A.; Lyon, Nathanael L.
2018-01-30
The present invention relates to glass-ceramic compositions, as well as methods for forming such composition. In particular, the compositions include various polymorphs of silica that provide beneficial thermal expansion characteristics (e.g., a near linear thermal strain). Also described are methods of forming such compositions, as well as connectors including hermetic seals containing such compositions.
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2014-09-01
Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.
International Nuclear Information System (INIS)
Ibrahim, R.S.
2003-01-01
The equations of magnetohydrodynamic (MHD) equilibria for a plasma in gravitational field are investigated. For equilibria with one ignorable spatial coordinate, the MHD equations are reduced to a single nonlinear elliptic equation for the magnetic potential u-tilde, known as the Grad-Shafranov equation. Specifying the arbitrary functions in this equation, the Bullough-Dodd equation can be obtained. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the travelling wave solutions of the Bullough-Dodd equation for the case of isothermal magnetostatic atmosphere, in which the current density J is proportional to the exponentially of the magnetic flux and moreover falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height
Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef
2013-01-01
The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.
Directory of Open Access Journals (Sweden)
Wang Mingjie
2017-01-01
Full Text Available A framework of non-intrusive polynomial chaos expansion method (PC was proposed to investigate the statistic characteristics of the response of structural-acoustic system containing random uncertainty. The PC method does not need to reformulate model equations, and the statistics of the response can be evaluated directly. The results show that compared to the direct Monte Carlo method (MCM based on the original numerical model, the PC method is effective and more efficient.
Forecasting ocean wave energy: A Comparison of the ECMWF wave model with time series methods
DEFF Research Database (Denmark)
Reikard, Gordon; Pinson, Pierre; Bidlot, Jean
2011-01-01
Recently, the technology has been developed to make wave farms commercially viable. Since electricity is perishable, utilities will be interested in forecasting ocean wave energy. The horizons involved in short-term management of power grids range from as little as a few hours to as long as several...... days. In selecting a method, the forecaster has a choice between physics-based models and statistical techniques. A further idea is to combine both types of models. This paper analyzes the forecasting properties of a well-known physics-based model, the European Center for Medium-Range Weather Forecasts...... (ECMWF) Wave Model, and two statistical techniques, time-varying parameter regressions and neural networks. Thirteen data sets at locations in the Atlantic and Pacific Oceans and the Gulf of Mexico are tested. The quantities to be predicted are the significant wave height, the wave period, and the wave...
A Study on the Profile Change Measurement of Steam Generator Tubes with Tube Expansion Methods
International Nuclear Information System (INIS)
Kim, Young Kyu; Song Myung Ho; Choi, Myung Sik
2011-01-01
Steam generator tubes for nuclear power plants contain the local shape transitions on their inner or outer surface such as dent, bulge, over-expansion, eccentricity, deflection, and so on by the application of physical force during the tube manufacturing and steam generator assembling and by the sludge (that is, corrosion products) produced during the plant operation. The structural integrity of tubes will be degraded by generating the corrosive crack at that location. The profilometry using the traditional bobbin probes which are currently applied for measuring the profile change of tubes gives us basic information such as axial locations and average magnitudes of deformations. However, the three-dimensional quantitative evaluation on circumferential locations, distributional angle, and size of deformations will have to be conducted to understand the effects of residual stresses increased by local deformations on corrosive cracking of tubes. Steam generator tubes of Korean standard nuclear power plants expanded within their tube-sheets by the explosive expansion method and suffered from corrosive cracks in the early stage of power operation. Thus, local deformations of steam generator tubes at the top of tube-sheet were measured with an advanced rotating probe and a laser profiling system for the two cases where the tubes expanded by the explosive expansion method and hydraulic expansion. Also, the trends of eccentricity, deflection, and over-expansion of tubes were evaluated. The advanced eddy current profilometry was confirmed to provide accurate information of local deformations compared with laser profilometry
Expansion of X-ray form factor for close shell using uncorrelated wave function
Energy Technology Data Exchange (ETDEWEB)
AL-Robayi, Enas M. [Babylon University , College of Science for Women, laser Physics Department, Hilla (Iraq)
2013-12-16
The atomic scattering factor has been studied for Be+ve, and B+2ve ions using the uncorrelated wave function (Hartree-Fock (HF)) for inter particle electronic shells. The physical importance of this factor appears in its relation to several important atomic properties as, the coherent scattering intensity, the total scattering intensity, the incoherent scattering function, the coherent scattering cross section, the total incoherent cross section, the nuclear magnetic shielding constant, the geometrical structure factor. Also there is one atomic properties the one particle radial density distribution function D(r)has been studied using the partitioning technique.
A fast method for linear waves based on geometrical optics
Stolk, C.C.
2009-01-01
We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the
Li, Zheng-Wei; Xi, Xiao-Li; Zhang, Jin-Sheng; Liu, Jiang-fan
2015-12-14
The unconditional stable finite-difference time-domain (FDTD) method based on field expansion with weighted Laguerre polynomials (WLPs) is applied to model electromagnetic wave propagation in gyrotropic materials. The conventional Yee cell is modified to have the tightly coupled current density components located at the same spatial position. The perfectly matched layer (PML) is formulated in a stretched-coordinate (SC) system with the complex-frequency-shifted (CFS) factor to achieve good absorption performance. Numerical examples are shown to validate the accuracy and efficiency of the proposed method.
DEFF Research Database (Denmark)
Gomes, J.; Hald, J.; Juhl, P.
2009-01-01
regularization (the truncated singular value decomposition) is introduced. Important differences between applying the method when using a microphone array surrounding the source completely and an array covering only a part of the source are described. Another relevant issue is the scaling of the wave functions...
Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)
Pestana, Reynam C.; Stoffa, Paul L.
2009-01-01
an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2014-01-01
Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.
Directory of Open Access Journals (Sweden)
SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
The Taylor-expansion method of moments for the particle system with bimodal distribution
Directory of Open Access Journals (Sweden)
Liu Yan-Hua
2013-01-01
Full Text Available This paper derives the multipoint Taylor expansion method of moments for the bimodal particle system. The collision effects are modeled by the internal and external coagulation terms. Simple theory and numerical tests are performed to prove the effect of the current model.
A two-dimensional, semi-analytic expansion method for nodal calculations
International Nuclear Information System (INIS)
Palmtag, S.P.
1995-08-01
Most modern nodal methods used today are based upon the transverse integration procedure in which the multi-dimensional flux shape is integrated over the transverse directions in order to produce a set of coupled one-dimensional flux shapes. The one-dimensional flux shapes are then solved either analytically or by representing the flux shape by a finite polynomial expansion. While these methods have been verified for most light-water reactor applications, they have been found to have difficulty predicting the large thermal flux gradients near the interfaces of highly-enriched MOX fuel assemblies. A new method is presented here in which the neutron flux is represented by a non-seperable, two-dimensional, semi-analytic flux expansion. The main features of this method are (1) the leakage terms from the node are modeled explicitly and therefore, the transverse integration procedure is not used, (2) the corner point flux values for each node are directly edited from the solution method, and a corner-point interpolation is not needed in the flux reconstruction, (3) the thermal flux expansion contains hyperbolic terms representing analytic solutions to the thermal flux diffusion equation, and (4) the thermal flux expansion contains a thermal to fast flux ratio term which reduces the number of polynomial expansion functions needed to represent the thermal flux. This new nodal method has been incorporated into the computer code COLOR2G and has been used to solve a two-dimensional, two-group colorset problem containing uranium and highly-enriched MOX fuel assemblies. The results from this calculation are compared to the results found using a code based on the traditional transverse integration procedure
Numerical method for wave forces acting on partially perforated caisson
Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou
2015-04-01
The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.
Analysis shear wave velocity structure obtained from surface wave methods in Bornova, Izmir
Energy Technology Data Exchange (ETDEWEB)
Pamuk, Eren, E-mail: eren.pamuk@deu.edu.tr; Akgün, Mustafa, E-mail: mustafa.akgun@deu.edu.tr [Department of Geophysical Engineering, Dokuz Eylul University, Izmir (Turkey); Özdağ, Özkan Cevdet, E-mail: cevdet.ozdag@deu.edu.tr [Dokuz Eylul University Rectorate, Izmir (Turkey)
2016-04-18
Properties of the soil from the bedrock is necessary to describe accurately and reliably for the reduction of earthquake damage. Because seismic waves change their amplitude and frequency content owing to acoustic impedance difference between soil and bedrock. Firstly, shear wave velocity and depth information of layers on bedrock is needed to detect this changing. Shear wave velocity can be obtained using inversion of Rayleigh wave dispersion curves obtained from surface wave methods (MASW- the Multichannel Analysis of Surface Waves, ReMi-Refraction Microtremor, SPAC-Spatial Autocorrelation). While research depth is limeted in active source study, a passive source methods are utilized for deep depth which is not reached using active source methods. ReMi method is used to determine layer thickness and velocity up to 100 m using seismic refraction measurement systems.The research carried out up to desired depth depending on radius using SPAC which is utilized easily in conditions that district using of seismic studies in the city. Vs profiles which are required to calculate deformations in under static and dynamic loads can be obtained with high resolution using combining rayleigh wave dispersion curve obtained from active and passive source methods. In the this study, Surface waves data were collected using the measurements of MASW, ReMi and SPAC at the İzmir Bornova region. Dispersion curves obtained from surface wave methods were combined in wide frequency band and Vs-depth profiles were obtained using inversion. Reliability of the resulting soil profiles were provided by comparison with theoretical transfer function obtained from soil paremeters and observed soil transfer function from Nakamura technique and by examination of fitting between these functions. Vs values are changed between 200-830 m/s and engineering bedrock (Vs>760 m/s) depth is approximately 150 m.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Wang, Wei; Liu, Huiming; Huang, Rongjin; Zhao, Yuqiang; Huang, Chuangjun; Guo, Shibin; Shan, Yi; Li, Laifeng
2018-01-01
Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra-low temperature (thermal expansion and magnetostriction at cryogenic temperature using the strain gauge method based on a Physical Properties Measurements System (PPMS). The interfacing software and automation were developed using LabVIEW. The sample temperature range can be tuned continuously between 1.8 and 400 K. With this PPMS-aided measuring system, we can observe temperature and magnetic field dependence of the linear thermal expansion of different solid materials easily and accurately.
Directory of Open Access Journals (Sweden)
Wei Wang
2018-03-01
Full Text Available Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra-low temperature (<77 K environment easily. This paper describes the design and test results of thermal expansion and magnetostriction at cryogenic temperature using the strain gauge method based on a Physical Properties Measurements System (PPMS. The interfacing software and automation were developed using LabVIEW. The sample temperature range can be tuned continuously between 1.8 and 400 K. With this PPMS-aided measuring system, we can observe temperature and magnetic field dependence of the linear thermal expansion of different solid materials easily and accurately.
Wang, Wei; Liu, Huiming; Huang, Rongjin; Zhao, Yuqiang; Huang, Chuangjun; Guo, Shibin; Shan, Yi; Li, Laifeng
2018-03-01
Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra low temperature (＜77 K) environment easily. This paper describes the design and test results of thermal expansion and magnetostriction at cryogenic temperature using the strain gage method based on a Physical Properties Measurements System (PPMS). The interfacing software and automation were developed using LabVIEW. The sample temperature range can be tuned continuously between 1.8 K and 400 K. With this PPMS-aided measuring system, we can observe temperature and magnetic field dependence of the linear thermal expansion of different solid materials easily and accurately.
Validation of Standing Wave Liner Impedance Measurement Method, Phase I
National Aeronautics and Space Administration — Hersh Acoustical Engineering, Inc. proposes to establish the feasibility and practicality of using the Standing Wave Method (SWM) to measure the impedance of...
Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method
International Nuclear Information System (INIS)
Bekir Ahmet; Güner Özkan
2013-01-01
In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations
Directory of Open Access Journals (Sweden)
Wei Li
2014-01-01
Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.
Symmetrized partial-wave method for density-functional cluster calculations
International Nuclear Information System (INIS)
Averill, F.W.; Painter, G.S.
1994-01-01
The computational advantage and accuracy of the Harris method is linked to the simplicity and adequacy of the reference-density model. In an earlier paper, we investigated one way the Harris functional could be extended to systems outside the limits of weakly interacting atoms by making the charge density of the interacting atoms self-consistent within the constraints of overlapping spherical atomic densities. In the present study, a method is presented for augmenting the interacting atom charge densities with symmetrized partial-wave expansions on each atomic site. The added variational freedom of the partial waves leads to a scheme capable of giving exact results within a given exchange-correlation approximation while maintaining many of the desirable convergence and stability properties of the original Harris method. Incorporation of the symmetry of the cluster in the partial-wave construction further reduces the level of computational effort. This partial-wave cluster method is illustrated by its application to the dimer C 2 , the hypothetical atomic cluster Fe 6 Al 8 , and the benzene molecule
Distorted wave method in reactions with composite particles
International Nuclear Information System (INIS)
Zelenskaya, N.S.; Teplov, I.B.
1980-01-01
The work deals with the distorbed wave method with a finite radius of interaction (DWBAFR) as applied to quantitative analysis of direct nuclear reactions with composite particles (including heavy ions) considering the reaction mechanisms other than the cluster stripping mechanism, in particular the exchange processes. The accurate equations of the distorbed-wave method in the three-body problem and the general formula dor calculating differential cross-sections of arbitrary binary reactions by DWBAFR are presented. Accurate and approximate methods allowing for finite interaction radius are discussed. Two main versions of exact account of recoil effects: separation of variables in wave functions of relative motion of particles and in interaction potentials and separation of variables in distorted waves are analysed. Given is a characteristic of the known calculated programs approximately and exactly taking account of recoil effects for direct and exchange processes [ru
Parametric form of QCD travelling waves
Peschanski, R.
2005-01-01
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a solvable hierarchy of differential equations. A universal parametric form of travelling waves emerges from the first two orders of the expansion.
Directory of Open Access Journals (Sweden)
Nur Alam
2016-02-01
Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.
Reflection and diffraction of atomic de Broglie waves by evanescent laser waves. Bare-state method
International Nuclear Information System (INIS)
Feng, Xiaoping; Witte, N.S.; Hollenberg, C.L.; Opat, G.
1994-01-01
Two methods are presented for the investigation of the reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both methods use the bare-state rather than dressed-state picture. One method is based on the Born series, whereas the other is based on the Laplace transformation of the coupled differential equations. The two methods yield the same theoretical expressions for the reflected and diffracted atomic waves in the whole space including the interaction and the asymptotic regions. 1 ref., 1 fig
A robust and efficient stepwise regression method for building sparse polynomial chaos expansions
Energy Technology Data Exchange (ETDEWEB)
Abraham, Simon, E-mail: Simon.Abraham@ulb.ac.be [Vrije Universiteit Brussel (VUB), Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, 1050 Brussels (Belgium); Raisee, Mehrdad [School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box: 11155-4563, Tehran (Iran, Islamic Republic of); Ghorbaniasl, Ghader; Contino, Francesco; Lacor, Chris [Vrije Universiteit Brussel (VUB), Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, 1050 Brussels (Belgium)
2017-03-01
Polynomial Chaos (PC) expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters. The computational cost of classical PC solution schemes is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension. This considerably restricts the practical use of PC at the industrial level. A common approach to address such problems is to make use of sparse PC expansions. This paper presents a non-intrusive regression-based method for building sparse PC expansions. The most important PC contributions are detected sequentially through an automatic search procedure. The variable selection criterion is based on efficient tools relevant to probabilistic method. Two benchmark analytical functions are used to validate the proposed algorithm. The computational efficiency of the method is then illustrated by a more realistic CFD application, consisting of the non-deterministic flow around a transonic airfoil subject to geometrical uncertainties. To assess the performance of the developed methodology, a detailed comparison is made with the well established LAR-based selection technique. The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem. Moreover, the most important stochastic features are captured at a reduced computational cost compared to the LAR method. The results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs.
Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar
2018-05-01
The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models
MURILLO, Carol Andrea; THOREL, Luc; CAICEDO, Bernardo
2009-01-01
The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge test...
International Nuclear Information System (INIS)
Takahashi, Akito; Yamamoto, Junji; Ebisuya, Mituo; Sumita, Kenji
1979-01-01
A new method for calculating the anisotropic neutron transport is proposed for the angular spectral analysis of D-T fusion reactor neutronics. The method is based on the transport equation with new type of anisotropic scattering kernels formulated by a single function I sub(i) (μ', μ) instead of polynomial expansion, for instance, Legendre polynomials. In the calculation of angular flux spectra by using scattering kernels with the Legendre polynomial expansion, we often observe the oscillation with negative flux. But in principle this oscillation disappears by this new method. In this work, we discussed anisotropic scattering kernels of the elastic scattering and the inelastic scatterings which excite discrete energy levels. The other scatterings were included in isotropic scattering kernels. An approximation method, with use of the first collision source written by the I sub(i) (μ', μ) function, was introduced to attenuate the ''oscillations'' when we are obliged to use the scattering kernels with the Legendre polynomial expansion. Calculated results with this approximation showed remarkable improvement for the analysis of the angular flux spectra in a slab system of lithium metal with the D-T neutron source. (author)
International Nuclear Information System (INIS)
Yang, W.; Wu, H.; Cao, L.
2012-01-01
More and more MOX fuels are used in all over the world in the past several decades. Compared with UO 2 fuel, it contains some new features. For example, the neutron spectrum is harder and more resonance interference effects within the resonance energy range are introduced because of more resonant nuclides contained in the MOX fuel. In this paper, the wavelets scaling function expansion method is applied to study the resonance behavior of plutonium isotopes within MOX fuel. Wavelets scaling function expansion continuous-energy self-shielding method is developed recently. It has been validated and verified by comparison to Monte Carlo calculations. In this method, the continuous-energy cross-sections are utilized within resonance energy, which means that it's capable to solve problems with serious resonance interference effects without iteration calculations. Therefore, this method adapts to treat the MOX fuel resonance calculation problem natively. Furthermore, plutonium isotopes have fierce oscillations of total cross-section within thermal energy range, especially for 240 Pu and 242 Pu. To take thermal resonance effect of plutonium isotopes into consideration the wavelet scaling function expansion continuous-energy resonance calculation code WAVERESON is enhanced by applying the free gas scattering kernel to obtain the continuous-energy scattering source within thermal energy range (2.1 eV to 4.0 eV) contrasting against the resonance energy range in which the elastic scattering kernel is utilized. Finally, all of the calculation results of WAVERESON are compared with MCNP calculation. (authors)
International Nuclear Information System (INIS)
Zheng Youqi; Wu Hongchun; Cao Liangzhi
2013-01-01
This paper describes the stability analysis for the coarse mesh finite difference (CMFD) acceleration used in the wavelet expansion method. The nonlinear CMFD acceleration scheme is transformed by linearization and the Fourier ansatz is introduced into the linearized formulae. The spectral radius is defined as the stability criterion, which is the least upper bound (LUB) of the largest eigenvalue of Fourier analysis matrix. The stability analysis considers the effect of mesh size (spectral length), coarse mesh division and scattering ratio. The results show that for the wavelet expansion method, the CMFD acceleration is conditionally stable. The small size of fine mesh brings stability and fast convergent. With the increase of the mesh size, the stability becomes worse. The scattering ratio does not impact the stability obviously. It makes the CMFD acceleration highly efficient in the strong scattering case. The results of Fourier analysis are verified by the numerical tests based on a homogeneous slab problem.
The verification of the Taylor-expansion moment method in solving aerosol breakage
Directory of Open Access Journals (Sweden)
Yu Ming-Zhou
2012-01-01
Full Text Available The combination of the method of moment, characterizing the particle population balance, and the computational fluid dynamics has been an emerging research issue in the studies on the aerosol science and on the multiphase flow science. The difficulty of solving the moment equation arises mainly from the closure of some fractal moment variables which appears in the transform from the non-linear integral-differential population balance equation to the moment equations. Within the Taylor-expansion moment method, the breakage-dominated Taylor-expansion moment equation is first derived here when the symmetric fragmentation mechanism is involved. Due to the high efficiency and the high precision, this proposed moment model is expected to become an important tool for solving population balance equations.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) ... mulation of Brookes & Hughes (1982) that implicitly incorporates numerical ..... functions and (c) SUPG method in the (kh − ω t)-plane for explicit Euler.
International Nuclear Information System (INIS)
Vitale, Salvatore; Zanolin, Michele
2011-01-01
This paper describes the most accurate analytical frequentist assessment to date of the uncertainties in the estimation of physical parameters from gravitational waves generated by nonspinning binary systems and Earth-based networks of laser interferometers. The paper quantifies how the accuracy in estimating the intrinsic parameters mostly depends on the network signal to noise ratio (SNR), but the resolution in the direction of arrival also strongly depends on the network geometry. We compare results for six different existing and possible global networks and two different choices of the parameter space. We show how the fraction of the sky where the one sigma angular resolution is below 2 square degrees increases about 3 times when transitioning from the Hanford (USA), Livingston (USA) and Cascina (Italy) network to a network made of five interferometers (while keeping the network SNR fixed). The technique adopted here is an asymptotic expansion of the uncertainties in inverse powers of the SNR where the first order is the inverse Fisher information matrix. We show that the commonly employed approach of using a simplified parameter spaces and only the Fisher information matrix can largely underestimate the uncertainties (the combined effect would lead to a factor 7 for the one sigma sky uncertainty in square degrees at a network SNR of 15).
International Nuclear Information System (INIS)
Ribeiro, R.D.M.; Vellozo, S.O.; Botelho, D.A.
1983-01-01
The EPON computer code based in a Nodal Polynomial Expansion Method, wrote in Fortran IV, for steady-state, square geometry, one-dimensional or two-dimensional geometry and for one or two-energy group is presented. The neutron and power flux distributions for nuclear power plants were calculated, comparing with codes that use similar or different methodologies. The availability, economy and speed of the methodology is demonstrated. (E.G.) [pt
Thermodynamics of non-ideal QGP using Mayers cluster expansion method
International Nuclear Information System (INIS)
Prasanth, J.P; Simji, P.; Bannur, Vishnu M.
2013-01-01
The Quark gluon plasma (QGP) is the state in which the individual hadrons dissolve into a system of free (or almost free) quarks and gluons in strongly compressed system at high temperature. The present paper aims to calculate the critical temperature at which a non-ideal three quark plasma condenses into droplet of three quarks (i.e., into a liquid of baryons) using Mayers cluster expansion method
Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method
Li, Xiaowang; Deng, Zhongmin
2016-01-01
A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white no...
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Comparison of matrix methods for elastic wave scattering problems
International Nuclear Information System (INIS)
Tsao, S.J.; Varadan, V.K.; Varadan, V.V.
1983-01-01
This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error
Wave field restoration using three-dimensional Fourier filtering method.
Kawasaki, T; Takai, Y; Ikuta, T; Shimizu, R
2001-11-01
A wave field restoration method in transmission electron microscopy (TEM) was mathematically derived based on a three-dimensional (3D) image formation theory. Wave field restoration using this method together with spherical aberration correction was experimentally confirmed in through-focus images of amorphous tungsten thin film, and the resolution of the reconstructed phase image was successfully improved from the Scherzer resolution limit to the information limit. In an application of this method to a crystalline sample, the surface structure of Au(110) was observed in a profile-imaging mode. The processed phase image showed quantitatively the atomic relaxation of the topmost layer.
International Nuclear Information System (INIS)
Hayward, Robert M.; Rahnema, Farzad; Zhang, Dingkang
2013-01-01
Highlights: ► A new hybrid stochastic–deterministic transport theory method to couple with diffusion theory. ► The method is implemented in 2D hexagonal geometry. ► The new method produces excellent results when compared with Monte Carlo reference solutions. ► The method is fast, solving all test cases in less than 12 s. - Abstract: A new hybrid stochastic–deterministic transport theory method, which is designed to couple with diffusion theory, is presented. The new method is an extension of the incident flux response expansion method, and it combines the speed of diffusion theory with the accuracy of transport theory. With ease of use in mind, the new method is derived in such a way that it can be implemented with only minimal modifications to an existing diffusion theory method. A new angular expansion, which is necessary for the diffusion theory coupling, is developed in 2D and 3D. The method is implemented in 2D hexagonal geometry, and an HTTR benchmark problem is used to test its accuracy in a standalone configuration. It is found that the new method produces excellent results (with average relative error in partial current less than 0.033%) when compared with Monte Carlo reference solutions. Furthermore, the method is fast, solving all test cases in less than 12 s
Chiral metamaterials characterisation using the wave propagation retrieval method
DEFF Research Database (Denmark)
Andryieuski, Andrei; Lavrinenko, Andrei; Malureanu, Radu
2010-01-01
In this presentation we extend the wave propagation method for the retrieval of the effective properties to the case of chiral metamaterials with circularly polarised eigenwaves. The method is unambiguous, simple and provides bulk effective parameters. Advantages and constraints are discussed...
International Nuclear Information System (INIS)
Dashti, H.G.; Hashemi, B.; Jahromi, S.A.
2011-01-01
Research highlights: → The produced residual stresses in the collector body due to hydraulic expansion method have been compared with explosive method. → The residual stresses were obtained using two methods of FEM and strain gauging tests. → The effect of clearance between tube and collector on the residual stresses was investigated. → The contact stresses between the tube and collector interface were modeled and the required connection strength between tube and collector is estimated based on ASME rules and compared with FE results. - Abstract: Investigations on steam generators failure due to cracking in collector ligaments at perforated parts determined that connection process of the tubes to collector could be one of the main breakdown causes. The stability and strength of tube to collector joint is dependent to the geometry of tube and collector, the joining process and the operational conditions. In this research hydraulic expansion method has been considered as connection method of tube to collector. The Finite Element Method (FEM) was used to simulate the hydraulic expansion process and determine stress condition of the joints. The contact stresses between the tube and collector interface were modeled using contact elements of ANSYS program. Furthermore, the effect of clearance between tube and collector on the residual stresses around of joints was investigated. Some specimens from collector and tube materials were tested at various temperatures and their results were used at rate-independent multi-linear Mises plasticity model for FE analysis. Required connection strength between tube and collector is estimated based on ASME rules and compared with FE results. The results show that the residual tensile stresses could be greatly increased by decreasing of initial clearance. The highest value of residual stresses was observed around of collector holes nevertheless it was considerably lesser than obtained residual stresses in explosive method. The
International Nuclear Information System (INIS)
Hong, Ser Gi; Kim, Jong Woon; Lee, Young Ouk; Kim, Kyo Youn
2010-01-01
The subcell balance methods have been developed for one- and two-dimensional SN transport calculations. In this paper, a linear discontinuous expansion method using sub-cell balances (LDEM-SCB) is developed for neutral particle S N transport calculations in 3D unstructured geometrical problems. At present, this method is applied to the tetrahedral meshes. As the name means, this method assumes the linear distribution of the particle flux in each tetrahedral mesh and uses the balance equations for four sub-cells of each tetrahedral mesh to obtain the equations for the four sub-cell average fluxes which are unknowns. This method was implemented in the computer code MUST (Multi-group Unstructured geometry S N Transport). The numerical tests show that this method gives more robust solution than DFEM (Discontinuous Finite Element Method)
Plume expansion of a laser-induced plasma studied with the particle-in-cell method
DEFF Research Database (Denmark)
Ellegaard, O.; Nedelea, T.; Schou, Jørgen
2002-01-01
energy as well as electron energy. We have estimated the time constant for energy transfer between the electrons and the ions. The scaling of these processes is given by a single parameter determined by the Debye length obtained from the electron density in the plasma outside the surface. (C) 2002......The initial stage of laser-induced plasma plume expansion from a solid in vacuum and the effect of the Coulomb field have been studied. We have performed a one-dimensional numerical calculation by mapping the charge on a computational grid according to the particle-in-cell (PIC) method of Birdsall...... et al. It is assumed that the particle ablation from a surface with a fixed temperature takes place as a pulse, i.e. within a finite period of time. A number of characteristic quantities for the plasma plume are compared with similar data for expansion of neutrals as well as fluid models: Density...
Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models
Murillo, Carol Andrea; Thorel, Luc; Caicedo, Bernardo
2009-06-01
The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge testing is a relevant method to characterize VS near the surface.
Non-linear triangle-based polynomial expansion nodal method for hexagonal core analysis
International Nuclear Information System (INIS)
Cho, Jin Young; Cho, Byung Oh; Joo, Han Gyu; Zee, Sung Qunn; Park, Sang Yong
2000-09-01
This report is for the implementation of triangle-based polynomial expansion nodal (TPEN) method to MASTER code in conjunction with the coarse mesh finite difference(CMFD) framework for hexagonal core design and analysis. The TPEN method is a variation of the higher order polynomial expansion nodal (HOPEN) method that solves the multi-group neutron diffusion equation in the hexagonal-z geometry. In contrast with the HOPEN method, only two-dimensional intranodal expansion is considered in the TPEN method for a triangular domain. The axial dependence of the intranodal flux is incorporated separately here and it is determined by the nodal expansion method (NEM) for a hexagonal node. For the consistency of node geometry of the MASTER code which is based on hexagon, TPEN solver is coded to solve one hexagonal node which is composed of 6 triangular nodes directly with Gauss elimination scheme. To solve the CMFD linear system efficiently, stabilized bi-conjugate gradient(BiCG) algorithm and Wielandt eigenvalue shift method are adopted. And for the construction of the efficient preconditioner of BiCG algorithm, the incomplete LU(ILU) factorization scheme which has been widely used in two-dimensional problems is used. To apply the ILU factorization scheme to three-dimensional problem, a symmetric Gauss-Seidel Factorization scheme is used. In order to examine the accuracy of the TPEN solution, several eigenvalue benchmark problems and two transient problems, i.e., a realistic VVER1000 and VVER440 rod ejection benchmark problems, were solved and compared with respective references. The results of eigenvalue benchmark problems indicate that non-linear TPEN method is very accurate showing less than 15 pcm of eigenvalue errors and 1% of maximum power errors, and fast enough to solve the three-dimensional VVER-440 problem within 5 seconds on 733MHz PENTIUM-III. In the case of the transient problems, the non-linear TPEN method also shows good results within a few minute of
Energy Technology Data Exchange (ETDEWEB)
Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)
2015-12-31
We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.
On-line reconstruction of in-core power distribution by harmonics expansion method
International Nuclear Information System (INIS)
Wang Changhui; Wu Hongchun; Cao Liangzhi; Yang Ping
2011-01-01
Highlights: → A harmonics expansion method for the on-line in-core power reconstruction is proposed. → A harmonics data library is pre-generated off-line and a code named COMS is developed. → Numerical results show that the maximum relative error of the reconstruction is less than 5.5%. → This method has a high computational speed compared to traditional methods. - Abstract: Fixed in-core detectors are most suitable in real-time response to in-core power distributions in pressurized water reactors (PWRs). In this paper, a harmonics expansion method is used to reconstruct the in-core power distribution of a PWR on-line. In this method, the in-core power distribution is expanded by the harmonics of one reference case. The expansion coefficients are calculated using signals provided by fixed in-core detectors. To conserve computing time and improve reconstruction precision, a harmonics data library containing the harmonics of different reference cases is constructed. Upon reconstruction of the in-core power distribution on-line, the two closest reference cases are searched from the harmonics data library to produce expanded harmonics by interpolation. The Unit 1 reactor of DayaBay Nuclear Power Plant (DayaBay NPP) in China is considered for verification. The maximum relative error between the measurement and reconstruction results is less than 5.5%, and the computing time is about 0.53 s for a single reconstruction, indicating that this method is suitable for the on-line monitoring of PWRs.
Modal Ring Method for the Scattering of Electromagnetic Waves
Baumeister, Kenneth J.; Kreider, Kevin L.
1993-01-01
The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.
An Unconditionally Stable Method for Solving the Acoustic Wave Equation
Directory of Open Access Journals (Sweden)
Zhi-Kai Fu
2015-01-01
Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.
Damage detection in composite materials using Lamb wave methods
Kessler, Seth S.; Spearing, S. Mark; Soutis, Constantinos
2002-04-01
Cost-effective and reliable damage detection is critical for the utilization of composite materials. This paper presents part of an experimental and analytical survey of candidate methods for in situ damage detection of composite materials. Experimental results are presented for the application of Lamb wave techniques to quasi-isotropic graphite/epoxy test specimens containing representative damage modes, including delamination, transverse ply cracks and through-holes. Linear wave scans were performed on narrow laminated specimens and sandwich beams with various cores by monitoring the transmitted waves with piezoceramic sensors. Optimal actuator and sensor configurations were devised through experimentation, and various types of driving signal were explored. These experiments provided a procedure capable of easily and accurately determining the time of flight of a Lamb wave pulse between an actuator and sensor. Lamb wave techniques provide more information about damage presence and severity than previously tested methods (frequency response techniques), and provide the possibility of determining damage location due to their local response nature. These methods may prove suitable for structural health monitoring applications since they travel long distances and can be applied with conformable piezoelectric actuators and sensors that require little power.
A robust absorbing layer method for anisotropic seismic wave modeling
Energy Technology Data Exchange (ETDEWEB)
Métivier, L., E-mail: ludovic.metivier@ujf-grenoble.fr [LJK, CNRS, Université de Grenoble, BP 53, 38041 Grenoble Cedex 09 (France); ISTerre, Université de Grenoble I, BP 53, 38041 Grenoble Cedex 09 (France); Brossier, R. [ISTerre, Université de Grenoble I, BP 53, 38041 Grenoble Cedex 09 (France); Labbé, S. [LJK, CNRS, Université de Grenoble, BP 53, 38041 Grenoble Cedex 09 (France); Operto, S. [Géoazur, Université de Nice Sophia-Antipolis, CNRS, IRD, OCA, Villefranche-sur-Mer (France); Virieux, J. [ISTerre, Université de Grenoble I, BP 53, 38041 Grenoble Cedex 09 (France)
2014-12-15
When applied to wave propagation modeling in anisotropic media, Perfectly Matched Layers (PML) exhibit instabilities. Incoming waves are amplified instead of being absorbed. Overcoming this difficulty is crucial as in many seismic imaging applications, accounting accurately for the subsurface anisotropy is mandatory. In this study, we present the SMART layer method as an alternative to PML approach. This method is based on the decomposition of the wavefield into components propagating inward and outward the domain of interest. Only outgoing components are damped. We show that for elastic and acoustic wave propagation in Transverse Isotropic media, the SMART layer is unconditionally dissipative: no amplification of the wavefield is possible. The SMART layers are not perfectly matched, therefore less accurate than conventional PML. However, a reasonable increase of the layer size yields an accuracy similar to PML. Finally, we illustrate that the selective damping strategy on which is based the SMART method can prevent the generation of spurious S-waves by embedding the source in a small zone where only S-waves are damped.
A robust absorbing layer method for anisotropic seismic wave modeling
International Nuclear Information System (INIS)
Métivier, L.; Brossier, R.; Labbé, S.; Operto, S.; Virieux, J.
2014-01-01
When applied to wave propagation modeling in anisotropic media, Perfectly Matched Layers (PML) exhibit instabilities. Incoming waves are amplified instead of being absorbed. Overcoming this difficulty is crucial as in many seismic imaging applications, accounting accurately for the subsurface anisotropy is mandatory. In this study, we present the SMART layer method as an alternative to PML approach. This method is based on the decomposition of the wavefield into components propagating inward and outward the domain of interest. Only outgoing components are damped. We show that for elastic and acoustic wave propagation in Transverse Isotropic media, the SMART layer is unconditionally dissipative: no amplification of the wavefield is possible. The SMART layers are not perfectly matched, therefore less accurate than conventional PML. However, a reasonable increase of the layer size yields an accuracy similar to PML. Finally, we illustrate that the selective damping strategy on which is based the SMART method can prevent the generation of spurious S-waves by embedding the source in a small zone where only S-waves are damped
American Society for Testing and Materials. Philadelphia
1995-01-01
1.1 This test method covers the interferometric determination of linear thermal expansion of premelted glaze frits and fired ceramic whiteware materials at temperatures lower than 1000°C (1830°F). 1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
Separable expansions of the NN t-matrix via exact half off the energy shell methods
International Nuclear Information System (INIS)
Pisent, G.; Amos, K.; Dortmans, P.J.
1992-01-01
Recently a method was proposed by which one can obtain rank 1 (for uncoupled channels) and rank 2 (for coupled channels), energy dependent t-matrix representations which are exact on- and half off of the energy shell. Fully off shell, this representation, though accurate at low energies, is flawed. For uncoupled channels, if the phase shift passes through zero, the representation has a pathology. Two methods which overcome this are investigated one due to Haberzettl which was extended to coupled channels, and the second which is based upon selective combination of the elements of Sturmian expansions. All methods of separation over a range of energies up to 250 MeV for the 1 S 0 and 3 S 1 channels are compared with the Paris interaction. Special attention is paid to the convergence of the higher order Haberzettl expansion and to the comparison of the extended methods for energies around the zero phase shift pathology for the 1 S 0 channel. The method describes well the fully off-shell properties of the t-matrices up to quite high energies, while keeping the rank of the separation as low as possible in order to be used in three or more body calculations. 39 refs., 10 figs
Solution of the agglomerate Brownian coagulation using Taylor-expansion moment method.
Yu, Mingzhou; Lin, Jianzhong
2009-08-01
The newly proposed Taylor-expansion moment method (TEMOM) is extended to solve agglomerate coagulation in the free-molecule regime and in the continuum regime, respectively. The moment equations with respect to fractal dimension are derived based on 3rd Taylor-series expansion technique. The validation of this method is done by comparing its result with the published data at each limited size regime. By comparing with analytical method, sectional method (SM) and quadrature method of moments (QMOMs), this new approach is shown to produce the most efficiency without losing much accuracy. At each limited size regime, the effect of fractal dimension on the decay of particle number and particle size growth is mainly investigated, and especially in the continuum regime the relation of mean diameters of size distributions with different fractal dimensions is first proposed. The agglomerate size distribution is found to be sensitive to the fractal dimension and the initial geometric mean deviation before the self-preserving size distribution is achieved in the continuum regime.
Rupp, K; Jungemann, C; Hong, S-M; Bina, M; Grasser, T; Jüngel, A
The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.
Simulation of the acoustic wave propagation using a meshless method
Directory of Open Access Journals (Sweden)
Bajko J.
2017-01-01
Full Text Available This paper presents numerical simulations of the acoustic wave propagation phenomenon modelled via Linearized Euler equations. A meshless method based on collocation of the strong form of the equation system is adopted. Moreover, the Weighted least squares method is used for local approximation of derivatives as well as stabilization technique in a form of spatial ltering. The accuracy and robustness of the method is examined on several benchmark problems.
Numerical simulation methods for wave propagation through optical waveguides
International Nuclear Information System (INIS)
Sharma, A.
1993-01-01
The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs
Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar
2018-06-01
The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.
Quadratic algebras in the noncommutative integration method of wave equation
International Nuclear Information System (INIS)
Varaksin, O.L.
1995-01-01
The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
Methods of abdominal wall expansion for repair of incisional herniae: a systematic review.
Alam, N N; Narang, S K; Pathak, S; Daniels, I R; Smart, N J
2016-04-01
To systematically review the available literature regarding methods for abdominal wall expansion and compare the outcome of primary fascial closure rates. A systematic search of Pubmed and Embase databases was conducted using the search terms "Abdominal wall hernia", "ventral hernia", "midline hernia", "Botulinum toxin", "botox", "dysport", "progressive preoperative pneumoperitoneum", and "tissue expanders". Study quality was assessed using the Methodological Index for Non-Randomised Studies. 21 of the 105 studies identified met the inclusion criteria. Progressive preoperative pneumoperitoneum (PPP) was performed in 269 patients across 15 studies with primary fascial closure being achieved in 226 (84%). 16 patients had a recurrence (7.2%) and the complication rate was 12% with 2 reported mortalities. There were 4 studies with 14 patients in total undergoing abdominal wall expansion using tissue expanders with a fascial closure rate of 92.9% (n = 13). A recurrence rate of 10.0% (n = 1) was reported with 1 complication and no mortalities. Follow up ranged from 3 to 36 months across the studies. There were 2 studies reporting the use of botulinum toxin with 29 patients in total. A primary fascial closure rate of 100% (n = 29) was demonstrated although a combination of techniques including component separation and Rives-Stoppa repair were used. There were no reported complications related to the use of Botulinum Toxin. However, the short-term follow up in many cases and the lack of routine radiological assessment for recurrence suggests that the recurrence rate has been underestimated. PPP, tissue expanders and Botulinum toxin are safe and feasible methods for abdominal wall expansion prior to incisional hernia repair. In combination with existing techniques for repair, these methods may help provide the crucial extra tissue mobility required to achieve primary closure.
International Nuclear Information System (INIS)
Poursalehi, N.; Zolfaghari, A.; Minuchehr, A.
2013-01-01
Highlights: ► A new adaptive h-refinement approach has been developed for a class of nodal method. ► The resulting system of nodal equations is more amenable to efficient numerical solution. ► The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. ► Spatially adaptive approach greatly enhances the accuracy of the solution. - Abstract: The aim of this work is to develop a spatially adaptive coarse mesh strategy that progressively refines the nodes in appropriate regions of domain to solve the neutron balance equation by zeroth order nodal expansion method. A flux gradient based a posteriori estimation scheme has been utilized for checking the approximate solutions for various nodes. The relative surface net leakage of nodes has been considered as an assessment criterion. In this approach, the core module is called in by adaptive mesh generator to determine gradients of node surfaces flux to explore the possibility of node refinements in appropriate regions and directions of the problem. The benefit of the approach is reducing computational efforts relative to the uniform fine mesh modeling. For this purpose, a computer program ANRNE-2D, Adaptive Node Refinement Nodal Expansion, has been developed to solve neutron diffusion equation using average current nodal expansion method for 2D rectangular geometries. Implementing the adaptive algorithm confirms its superiority in enhancing the accuracy of the solution without using fine nodes throughout the domain and increasing the number of unknown solution. Some well-known benchmarks have been investigated and improvements are reported
Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method
Directory of Open Access Journals (Sweden)
Xiaowang Li
2016-01-01
Full Text Available A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.
The investigation of the non-orthogonal basis expansion method for a three-fermion system
International Nuclear Information System (INIS)
Baoqiu Chen; Kentucky Univ., Lexington, KY
1992-01-01
In this paper, the non-orthogonal basis expansion method has been extended to solve a three-fermion system. The radial wavefunction of such a system is expanded in terms of a non-orthogonal Gaussian basis. All matrix elements of the Hamiltonian, including the central, tensor and spin-orbit potentials are derived in analytical forms. The new method simplifies the three-body system calculations, which are usually rather tedious by other methods. The method can be used to calculate energies for both the ground state and low excited states and has been used further to investigate the other nuclear properties of a three-body system such as Λ 3 H. (Author)
Energy Technology Data Exchange (ETDEWEB)
Yu, Xiaojiang, E-mail: slsyxj@nus.edu.sg; Diao, Caozheng; Breese, Mark B. H. [Singapore Synchrotron Light Source, National University of Singapore, Singapore 117603 (Singapore)
2016-07-27
An aberration calculation method which was developed by Lu [1] can treat individual aberration term precisely. Spectral aberration is the linear sum of these aberration terms, and the aberrations of multi-element systems also can be calculated correctly when the stretching ratio, defined herein, is unity. Evaluation of focusing mirror-grating systems which are optimized according to Lu’s method, along with the Light Path Function (LPF) and the Spot Diagram method (SD) are discussed to confirm the advantage of Lu’s methodology. Lu’s aberration terms are derived from a precise wave-front treatment, whereas the terms of the power series expansion of the light path function do not yield an accurate sum of the aberrations. Moreover, Lu’s aberration terms can be individually optimized. This is not possible with the analytical spot diagram formulae.
International Nuclear Information System (INIS)
Kaschner, R.; Graefenstein, J.; Ziesche, P.
1988-12-01
From the local momentum balance using density functional theory an expression for the local quantum-mechanical stress tensor (or stress field) σ(r) of non-relativistic Coulomb systems is found out within the Thomas-Fermi approximation and its generalizations including gradient expansion method. As an illustration the stress field σ(r) is calculated for the jellium model of the interface K-Cs, containing especially the adhesive force between the two half-space jellia. (author). 23 refs, 1 fig
International Nuclear Information System (INIS)
Zhou, Xiafeng; Guo, Jiong; Li, Fu
2015-01-01
Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of
Energy Technology Data Exchange (ETDEWEB)
Zhou, Xiafeng, E-mail: zhou-xf11@mails.tsinghua.edu.cn; Guo, Jiong, E-mail: guojiong12@tsinghua.edu.cn; Li, Fu, E-mail: lifu@tsinghua.edu.cn
2015-12-15
Highlights: • NEMs are innovatively applied to solve convection diffusion equation. • Stability, accuracy and numerical diffusion for NEM are analyzed for the first time. • Stability and numerical diffusion depend on the NEM expansion order and its parity. • NEMs have higher accuracy than both second order upwind and QUICK scheme. • NEMs with different expansion orders are integrated into a unified discrete form. - Abstract: The traditional finite difference method or finite volume method (FDM or FVM) is used for HTGR thermal-hydraulic calculation at present. However, both FDM and FVM require the fine mesh sizes to achieve the desired precision and thus result in a limited efficiency. Therefore, a more efficient and accurate numerical method needs to be developed. Nodal expansion method (NEM) can achieve high accuracy even on the coarse meshes in the reactor physics analysis so that the number of spatial meshes and computational cost can be largely decreased. Because of higher efficiency and accuracy, NEM can be innovatively applied to thermal-hydraulic calculation. In the paper, NEMs with different orders of basis functions are successfully developed and applied to multi-dimensional steady convection diffusion equation. Numerical results show that NEMs with three or higher order basis functions can track the reference solutions very well and are superior to second order upwind scheme and QUICK scheme. However, the false diffusion and unphysical oscillation behavior are discovered for NEMs. To explain the reasons for the above-mentioned behaviors, the stability, accuracy and numerical diffusion properties of NEM are analyzed by the Fourier analysis, and by comparing with exact solutions of difference and differential equation. The theoretical analysis results show that the accuracy of NEM increases with the expansion order. However, the stability and numerical diffusion properties depend not only on the order of basis functions but also on the parity of
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.
Analysis of Different Methods for Wave Generation and Absorption in a CFD-Based Numerical Wave Tank
Directory of Open Access Journals (Sweden)
Adria Moreno Miquel
2018-06-01
Full Text Available In this paper, the performance of different wave generation and absorption methods in computational fluid dynamics (CFD-based numerical wave tanks (NWTs is analyzed. The open-source CFD code REEF3D is used, which solves the Reynolds-averaged Navier–Stokes (RANS equations to simulate two-phase flow problems. The water surface is computed with the level set method (LSM, and turbulence is modeled with the k-ω model. The NWT includes different methods to generate and absorb waves: the relaxation method, the Dirichlet-type method and active wave absorption. A sensitivity analysis has been conducted in order to quantify and compare the differences in terms of absorption quality between these methods. A reflection analysis based on an arbitrary number of wave gauges has been adopted to conduct the study. Tests include reflection analysis of linear, second- and fifth-order Stokes waves, solitary waves, cnoidal waves and irregular waves generated in an NWT. Wave breaking over a sloping bed and wave forces on a vertical cylinder are calculated, and the influence of the reflections on the wave breaking location and the wave forces on the cylinder is investigated. In addition, a comparison with another open-source CFD code, OpenFOAM, has been carried out based on published results. Some differences in the calculated quantities depending on the wave generation and absorption method have been observed. The active wave absorption method is seen to be more efficient for long waves, whereas the relaxation method performs better for shorter waves. The relaxation method-based numerical beach generally results in lower reflected waves in the wave tank for most of the cases simulated in this study. The comparably better performance of the relaxation method comes at the cost of larger computational requirements due to the relaxation zones that have to be included in the domain. The reflections in the NWT in REEF3D are generally lower than the published results for
Linear density response function in the projector augmented wave method
DEFF Research Database (Denmark)
Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel
2011-01-01
We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...
Directory of Open Access Journals (Sweden)
V. S. Zarubin
2015-01-01
Full Text Available The rational use of composites as structural materials, while perceiving the thermal and mechanical loads, to a large extent determined by their thermoelastic properties. From the presented review of works devoted to the analysis of thermoelastic characteristics of composites, it follows that the problem of estimating these characteristics is important. Among the thermoelastic properties of composites occupies an important place its temperature coefficient of linear expansion.Along with fiber composites are widely used in the technique of dispersion hardening composites, in which the role of inclusions carry particles of high-strength and high-modulus materials, including nanostructured elements. Typically, the dispersed particles have similar dimensions in all directions, which allows the shape of the particles in the first approximation the ball.In an article for the composite with isotropic spherical inclusions of a plurality of different materials by the self-produced design formulas relating the temperature coefficient of linear expansion with volume concentration of inclusions and their thermoelastic characteristics, as well as the thermoelastic properties of the matrix of the composite. Feature of the method is the self-accountability thermomechanical interaction of a single inclusion or matrix particles with a homogeneous isotropic medium having the desired temperature coefficient of linear expansion. Averaging over the volume of the composite arising from such interaction perturbation strain and stress in the inclusions and the matrix particles and makes it possible to obtain such calculation formulas.For the validation of the results of calculations of the temperature coefficient of linear expansion of the composite of this type used two-sided estimates that are based on the dual variational formulation of linear thermoelasticity problem in an inhomogeneous solid containing two alternative functional (such as Lagrange and Castigliano
Rapid maxillary expansion effects: An alternative assessment method by means of cone-beam tomography
Directory of Open Access Journals (Sweden)
Camilo Aquino Melgaço
2014-10-01
Full Text Available INTRODUCTION: This study aims to develop a method to assess the changes in palatal and lingual cross-sectional areas in patients submitted to rapid maxillary expansion (RME. METHODS: The sample comprised 31 Class I malocclusion individuals submitted to RME and divided into two groups treated with Haas (17 patients and Hyrax (14 patients expanders. Cone-beam computed tomography scans were acquired at T0 (before expansion and T1 (six months after screw stabilization. Maxillary and mandibular cross-sectional areas were assessed at first permanent molars and first premolars regions and compared at T0 and T1. Mandibular occlusal area was also analyzed. RESULTS: Maxillary cross-sectional areas increased in 56.18 mm2 and 44.32 mm2 for the posterior and anterior regions. These values were smaller for the mandible, representing augmentation of 40.32 mm2 and 39.91 mm2 for posterior and anterior sections. No differences were found when comparing both expanders. Mandibular occlusal area increased 43.99mm2 and mandibular incisors proclined. Increments of 1.74 mm and 1.7 mm occurred in mandibular intermolar and interpremolar distances. These same distances presented increments of 5.5 mm and 5.57 mm for the maxillary arch. CONCLUSION: Occlusal and cross-sectional areas increased significantly after RME. The method described seems to be reliable and precise to assess intraoral area changes.
Comparison of Transmission Line Methods for Surface Acoustic Wave Modeling
Wilson, William; Atkinson, Gary
2009-01-01
Surface Acoustic Wave (SAW) technology is low cost, rugged, lightweight, extremely low power and can be used to develop passive wireless sensors. For these reasons, NASA is investigating the use of SAW technology for Integrated Vehicle Health Monitoring (IVHM) of aerospace structures. To facilitate rapid prototyping of passive SAW sensors for aerospace applications, SAW models have been developed. This paper reports on the comparison of three methods of modeling SAWs. The three models are the Impulse Response Method (a first order model), and two second order matrix methods; the conventional matrix approach, and a modified matrix approach that is extended to include internal finger reflections. The second order models are based upon matrices that were originally developed for analyzing microwave circuits using transmission line theory. Results from the models are presented with measured data from devices. Keywords: Surface Acoustic Wave, SAW, transmission line models, Impulse Response Method.
Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet
Groves, M. D.; Nilsson, D. V.
2018-04-01
This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general (nonlinear) magnetisation law, is subject to an azimuthal magnetic field generated by an electric current flowing along the rod. The ferrohydrodynamic problem for axisymmetric travelling waves is formulated as an infinite-dimensional Hamiltonian system in which the axial direction is the time-like variable. A centre-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom, and homoclinic solutions to the reduced system, which correspond to solitary waves, are detected by dynamical-systems methods.
International Nuclear Information System (INIS)
Ahmadigorji, Masoud; Amjady, Nima
2014-01-01
Highlights: • A new dynamic distribution network expansion planning model is presented. • A Binary Enhanced Particle Swarm Optimization (BEPSO) algorithm is proposed. • A Modified Differential Evolution (MDE) algorithm is proposed. • A new bi-level optimization approach composed of BEPSO and MDE is presented. • The effectiveness of the proposed optimization approach is extensively illustrated. - Abstract: Reconstruction in the power system and appearing of new technologies for generation capacity of electrical energy has led to significant innovation in Distribution Network Expansion Planning (DNEP). Distributed Generation (DG) includes the application of small/medium generation units located in power distribution networks and/or near the load centers. Appropriate utilization of DG can affect the various technical and operational indices of the distribution network such as the feeder loading, energy losses and voltage profile. In addition, application of DG in proper size is an essential tool to achieve the DG maximum potential benefits. In this paper, a time-based (dynamic) model for DNEP is proposed to determine the optimal size, location and installation year of DG in distribution system. Also, in this model, the Optimal Power Flow (OPF) is exerted to determine the optimal generation of DGs for every potential solution in order to minimize the investment and operation costs following the load growth in a specified planning period. Besides, the reinforcement requirements of existing distribution feeders are considered, simultaneously. The proposed optimization problem is solved by the combination of evolutionary methods of a new Binary Enhanced Particle Swarm Optimization (BEPSO) and Modified Differential Evolution (MDE) to find the optimal expansion strategy and solve OPF, respectively. The proposed planning approach is applied to two typical primary distribution networks and compared with several other methods. These comparisons illustrate the
A design of a mode converter for electron cyclotron heating by the method of normal mode expansion
International Nuclear Information System (INIS)
Hoshino, Katsumichi; Kawashima, Hisato; Hata, Kenichiro; Yamamoto, Takumi
1983-09-01
Mode conversion of electromagnetic wave propagating in the over-size circular waveguide is attained by giving a periodical perturbation in the guide wall. Mode coupling equation is expressed by ''generalized telegraphist's equations'' which are derived from the Maxwell's equations using a normal mode expansion. A computer code to solve the coupling equations is developed and mode amplitude, conversion efficiency, etc. of a particular type of mode converter for the 60 GHz electron cyclotron heating are obtained. (author)
The Nodal Polynomial Expansion method to solve the multigroup diffusion equations
International Nuclear Information System (INIS)
Ribeiro, R.D.M.
1983-03-01
The methodology of the solutions of the multigroup diffusion equations and uses the Nodal Polynomial Expansion Method is covered. The EPON code was developed based upon the above mentioned method for stationary state, rectangular geometry, one-dimensional or two-dimensional and for one or two energy groups. Then, one can study some effects such as the influence of the baffle on the thermal flux by calculating the flux and power distribution in nuclear reactors. Furthermore, a comparative study with other programs which use Finite Difference (CITATION and PDQ5) and Finite Element (CHD and FEMB) Methods was undertaken. As a result, the coherence, feasibility, speed and accuracy of the methodology used were demonstrated. (Author) [pt
International Nuclear Information System (INIS)
Bogdanova, N.B.; Todorov, S.T.; Ososkov, G.A.
2015-01-01
Orthonormal polynomial expansion method (OPEM) is applied to the data obtained by the method of energy spectra to the liquid of the biomass of wheat in the case when herbicides are used. Since the biomass of a biological object contains liquid composed mainly of water, the method of water spectra is applicable to this case as well. For comparison, the similar data obtained from control sample consisting of wheat liquid without the application of herbicides are shown. The total variance OPEM is involved including errors in both dependent and independent variables. Special criteria are used for evaluating the optimal polynomial degree and the number of iterations. The presented numerical results show good agreement with the experimental data. The developed analysis frame is of interest for future analysis in theoretical ecology.
Directory of Open Access Journals (Sweden)
Sun Huan
2016-01-01
Full Text Available In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.
A tuning method for nonuniform traveling-wave accelerating structures
International Nuclear Information System (INIS)
Gong Cunkui; Zheng Shuxin; Shao Jiahang; Jia Xiaoyu; Chen Huaibi
2013-01-01
The tuning method of uniform traveling-wave structures based on non-resonant perturbation field distribution measurement has been widely used in tuning both constant-impedance and constant-gradient structures. In this paper, the method of tuning nonuniform structures is proposed on the basis of the above theory. The internal reflection coefficient of each cell is obtained from analyzing the normalized voltage distribution. A numerical simulation of tuning process according to the coupled cavity chain theory has been done and the result shows each cell is in right phase advance after tuning. The method will be used in the tuning of a disk-loaded traveling-wave structure being developed at the Accelerator Laboratory, Tsinghua University. (authors)
Microstrip natural wave spectrum mathematical model using partial inversion method
International Nuclear Information System (INIS)
Pogarsky, S.A.; Litvinenko, L.N.; Prosvirnin, S.L.
1995-01-01
It is generally agreed that both microstrip lines itself and different discontinuities based on microstrips are the most difficult problem for accurate electrodynamic analysis. Over the last years much has been published about principles and accurate (or full wave) methods of microstrip lines investigations. The growing interest for this problem may be explained by the microstrip application in the millimeter-wave range for purpose of realizing interconnects and a variety of passive components. At these higher operating rating frequencies accurate component modeling becomes more critical. A creation, examination and experimental verification of the accurate method for planar electrodynamical structures natural wave spectrum investigations are the objects of this manuscript. The moment method with partial inversion operator method using may be considered as a basical way for solving this problem. This method is outlook for accurate analysis of different planar discontinuities in microstrip: such as step discontinuities, microstrip turns, Y- and X-junctions and etc., substrate space steps dielectric constants and other anisotropy types
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a
S-wave velocity measurements along levees in New Orleans using passive surface wave methods
Hayashi, K.; Lorenzo, J. M.; Craig, M. S.; Gostic, A.
2017-12-01
In order to develop non-invasive methods for levee inspection, geophysical investigations were carried out at four sites along levees in the New Orleans area: 17th Street Canal, London Avenue Canal, Marrero Levee, and Industrial Canal. Three of the four sites sustained damage from Hurricane Katrina in 2005 and have since been rebuilt. The geophysical methods used include active and passive surface wave methods, and capacitively coupled resistivity. This paper summarizes the acquisition and analysis of the 1D and 2D passive surface wave data. Twelve wireless seismic data acquisition units with 2 Hz vertical component geophones were used to record data. Each unit includes a GPS receiver so that all units can be synchronized over any distance without cables. The 1D passive method used L shaped arrays of three different sizes with geophone spacing ranging from 5 to 340 m. Ten minutes to one hour of ambient noise was recorded with each array, and total data acquisition took approximately two hours at each site. The 2D method used a linear array with a geophone spacing of 5m. Four geophones were moved forward every 10 minutes along 400 1000 m length lines. Data acquisition took several hours for each line. Recorded ambient noise was processed using the spatial autocorrelation method and clear dispersion curves were obtained at all sites (Figure 1a). Minimum frequencies ranged from 0.4 to 0.7 Hz and maximum frequencies ranged from 10 to 30 Hz depending on the site. Non-linear inversion was performed and 1D and 2D S-wave velocity models were obtained. The 1D method penetrated to depths ranging from 200 to 500 m depending on the site (Figure 1b). The 2D method penetrated to a depth of 40 60 m and provided 400 1000 m cross sections along the levees (Figure 2). The interpretation focused on identifying zones beneath the levees or canal walls having low S-wave velocities corresponding to saturated, unconsolidated sands, or low-rigidity clays. Resultant S-wave velocity profiles
Directory of Open Access Journals (Sweden)
A. D. Chernyshov
2017-01-01
Full Text Available The brief presentation of the method of fast expansions is given to solve nonlinear differential equations. Application rules of the operator of fast expansions are specified for solving differential equations. According to the method of fast expansions, an unknown function can be represented as the sum of the boundary function and Fourier series sines and cosines for one variable. The special construction of the boundary functions leads to reasonably fast convergence of the Fourier series, so that for engineering calculations, it is sufficient to consider only the first three members. The method is applicable both to linear and nonlinear integro-differential systems. By means of applying the method of fast expansions to nonlinear Navier-Stokes equations the problem is reduced to a closed system of ordinary differential equations, which solution doesn't represent special difficulties. We can reapply the method of fast expansions to the resulting system of differential equations and reduce the original problem to a system of algebraic equations. If the problem is n-dimensional, then after n-fold application of the method of fast expansions the problem will be reduced to a closed algebraic system. Finally, we obtain an analytic-form solution of complicated boundary value problem in partial derivatives. The flow of an incompressible viscous fluid of Navier–Stokes is considered in a curvilinear pipe. The problem is reduced to solving a closed system of ordinary differential equations with boundary conditions by the method of fast expansions. The article considers peculiarities of finding the coefficients of boundary functions and Fourier coefficients for the zero-order and first-order operators of fast expansions. Obtaining the analytic-form solution is of great interest, because it allows to analyze and to investigate the influence of various factors on the properties of the viscous fluid in specific cases.
Towards automatic global error control: Computable weak error expansion for the tau-leap method
Karlsson, Peer Jesper; Tempone, Raul
2011-01-01
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error approximations are the basis for adaptive algorithms, a fundamental tool for numerical simulation of both deterministic and stochastic dynamical systems. These pure jump processes are simulated either by the tau-leap method, or by exact simulation, also referred to as dynamic Monte Carlo, the Gillespie Algorithm or the Stochastic Simulation Slgorithm. Two types of estimates are presented: an a priori estimate for the relative error that gives a comparison between the work for the two methods depending on the propensity regime, and an a posteriori estimate with computable leading order term. © de Gruyter 2011.
Pellet by pellet neutron flux calculations coupled with nodal expansion method
International Nuclear Information System (INIS)
Aldo, Dall'Osso
2003-01-01
We present a technique whose aim is to replace 2-dimensional pin by pin de-homogenization, currently done in core reactor calculations with the nodal expansion method (NEM), by a 3-dimensional finite difference diffusion calculation. This fine calculation is performed as a zoom in each node taking as boundary conditions the results of the NEM calculations. The size of fine mesh is of the order of a fuel pellet. The coupling between fine and NEM calculations is realised by an albedo like boundary condition. Some examples are presented showing fine neutron flux shape near control rods or assembly grids. Other fine flux behaviour as the thermal flux rise in the fuel near the reflector is emphasised. In general the results show the interest of the method in conditions where the separability of radial and axial directions is not granted. (author)
Validation of the activity expansion method with ultrahigh pressure shock equations of state
International Nuclear Information System (INIS)
Rogers, F.J.; Young, D.A.
1997-01-01
Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. copyright 1997 The American Physical Society
Validation of the activity expansion method with ultrahigh pressure shock equations of state
Rogers, Forrest J.; Young, David A.
1997-11-01
Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter.
Validation of the activity expansion method with ultrahigh pressure shock equations of state
Energy Technology Data Exchange (ETDEWEB)
Rogers, F.J.; Young, D.A. [Physics Department, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94550 (United States)
1997-11-01
Laser shock experiments have recently been used to measure the equation of state (EOS) of matter in the ultrahigh pressure region between condensed matter and a weakly coupled plasma. Some ultrahigh pressure data from nuclear-generated shocks are also available. Matter at these conditions has proven very difficult to treat theoretically. The many-body activity expansion method (ACTEX) has been used for some time to calculate EOS and opacity data in this region, for use in modeling inertial confinement fusion and stellar interior plasmas. In the present work, we carry out a detailed comparison with the available experimental data in order to validate the method. The agreement is good, showing that ACTEX adequately describes strongly shocked matter. {copyright} {ital 1997} {ital The American Physical Society}
Full wave simulation of waves in ECRIS plasmas based on the finite element method
Energy Technology Data Exchange (ETDEWEB)
Torrisi, G. [INFN - Laboratori Nazionali del Sud, via S. Sofia 62, 95123, Catania, Italy and Università Mediterranea di Reggio Calabria, Dipartimento di Ingegneria dell' Informazione, delle Infrastrutture e dell' Energia Sostenibile (DIIES), Via Graziella, I (Italy); Mascali, D.; Neri, L.; Castro, G.; Patti, G.; Celona, L.; Gammino, S.; Ciavola, G. [INFN - Laboratori Nazionali del Sud, via S. Sofia 62, 95123, Catania (Italy); Di Donato, L. [Università degli Studi di Catania, Dipartimento di Ingegneria Elettrica Elettronica ed Informatica (DIEEI), Viale Andrea Doria 6, 95125 Catania (Italy); Sorbello, G. [INFN - Laboratori Nazionali del Sud, via S. Sofia 62, 95123, Catania, Italy and Università degli Studi di Catania, Dipartimento di Ingegneria Elettrica Elettronica ed Informatica (DIEEI), Viale Andrea Doria 6, 95125 Catania (Italy); Isernia, T. [Università Mediterranea di Reggio Calabria, Dipartimento di Ingegneria dell' Informazione, delle Infrastrutture e dell' Energia Sostenibile (DIIES), Via Graziella, I-89100 Reggio Calabria (Italy)
2014-02-12
This paper describes the modeling and the full wave numerical simulation of electromagnetic waves propagation and absorption in an anisotropic magnetized plasma filling the resonant cavity of an electron cyclotron resonance ion source (ECRIS). The model assumes inhomogeneous, dispersive and tensorial constitutive relations. Maxwell's equations are solved by the finite element method (FEM), using the COMSOL Multiphysics{sup ®} suite. All the relevant details have been considered in the model, including the non uniform external magnetostatic field used for plasma confinement, the local electron density profile resulting in the full-3D non uniform magnetized plasma complex dielectric tensor. The more accurate plasma simulations clearly show the importance of cavity effect on wave propagation and the effects of a resonant surface. These studies are the pillars for an improved ECRIS plasma modeling, that is mandatory to optimize the ion source output (beam intensity distribution and charge state, especially). Any new project concerning the advanced ECRIS design will take benefit by an adequate modeling of self-consistent wave absorption simulations.
Baron, Frédéric; Ruggeri, Annalisa; Nagler, Arnon
2016-03-01
More than 40,000 unrelated cord blood transplantations (UCBT) have been performed worldwide as treatment for patients with malignant or non-malignant life threatening hematologic disorders. However, low absolute numbers of hematopoietic stem and progenitor cells (HSPCs) within a single cord blood unit has remained a limiting factor for this transplantation modality, particularly in adult recipients. Further, because UCB contains low numbers of mostly naïve T cells, immune recovery after UCBT is slow, predisposing patients to severe infections. Other causes of UCBT failure has included graft-versus-host disease (GVHD) and relapse of the underlying disease. In this article, we first review the current landscape of cord blood engineering aimed at improving engraftment. This includes approaches of UCB-HSPCs expansion and methods aimed at improving UCB-HSCPs homing. We then discuss recent approaches of cord blood engineering developed to prevent infection [generation of multivirus-specific cytotoxic T cells (VSTs) from UCB], relapse [transduction of UCB-T cells with tumor-specific chimeric receptor antigens (CARs)] and GVHD (expansion of regulatory T cells from UCB). Although many of these techniques of UCB engineering remain currently technically challenging and expensive, they are likely to revolutionize the field of UCBT in the next decades.
Integral Equation Methods for Electromagnetic and Elastic Waves
Chew, Weng; Hu, Bin
2008-01-01
Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral eq
International Nuclear Information System (INIS)
Sabundjian, Gaiane
1999-01-01
This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)
International Nuclear Information System (INIS)
Andriyash, A. V.; Astashkin, M. V.; Baranov, V. K.; Golubinskii, A. G.; Irinichev, D. A.; Kondrat’ev, A. N.; Kuratov, S. E.; Mazanov, V. A.; Rogozkin, D. B.; Stepushkin, S. N.; Khatunkin, V. Yu.
2016-01-01
The results of optoheterodyne Doppler measurements of the ballistic expansion of the products of surface destruction under shock-wave loading are presented. The possibility of determining the physical characteristics of a rapidly flying dust cloud, including the microparticle velocities, the microparticle sizes, and the areal density of the dust cloud, is shown. A compact stand for performing experiments on shock-wave loading of metallic samples is described. Shock-wave loading is performed by a 100-µm-thick tantalum flyer plate accelerated to a velocity of 2.8 km/s. As the samples, lead plates having various thicknesses and the same surface roughness are used. At a shock-wave pressure of 31.5 GPa, the destruction products are solid microparticles about 50 µm in size. At a pressure of 42 and 88 GPa, a liquid-drop dust cloud with a particle size of 10–15 µm is formed. To interpret the spectral data on the optoheterodyne Doppler measurements of the expansion of the surface destruction products (spalled fragments, dust microparticles), a transport equation for the function of mutual coherence of a multiply scattered field is used. The Doppler spectra of a backscattered signal are calculated with the model developed for the dust cloud that appears when a shock wave reaches the sample surface at the parameters that are typical of an experimental situation. Qualitative changes are found in the spectra, depending on the optical thickness of the dust cloud. The obtained theoretical results are in agreement with the experimental data.
Energy Technology Data Exchange (ETDEWEB)
Andriyash, A. V. [All-Russia Research Institute of Automatics (Russian Federation); Astashkin, M. V.; Baranov, V. K.; Golubinskii, A. G.; Irinichev, D. A. [Russian Federal Nuclear Center, All-Russia Research Institute of Experimental Physics (VNIIEF) (Russian Federation); Kondrat’ev, A. N., E-mail: an.kondratev@physics.msu.ru; Kuratov, S. E. [All-Russia Research Institute of Automatics (Russian Federation); Mazanov, V. A. [Russian Federal Nuclear Center, All-Russia Research Institute of Experimental Physics (VNIIEF) (Russian Federation); Rogozkin, D. B. [All-Russia Research Institute of Automatics (Russian Federation); Stepushkin, S. N.; Khatunkin, V. Yu. [Russian Federal Nuclear Center, All-Russia Research Institute of Experimental Physics (VNIIEF) (Russian Federation)
2016-06-15
The results of optoheterodyne Doppler measurements of the ballistic expansion of the products of surface destruction under shock-wave loading are presented. The possibility of determining the physical characteristics of a rapidly flying dust cloud, including the microparticle velocities, the microparticle sizes, and the areal density of the dust cloud, is shown. A compact stand for performing experiments on shock-wave loading of metallic samples is described. Shock-wave loading is performed by a 100-µm-thick tantalum flyer plate accelerated to a velocity of 2.8 km/s. As the samples, lead plates having various thicknesses and the same surface roughness are used. At a shock-wave pressure of 31.5 GPa, the destruction products are solid microparticles about 50 µm in size. At a pressure of 42 and 88 GPa, a liquid-drop dust cloud with a particle size of 10–15 µm is formed. To interpret the spectral data on the optoheterodyne Doppler measurements of the expansion of the surface destruction products (spalled fragments, dust microparticles), a transport equation for the function of mutual coherence of a multiply scattered field is used. The Doppler spectra of a backscattered signal are calculated with the model developed for the dust cloud that appears when a shock wave reaches the sample surface at the parameters that are typical of an experimental situation. Qualitative changes are found in the spectra, depending on the optical thickness of the dust cloud. The obtained theoretical results are in agreement with the experimental data.
Crosnier de Bellaistre, C.; Trefzger, C.; Aspect, A.; Georges, A.; Sanchez-Palencia, L.
2018-01-01
We study numerically the expansion dynamics of an initially confined quantum wave packet in the presence of a disordered potential and a uniform bias force. For white-noise disorder, we find that the wave packet develops asymmetric algebraic tails for any ratio of the force to the disorder strength. The exponent of the algebraic tails decays smoothly with that ratio and no evidence of a critical behavior on the wave density profile is found. Algebraic localization features a series of critical values of the force-to-disorder strength where the m th position moment of the wave packet diverges. Below the critical value for the m th moment, we find fair agreement between the asymptotic long-time value of the m th moment and the predictions of diagrammatic calculations. Above it, we find that the m th moment grows algebraically in time. For correlated disorder, we find evidence of systematic delocalization, irrespective to the model of disorder. More precisely, we find a two-step dynamics, where both the center-of-mass position and the width of the wave packet show transient localization, similar to the white-noise case, at short time and delocalization at sufficiently long time. This correlation-induced delocalization is interpreted as due to the decrease of the effective de Broglie wavelength, which lowers the effective strength of the disorder in the presence of finite-range correlations.
Nolinear stability analysis of nuclear reactors : expansion methods for stability domains
International Nuclear Information System (INIS)
Yang, Chae Yong
1992-02-01
Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are developed in this study: an improved Chang and Thorp's method based on expansion of a Lyapunov function and a new method based on expansion of any positive definite function. The methods are established on the concept of stability definitions of Lyapunov itself. The first method provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions in order to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most dynamic systems are stiff. The second method (new method) requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for stiff systems. The methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared. A reactor feedback model for a pressurized water reactor (PWR) considering fuel and moderator temperature effects is developed and the nonlinear stability regions are estimated for the various values of design parameters by using the new method. The steady-state properties of the nonlinear reactor system are analyzed via bifurcation theory. The analysis of nonlinear phenomena is carried out for the various forms of reactivity feedback coefficients that are both temperature- (or power-) independent and dependent. If one of two temperature coefficients is positive, unstable limit cycles or multiplicity of the steady-state solutions appear when the other temperature coefficient exceeds a certain critical value. As an example, even though the fuel temperature coefficient is negative, if the moderator temperature
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
The generalized (G′/G)-expansion method; Burgers equation; Fisher's equation; ... the travelling wave solutions plays an important role in nonlinear sciences. ... Burgers, Fisher, Huxley equations and combined forms of these equations will ...
A new diffusion nodal method based on analytic basis function expansion
International Nuclear Information System (INIS)
Noh, J.M.; Cho, N.Z.
1993-01-01
The transverse integration procedure commonly used in most advanced nodal methods results in some limitations. The first is that the transverse leakage term that appears in the transverse integration procedure must be appropriately approximated. In most advanced nodal methods, this term is expanded in a quadratic polynomial. The second arises when reconstructing the pinwise flux distribution within a node. The available one-dimensional flux shapes from nodal calculation in each spatial direction cannot be used directly in the flux reconstruction. Finally, the transverse leakage defined for a hexagonal node becomes so complicated as not to be easily handled and contains nonphysical singular terms. In this paper, a new nodal method called the analytic function expansion nodal (AFEN) method is described for both the rectangular geometry and the hexagonal geometry in order to overcome these limitations. This method does not solve the transverse-integrated one-dimensional diffusion equations but instead solves directly the original multidimensional diffusion equation within a node. This is a accomplished by expanding the solution (or the intranodal homogeneous flux distribution) in terms of nonseparable analytic basis functions satisfying the diffusion equation at any point in the node
International Nuclear Information System (INIS)
Omarov, O. A.; Kurbanismailov, V. S.; Arslanbekov, M. A.; Gadzhiev, M. Kh.; Ragimkhanov, G. B.; Al-Shatravi, Ali J. G.
2012-01-01
The expansion of the cathode spot and the generation of shock waves during the formation and development of a pulsed volume discharge in atmospheric-pressure helium were studied by analyzing the emission spectra of the cathode plasma and the spatiotemporal behavior of the plasma glow. The transition of a diffuse volume discharge in a centimeter-long gap into a high-current diffuse mode when the gas pressure increased from 1 to 5 atm and the applied voltage rose from the statistical breakdown voltage to a 100% overvoltage was investigated. Analytical expressions for the radius of the cathode spot and its expansion velocity obtained in the framework of a spherically symmetric model agree satisfactorily with the experimental data.
High order spatial expansion for the method of characteristics applied to 3-D geometries
International Nuclear Information System (INIS)
Naymeh, L.; Masiello, E.; Sanchez, R.
2013-01-01
The method of characteristics is an efficient and flexible technique to solve the neutron transport equation and has been extensively used in two-dimensional calculations because it permits to deal with complex geometries. However, because of a very fast increase in storage requirements and number of floating operations, its direct application to three-dimensional routine transport calculations it is not still possible. In this work we introduce and analyze several modifications aimed to reduce memory requirements and to diminish the computing burden. We explore high-order spatial approximation, the use of intermediary trajectory-dependent flux expansions and the possibility of dynamic trajectory reconstruction from local tracking for typed subdomains. (authors)
Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.
Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko
2014-04-01
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.
International Nuclear Information System (INIS)
Shang Yadong
2008-01-01
The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions
International Nuclear Information System (INIS)
Wang Baodong; Song Lina; Zhang Hongqing
2007-01-01
In this paper, we present a new elliptic equation rational expansion method to uniformly construct a series of exact solutions for nonlinear partial differential equations. As an application of the method, we choose the (2 + 1)-dimensional Burgers equation to illustrate the method and successfully obtain some new and more general solutions
Investigation on the reliability of expansion joint for piping with probabilistic method
International Nuclear Information System (INIS)
Ishii, Y.; Kambe, M.
1980-01-01
The reduction of the plant size is necessitated as one of the major targets in LMFBR design. Usually, piping work system is extensively used to absorb thermal expansion between two components anywhere. Besides above, expansion joint for piping seems to be attractive lately for the same object. This paper describes the significance of expansion joint with multiple boundaries, breakdown probability of expansion joint assembly and partly the bellows by introducing several hypothetical conditions in connection with piping. Also, an importance of in-service inspection (ISI) for expansion joint was discussed using a comparative table and probabilities on reliability from partly broken to full penetration. In conclusion, the expansion joint with ISI should be manufactured with excellent reliability in order to cope with piping work system; several conditions of the practical application for piping systems are suggested. (author)
Investigation on the reliability of expansion joint for piping with probabilistic method
Energy Technology Data Exchange (ETDEWEB)
Ishii, Y; Kambe, M
1980-02-01
The reduction of the plant size is necessitated as one of the major targets in LMFBR design. Usually, piping work system is extensively used to absorb thermal expansion between two components anywhere. Besides above, expansion joint for piping seems to be attractive lately for the same object. This paper describes the significance of expansion joint with multiple boundaries, breakdown probability of expansion joint assembly and partly the bellows by introducing several hypothetical conditions in connection with piping. Also, an importance of in-service inspection (ISI) for expansion joint was discussed using a comparative table and probabilities on reliability from partly broken to full penetration. In conclusion, the expansion joint with ISI should be manufactured with excellent reliability in order to cope with piping work system; several conditions of the practical application for piping systems are suggested. (author)
Investigation on the reliability of expansion joint for piping with probabilistic method
International Nuclear Information System (INIS)
Ishii, Yoichiro; Kambe, Mitsuru.
1979-11-01
The reduction of the plant size if necessitated as one of the major target in LMFBR design. Usually, piping work system is extensively used to absorb thermal expansion between two components anywhere. Besides above, expansion joint for piping seems to be attractive lately for the same object. This paper describes about the significance of expansion joint with multiple boundaries, breakdown probability of expansion joint assembly and partly the bellows by introducing several hypothetical conditions in connection with piping. Also, an importance of inservice inspection (ISI) for expansion joint was discussed using by comparative table and probabilities on reliability from partly broken to full penetration. In the conclusion, the expansion joint with ISI should be manufactured with excellent reliability in order to cope with piping work system, and several conditions of the practical application for piping systems are suggested. (author)
Methods for use in detecting seismic waves in a borehole
West, Phillip B.; Fincke, James R.; Reed, Teddy R.
2007-02-20
The invention provides methods and apparatus for detecting seismic waves propagating through a subterranean formation surrounding a borehole. In a first embodiment, a sensor module uses the rotation of bogey wheels to extend and retract a sensor package for selective contact and magnetic coupling to casing lining the borehole. In a second embodiment, a sensor module is magnetically coupled to the casing wall during its travel and dragged therealong while maintaining contact therewith. In a third embodiment, a sensor module is interfaced with the borehole environment to detect seismic waves using coupling through liquid in the borehole. Two or more of the above embodiments may be combined within a single sensor array to provide a resulting seismic survey combining the optimum of the outputs of each embodiment into a single data set.
8760-Based Method for Representing Variable Generation Capacity Value in Capacity Expansion Models
Energy Technology Data Exchange (ETDEWEB)
Frew, Bethany A [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2017-08-03
Capacity expansion models (CEMs) are widely used to evaluate the least-cost portfolio of electricity generators, transmission, and storage needed to reliably serve load over many years or decades. CEMs can be computationally complex and are often forced to estimate key parameters using simplified methods to achieve acceptable solve times or for other reasons. In this paper, we discuss one of these parameters -- capacity value (CV). We first provide a high-level motivation for and overview of CV. We next describe existing modeling simplifications and an alternate approach for estimating CV that utilizes hourly '8760' data of load and VG resources. We then apply this 8760 method to an established CEM, the National Renewable Energy Laboratory's (NREL's) Regional Energy Deployment System (ReEDS) model (Eurek et al. 2016). While this alternative approach for CV is not itself novel, it contributes to the broader CEM community by (1) demonstrating how a simplified 8760 hourly method, which can be easily implemented in other power sector models when data is available, more accurately captures CV trends than a statistical method within the ReEDS CEM, and (2) providing a flexible modeling framework from which other 8760-based system elements (e.g., demand response, storage, and transmission) can be added to further capture important dynamic interactions, such as curtailment.
Critical node treatment in the analytic function expansion method for Pin Power Reconstruction
International Nuclear Information System (INIS)
Gao, Z.; Xu, Y.; Downar, T.
2013-01-01
Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)
Critical node treatment in the analytic function expansion method for Pin Power Reconstruction
Energy Technology Data Exchange (ETDEWEB)
Gao, Z. [Rice University, MS 318, 6100 Main Street, Houston, TX 77005 (United States); Xu, Y. [Argonne National Laboratory, 9700 South Case Ave., Argonne, IL 60439 (United States); Downar, T. [Department of Nuclear Engineering, University of Michigan, 2355 Bonisteel blvd., Ann Arbor, MI 48109 (United States)
2013-07-01
Pin Power Reconstruction (PPR) was implemented in PARCS using the eight term analytic function expansion method (AFEN). This method has been demonstrated to be both accurate and efficient. However, similar to all the methods involving analytic functions, such as the analytic node method (ANM) and AFEN for nodal solution, the use of AFEN for PPR also has potential numerical issue with critical nodes. The conventional analytic functions are trigonometric or hyperbolic sine or cosine functions with an angular frequency proportional to buckling. For a critic al node the buckling is zero and the sine functions becomes zero, and the cosine function become unity. In this case, the eight terms of the analytic functions are no longer distinguishable from ea ch other which makes their corresponding coefficients can no longer be determined uniquely. The mode flux distribution of critical node can be linear while the conventional analytic functions can only express a uniform distribution. If there is critical or near critical node in a plane, the reconstructed pin power distribution is often be shown negative or very large values using the conventional method. In this paper, we propose a new method to avoid the numerical problem wit h critical nodes which uses modified trigonometric or hyperbolic sine functions which are the ratio of trigonometric or hyperbolic sine and its angular frequency. If there are no critical or near critical nodes present, the new pin power reconstruction method with modified analytic functions are equivalent to the conventional analytic functions. The new method is demonstrated using the L336C5 benchmark problem. (authors)
Directory of Open Access Journals (Sweden)
Mahmoud Paripour
2014-08-01
Full Text Available In this paper, the Bernstein polynomials are used to approximatethe solutions of linear integral equations with multiple time lags (IEMTL through expansion methods (collocation method, partition method, Galerkin method. The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is carried out
Modelling viscoacoustic wave propagation with the lattice Boltzmann method.
Xia, Muming; Wang, Shucheng; Zhou, Hui; Shan, Xiaowen; Chen, Hanming; Li, Qingqing; Zhang, Qingchen
2017-08-31
In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.
Yang, Lei; Yan, Hongyong; Liu, Hong
2017-03-01
Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.
Treatment of divergent expansions in scattering theory
International Nuclear Information System (INIS)
Gersten, A.; Malin, S.
1978-01-01
One of the biggest obstacles in applying quantum field theory to realistic scattering problems are the divergencies of pertubation expansions for large coupling constants and the divergencies of partial wave expansions for massless particles exchanges. There exist, however, methods of summation of the divergent expansions which can lead to significant application in physics. In this paper we treat the problem of summing such expansions using three methods: (i) a generalization of the Pade approximation to the multivariable case. The suggested definition is unique and preserves unitarity. (ii) The summation of divergent partial waves for arbitrary spins. (iii) A successful application of a series inversion to the 3 P 1 nucleon-nucleon phase shift up to 200 MeV. (orig./WL) [de
PENETRATION OF A SHOCK WAVE IN A FULLY SUPERSONIC FLAME FRONT WITH THE FORMATION OF AN EXPANSION FAN
Directory of Open Access Journals (Sweden)
Dan PANTAZOPOL
2011-03-01
Full Text Available In a previous paper [3] was treated the ,,simple penetration” of an incident shock wavethrough a fully supersonic flame front in the space of the hot burnt gases, situated in a supersonictwo-dimensional flow of an ideal homogeneous /combustible gas was treated in a previous paper [3].In the present paper takes into consideration, a configuration, in which an expansion fan is produced,is take into consideration the shock polar and expansion polar are used for the analyze of theinterference phenomena.
International Nuclear Information System (INIS)
Eleonskij, V.M.; Kulagin, N.E.; Novozhilova, N.S.; Silin, V.P.
1984-01-01
The reasons which prevent the existence of periodic in time and self-localised in space solutions of the nonlinear wave equation u=F (u) are determined by the methods of qualitative theory of dynamical systems. The correspondence between the qualitative behaviour of special (separatrix) trajectories in the phase space and asymptotic solutions of the nonlinear wave equation is analysed
Dhawan, Anuj; Norton, Stephen J; Gerhold, Michael D; Vo-Dinh, Tuan
2009-06-08
This paper describes a comparative study of finite-difference time-domain (FDTD) and analytical evaluations of electromagnetic fields in the vicinity of dimers of metallic nanospheres of plasmonics-active metals. The results of these two computational methods, to determine electromagnetic field enhancement in the region often referred to as "hot spots" between the two nanospheres forming the dimer, were compared and a strong correlation observed for gold dimers. The analytical evaluation involved the use of the spherical-harmonic addition theorem to relate the multipole expansion coefficients between the two nanospheres. In these evaluations, the spacing between two nanospheres forming the dimer was varied to obtain the effect of nanoparticle spacing on the electromagnetic fields in the regions between the nanostructures. Gold and silver were the metals investigated in our work as they exhibit substantial plasmon resonance properties in the ultraviolet, visible, and near-infrared spectral regimes. The results indicate excellent correlation between the two computational methods, especially for gold nanosphere dimers with only a 5-10% difference between the two methods. The effect of varying the diameters of the nanospheres forming the dimer, on the electromagnetic field enhancement, was also studied.
The renormalized Hamiltonian truncation method in the large E{sub T} expansion
Energy Technology Data Exchange (ETDEWEB)
Elias-Miró, J. [SISSA and INFN, I-34136 Trieste (Italy); Montull, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); Riembau, M. [Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology (BIST), Campus UAB, E-08193 Bellaterra (Spain); DESY, Notkestrasse 85, 22607 Hamburg (Germany)
2016-04-22
Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in refs. http://dx.doi.org/10.1103/PhysRevD.91.085011; http://dx.doi.org/10.1103/PhysRevD.93.065014; http://dx.doi.org/10.1103/PhysRevD.91.025005. The method is general but as an example we calculate the exact g{sup 2} and some of the g{sup 3} contributions for the ϕ{sup 4} theory in two dimensions. The coefficients of the local expansion calculated in ref. http://dx.doi.org/10.1103/PhysRevD.91.085011 are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.
DEFF Research Database (Denmark)
Margheritini, Lucia; Stratigaki, Vasiliki; Troch, Peter
2012-01-01
breakwater is 1.5 km and the water depth ranges approximately from 8.0 m up to 14 m with localized influences on the wave climate. The study is conducted numerically in order to present the expected power production and overall performance of the SSG breakwater in Hanstholm. The price par kWh is also......The study presented here describes the geometry optimization of the Sea wave Slot cone Generator (SSG) overtopping wave energy converter as part of the feasibility study for the implementation of the device in the development plan of Hanstholm harbour in Denmark. The total length of the new planned...
Expansion of the tuning range of injection-seeded terahertz-wave parametric generator up to 5 THz
Murate, Kosuke; Hayashi, Shin'ichiro; Kawase, Kodo
2016-01-01
In this paper, we report the improvement of the frequency tuning range of an injection-seeded terahertz (THz)-wave parametric generator (is-TPG). A significant previous limitation was the high absorption coefficient in the higher-frequency region of a MgO:LiNbO3 crystal. Here, we inclined the crystal slightly, so that a fraction of the pump beam was internally reflected at the THz-wave exit surface of the crystal. In this configuration, it was easier for a higher-frequency THz wave to reach t...
Dispersive photonic crystals from the plane wave method
Energy Technology Data Exchange (ETDEWEB)
Guevara-Cabrera, E.; Palomino-Ovando, M.A. [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Post. 165, Puebla, Pue. 72000, México (Mexico); Flores-Desirena, B., E-mail: bflores@fcfm.buap.mx [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Post. 165, Puebla, Pue. 72000, México (Mexico); Gaspar-Armenta, J.A. [Departamento de Investigación en Física de la Universidad de Sonora Apdo, Post 5-088, Hermosillo Sonora 83190, México (Mexico)
2016-03-01
Nowadays photonic crystals are widely used in many different applications. One of the most used methods to compute their band structure is the plane wave method (PWM). However, it can only be applied directly to non-dispersive media and be extended to systems with a few model dielectric functions. We explore an extension of the PWM to photonic crystals containing dispersive materials, that solves an eigenvalue equation for the Bloch wave vectors. First we compare our calculation with analytical results for one dimensional photonic crystals containing Si using experimental values of its optical parameters, and obtainig very well agreement, even for the spectrum region with strong absorption. Then, using the same method, we computed the band structure for a two dimensional photonic crystal without absorption, formed by an square array of MgO cylinders in air. The optical parameters for MgO were modeled with the Lorentz dielectric function. Finally, we studied an array of MgO cylinders in a metal, using Drude model without absorption, for the metal dielectric function. For this last case, we study the gap–midgap ratio as a function of the filling fraction for both the square and triangular lattice. The gap–midgap ratio is larger for the triangular lattice, with a maximum value of 10% for a filling fraction of 0.6. Our results show that the method can be applied to dispersive materials, and then to a wide range of applications where photonic crystals can be used.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
Linear augmented plane wave method for self-consistent calculations
International Nuclear Information System (INIS)
Takeda, T.; Kuebler, J.
1979-01-01
O.K. Andersen has recently introduced a linear augmented plane wave method (LAPW) for the calculation of electronic structure that was shown to be computationally fast. A more general formulation of an LAPW method is presented here. It makes use of a freely disposable number of eigenfunctions of the radial Schroedinger equation. These eigenfunctions can be selected in a self-consistent way. The present formulation also results in a computationally fast method. It is shown that Andersen's LAPW is obtained in a special limit from the present formulation. Self-consistent test calculations for copper show the present method to be remarkably accurate. As an application, scalar-relativistic self-consistent calculations are presented for the band structure of FCC lanthanum. (author)
Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method
Chu, Chunlei; Stoffa, Paul L.
2012-01-01
Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
Wave reflections from breakwaters
Dickson, William S.
1994-01-01
A new method is presented for estimating the reflection of a random, multi-directional sea from a coastal structure. The technique is applicable to an array of wave gauges of arbitrary geometry deployed seaward of the reflector. An expansion for small oblique wave incidence angles is used to derive an approximate relationship between measured array cross-spectra and a small number of parameters that describe the incident wave properties and the reflectivity of the structure. Model tests with ...
Numerical divergence effects of equivalence theory in the nodal expansion method
International Nuclear Information System (INIS)
Zika, M.R.; Downar, T.J.
1993-01-01
Accurate solutions of the advanced nodal equations require the use of discontinuity factors (DFs) to account for the homogenization errors that are inherent in all coarse-mesh nodal methods. During the last several years, nodal equivalence theory (NET) has successfully been implemented for the Cartesian geometry and has received widespread acceptance in the light water reactor industry. The extension of NET to other reactor types has had limited success. Recent efforts to implement NET within the framework of the nodal expansion method have successfully been applied to the fast breeder reactor. However, attempts to apply the same methods to thermal reactors such as the Modular High-Temperature Gas Reactor (MHTGR) have led to numerical divergence problems that can be attributed directly to the magnitude of the DFs. In the work performed here, it was found that the numerical problems occur in the inner and upscatter iterations of the solution algorithm. These iterations use a Gauss-Seidel iterative technique that is always convergent for problems with unity DFs. However, for an MHTGR model that requires large DFs, both the inner and upscatter iterations were divergent. Initial investigations into methods for bounding the DFs have proven unsatisfactory as a means of remedying the convergence problems. Although the DFs could be bounded to yield a convergent solution, several cases were encountered where the resulting flux solution was less accurate than the solution without DFs. For the specific case of problems without upscattering, an alternate numerical method for the inner iteration, an LU decomposition, was identified and shown to be feasible
An analytic method for S-expansion involving resonance and reduction
Energy Technology Data Exchange (ETDEWEB)
Ipinza, M.C.; Penafiel, D.M. [Departamento de Fisica, Universidad de Concepcion (Chile); DISAT, Politecnico di Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino (Italy); Lingua, F. [DISAT, Politecnico di Torino (Italy); Ravera, L. [DISAT, Politecnico di Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino (Italy)
2016-11-15
In this paper we describe an analytic method able to give the multiplication table(s) of the set(s) involved in an S-expansion process (with either resonance or 0{sub S}-resonant-reduction) for reaching a target Lie (super)algebra from a starting one, after having properly chosen the partitions over subspaces of the considered (super)algebras. This analytic method gives us a simple set of expressions to find the subset decomposition of the set(s) involved in the process. Then, we use the information coming from both the initial (super)algebra and the target one for reaching the multiplication table(s) of the mentioned set(s). Finally, we check associativity with an auxiliary computational algorithm, in order to understand whether the obtained set(s) can describe semigroup(s) or just abelian set(s) connecting two (super)algebras. We also give some interesting examples of application, which check and corroborate our analytic procedure and also generalize some result already presented in the literature. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The cross-section dividing method and a stochastic interpretation of the moliere expansion
International Nuclear Information System (INIS)
Nakatsuka, T.; Okei, K.
2004-01-01
Properties of Moliere scattering process are investigated through the cross-section dividing method. We divide the single-scattering at an adequate angle into the moderate scattering and the large-angle scattering. We have found the expansion parameter or the shape parameter B of Moliere, which corresponds to the splitting angle of the single scattering at e B/2 times the screening angle, acts as the probability parameter to receive the large-angle scattering. A mathematical formulation to derive the angular distribution through the cross-section dividing method is proposed. Small distortions from the gaussian distribution were found in the central distribution produced by the moderate scattering of Moliere, due to the higher Fourier components. Smaller splitting angles than Moliere, e.g. the one-scattering angle χ C , will be effective for rapid sampling sequences of Moliere angular distribution, giving almost gaussian central distributions as the product of moderate scattering and low-frequent single-scatterings as the product of large-angle scatterings. (author)
Method of synthesizing silica nanofibers using sound waves
Sharma, Jaswinder K.; Datskos, Panos G.
2015-09-15
A method for synthesizing silica nanofibers using sound waves is provided. The method includes providing a solution of polyvinyl pyrrolidone, adding sodium citrate and ammonium hydroxide to form a first mixture, adding a silica-based compound to the solution to form a second mixture, and sonicating the second mixture to synthesize a plurality of silica nanofibers having an average cross-sectional diameter of less than 70 nm and having a length on the order of at least several hundred microns. The method can be performed without heating or electrospinning, and instead includes less energy intensive strategies that can be scaled up to an industrial scale. The resulting nanofibers can achieve a decreased mean diameter over conventional fibers. The decreased diameter generally increases the tensile strength of the silica nanofibers, as defects and contaminations decrease with the decreasing diameter.
A Comparison of Surface Acoustic Wave Modeling Methods
Wilson, W. c.; Atkinson, G. M.
2009-01-01
Surface Acoustic Wave (SAW) technology is low cost, rugged, lightweight, extremely low power and can be used to develop passive wireless sensors. For these reasons, NASA is investigating the use of SAW technology for Integrated Vehicle Health Monitoring (IVHM) of aerospace structures. To facilitate rapid prototyping of passive SAW sensors for aerospace applications, SAW models have been developed. This paper reports on the comparison of three methods of modeling SAWs. The three models are the Impulse Response Method a first order model, and two second order matrix methods; the conventional matrix approach, and a modified matrix approach that is extended to include internal finger reflections. The second order models are based upon matrices that were originally developed for analyzing microwave circuits using transmission line theory. Results from the models are presented with measured data from devices.
International Nuclear Information System (INIS)
Valeo, Ernest; Johnson, Jay R.; Kim, Eun-Hwa; Phillips, Cynthia
2012-01-01
A wide variety of plasma waves play an important role in the energization and loss of particles in the inner magnetosphere. Our ability to understand and model wave-particle interactions in this region requires improved knowledge of the spatial distribution and properties of these waves as well as improved understanding of how the waves depend on changes in solar wind forcing and/or geomagnetic activity. To this end, we have developed a two-dimensional, finite element code that solves the full wave equations in global magnetospheric geometry. The code describes three-dimensional wave structure including mode conversion when ULF, EMIC, and whistler waves are launched in a two-dimensional axisymmetric background plasma with general magnetic field topology. We illustrate the capabilities of the code by examining the role of plasmaspheric plumes on magnetosonic wave propagation; mode conversion at the ion-ion and Alfven resonances resulting from external, solar wind compressions; and wave structure and mode conversion of electromagnetic ion cyclotron waves launched in the equatorial magnetosphere, which propagate along the magnetic field lines toward the ionosphere. We also discuss advantages of the finite element method for resolving resonant structures, and how the model may be adapted to include nonlocal kinetic effects.
A numerical method for determining the radial wave motion correction in plane wave couplers
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Barrera Figueroa, Salvador; Torras Rosell, Antoni
2016-01-01
Microphones are used for realising the unit of sound pressure level, the pascal (Pa). Electro-acoustic reciprocity is the preferred method for the absolute determination of the sensitivity. This method can be applied in different sound fields: uniform pressure, free field or diffuse field. Pressure...... solution is an analytical expression that estimates the difference between the ideal plane wave sound field and a more complex lossless sound field created by a non-planar movement of the microphone’s membranes. Alternatively, a correction may be calculated numerically by introducing a full model...... of the microphone-coupler system in a Boundary Element formulation. In order to obtain a realistic representation of the sound field, viscous losses must be introduced in the model. This paper presents such a model, and the results of the simulations for different combinations of microphones and couplers...
Huang, Hao; Ouyang, Zhengbiao
2018-01-01
We propose a general method for eliminating the reflection of waves in 2 dimensional photonic crystal waveguides (2D-PCWs), a kind of 2D material, by introducing extra scatterers inside the 2D-PCWs. The intrinsic reflection in 2D-PCWs is compensated by the backward-scattered waves from these scatterers, so that the overall reflection is greatly reduced and the insertion loss is improved accordingly. We first present the basic theory for the compensation method. Then, as a demonstration, we give four examples of extremely-low-reflection and high-transmission 90°bent 2D-PCWs created according to the method proposed. In the four examples, it is demonstrated by plane-wave expansion method and finite-difference time-domain method that the 90°bent 2D-PCWs can have high transmission ratio greater than 90% in a wide range of operating frequency, and the highest transmission ratio can be greater than 99.95% with a return loss higher than 43 dB, better than that in other typical 90°bent 2D-PCWs. With our method, the bent 2D-PCWs can be optimized to obtain high transmission ratio at different operating wavelengths. As a further application of this method, a waveguide-based optical bridge for light crossing is presented, showing an optimum return loss of 46.85 dB, transmission ratio of 99.95%, and isolation rates greater than 41.77 dB. The method proposed provides also a useful way for improving conventional waveguides made of cables, fibers, or metal walls in the optical, infrared, terahertz, and microwave bands.
Barbieri, Ana A; Scoralick, Raquel A; Naressi, Suely C M; Moraes, Mari E L; Daruge, Eduardo; Daruge, Eduardo
2013-01-01
The objective of this study was to demonstrate the effectiveness of rugoscopy as a human identification method, even when the patient is submitted to rapid palatal expansion, which in theory would introduce doubt. With this intent, the Rugoscopic Identity was obtained for each subject using the classification formula proposed by Santos based on the intra-oral casts made before and after treatment from patients who were subjected to palatal expansion. The casts were labeled with the patients' initials and randomly arranged for studying. The palatine rugae kept the same patterns in every case studied. The technical error of the intra-evaluator measurement provided a confidence interval of 95%, making rugoscopy a reliable identification method for patients who were submitted to rapid palatal expansion, because even in the presence of intra-oral changes owing to the use of palatal expanders, the palatine rugae retained the biological and technical requirements for the human identification process. © 2012 American Academy of Forensic Sciences.
Seiffert, Betsy R.; Ducrozet, Guillaume; Bonnefoy, Félicien
2017-11-01
This study investigates a wave-breaking onset criteria to be implemented in the non-linear potential flow solver HOS-NWT. The model is a computationally efficient, open source code, which solves for the free surface in a numerical wave tank using the High-Order Spectral (HOS) method. The goal of this study is to determine the best method to identify the onset of random single and multiple breaking waves over a large domain at the exact time they occur. To identify breaking waves, a breaking onset criteria based on the ratio of local energy flux velocity to the local crest velocity, introduced by Barthelemy et al. (2017) is selected. The breaking parameter is uniquely applied in the numerical model in that calculations of the breaking onset criteria ratio are not made only at the location of the wave crest, but at every point in the domain and at every time step. This allows the model to calculate the onset of a breaking wave the moment it happens, and without knowing anything about the wave a priori. The application of the breaking criteria at every point in the domain and at every time step requires the phase velocity to be calculated instantaneously everywhere in the domain and at every time step. This is achieved by calculating the instantaneous phase velocity using the Hilbert transform and dispersion relation. A comparison between more traditional crest-tracking techniques shows the calculation of phase velocity using Hilbert transform at the location of the breaking wave crest provides a good approximation of crest velocity. The ability of the selected wave breaking criteria to predict single and multiple breaking events in two dimensions is validated by a series of large-scale experiments. Breaking waves are generated by energy focusing and modulational instability methods, with a wide range of primary frequencies. Steep irregular waves which lead to breaking waves, and irregular waves with an energy focusing wave superimposed are also generated. This set of
Analytic moment method calculations of the drift wave spectrum
International Nuclear Information System (INIS)
Thayer, D.R.; Molvig, K.
1985-11-01
A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formation. An analytic moment method is developed to approximate the solution of the nonlinear spectrum integral equations. The solution method employs trial functions to reduce the integral equations to algebraic equations in basic parameters describing the spectrum. An approximate solution of the spectrum equations is first obtained for a mode dissipation with known solution, and second for an electron dissipation in the NSA
Dominant partition method. [based on a wave function formalism
Dixon, R. M.; Redish, E. F.
1979-01-01
By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.
Determination of optimum "multi-channel surface wave method" field parameters.
2012-12-01
Multi-channel surface wave methods (especially the multi-channel analyses of surface wave method; MASW) are routinely used to : determine the shear-wave velocity of the subsurface to depths of 100 feet for site classification purposes. Users are awar...
Seiffert, Betsy R.; Ducrozet, Guillaume
2018-01-01
We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf, submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642-658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation
Semiclassical expansions on and near caustics
International Nuclear Information System (INIS)
Meetz, K.
1984-09-01
We show that the standard WKB expansion can be generalized so that it reproduces the behavior of the wave function on and near a caustic in two-dimensional space time. The expansion is related to the unfolding polynomials of the elementary catastrophes occurring in two dimensions: the fold and the cusp catastrophe. The method determines control parameters and transport coefficients in a self-consistent way from differential equations and does not refer to the asymptotic expansion of Feynman path integrals. The lowest order equations are solved explicitly in terms of the multivalued classical action. The result is a generalized semiclassical approximation on and beyond a caustic. (orig.)
Supersonic wave detection method and supersonic detection device
International Nuclear Information System (INIS)
Machida, Koichi; Seto, Takehiro; Ishizaki, Hideaki; Asano, Rin-ichi.
1996-01-01
The present invention provides a method of and device for a detection suitable to a channel box which is used while covering a fuel assembly of a BWR type reactor. Namely, a probe for transmitting/receiving supersonic waves scans on the surface of the channel box. A data processing device determines an index showing a selective orientation degree of crystal direction of the channel box based on the signals received by the probe. A judging device compares the determined index with a previously determined allowable range to judge whether the channel box is satisfactory or not based on the result of the comparison. The judgement are on the basis that (1) the bending of the channel box is caused by the difference of elongation of opposed surfaces, (2) the elongation due to irradiation is caused by the selective orientation of crystal direction, and (3) the bending of the channel box can be suppressed within a predetermined range by suppressing the index determined by the measurement of supersonic waves having a correlation with the selective orientation of the crystal direction. As a result, the performance of the channel box capable of enduring high burnup region can be confirmed in a nondestructive manner. (I.S.)
Multimodal method for scattering of sound at a sudden area expansion in a duct with subsonic flow
Kooijman, G.; Testud, P.; Aurégan, Y.; Hirschberg, A.
2008-01-01
The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both two-dimensional (2D) rectangular
A stochastic collocation method for the second order wave equation with a discontinuous random speed
Motamed, Mohammad; Nobile, Fabio; Tempone, Raul
2012-01-01
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical
International Nuclear Information System (INIS)
Xia, L.; Wen, G.W.; Qin, C.L.; Wang, X.Y.; Song, L.
2011-01-01
Research highlights: → Dense LAS glass-ceramics were fabricated by sol-gel and hot pressing technique. → The LAS glass-ceramics have relative good mechanical properties. → The negative thermal expansion behavior of LAS glass-ceramics was investigated. -- Abstract: The microstructures, mechanical properties and thermal expansion behavior of monolithic lithium aluminosilicate glass-ceramics, prepared by sol-gel method and hot pressing, were investigated by using X-ray diffraction, scanning and transmission electron microscopies, three-point bend tests and dilatometry. β-eucryptite appeared as main phase in the monolithic lithium aluminosilicate glass-ceramics. The glass ceramics exhibited high relative densities and the average flexural strength and fracture toughness values were 154 MPa and 2.46 MPa m 1/2 , respectively. The lithium aluminosilicate glass-ceramics hot pressed 1300 and 1350 o C demonstrated negative coefficient of thermal expansion, which was affected by amount and type of crystalline phases.
The Ion Cyclotron, Lower Hybrid, and Alfven Wave Heating Methods
International Nuclear Information System (INIS)
Koch, R.
2004-01-01
This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfven wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented
Energy Technology Data Exchange (ETDEWEB)
Frew, Bethany A [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Cole, Wesley J [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Sun, Yinong [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Mai, Trieu T [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Richards, James [National Renewable Energy Laboratory (NREL), Golden, CO (United States)
2017-08-01
Capacity expansion models (CEMs) are widely used to evaluate the least-cost portfolio of electricity generators, transmission, and storage needed to reliably serve demand over the evolution of many years or decades. Various CEM formulations are used to evaluate systems ranging in scale from states or utility service territories to national or multi-national systems. CEMs can be computationally complex, and to achieve acceptable solve times, key parameters are often estimated using simplified methods. In this paper, we focus on two of these key parameters associated with the integration of variable generation (VG) resources: capacity value and curtailment. We first discuss common modeling simplifications used in CEMs to estimate capacity value and curtailment, many of which are based on a representative subset of hours that can miss important tail events or which require assumptions about the load and resource distributions that may not match actual distributions. We then present an alternate approach that captures key elements of chronological operation over all hours of the year without the computationally intensive economic dispatch optimization typically employed within more detailed operational models. The updated methodology characterizes the (1) contribution of VG to system capacity during high load and net load hours, (2) the curtailment level of VG, and (3) the potential reductions in curtailments enabled through deployment of storage and more flexible operation of select thermal generators. We apply this alternate methodology to an existing CEM, the Regional Energy Deployment System (ReEDS). Results demonstrate that this alternate approach provides more accurate estimates of capacity value and curtailments by explicitly capturing system interactions across all hours of the year. This approach could be applied more broadly to CEMs at many different scales where hourly resource and load data is available, greatly improving the representation of challenges
International Nuclear Information System (INIS)
Alexander, J.E.
1978-06-01
The report describes a test which was conducted to determine the variation in thermal expansion coefficients of specimens from several material heats of Type 304 stainless steel. The purpose of this document is to identify the procedures, equipment, and analysis used in performing this test. From a review of the data which were used in establishing the values given for mean coefficient of thermal expansion in the 1968 ASME Boiler and Pressure Vessel Code, Section III, a +-3.3-percent maximum variation was determined for Type 304 CRES in the temperature range of interest. The results of the test reduced this variation to +-0.53 percent based on a 95/99-percent tolerance interval for the material tested. The testing equipment, procedure, and analysis are not complicated and this type of test is recommended for applications in which the variation in thermal expansion coefficients is desired for a limited number of material heats
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 85; Issue 1. Solitary wave and periodic wave solutions for Burgers, Fisher, Huxley and combined forms of these equations by the (′/)-expansion method. Jalil Manafian Mehrdad Lakestani. Volume 85 Issue 1 July 2015 pp 31-52 ...
Energy Technology Data Exchange (ETDEWEB)
Tamanini, Nicola; Caprini, Chiara [Institut de Physique Théorique, CEA-Saclay, CNRS UMR 3681, Université Paris-Saclay, F-91191 Gif-sur-Yvette (France); Barausse, Enrico [Sorbonne Universités, UPMC Université Paris 6, UMR 7095, Institut d' Astrophysique de Paris, 98 bis Bd Arago, 75014 Paris (France); Sesana, Alberto [School of Physics and Astronomy, The University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom); Klein, Antoine [Department of Physics and Astronomy, The University of Mississippi, University, MS 38677 (United States); Petiteau, Antoine, E-mail: nicola.tamanini@cea.fr, E-mail: chiara.caprini@cea.fr, E-mail: barausse@iap.fr, E-mail: asesana@star.sr.bham.ac.uk, E-mail: aklein@physics.montana.edu, E-mail: antoine.petiteau@apc.univ-paris7.fr [APC, Université Paris Diderot, Observatoire de Paris, Sorbonne Paris Cité, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13 (France)
2016-04-01
We investigate the capability of various configurations of the space interferometer eLISA to probe the late-time background expansion of the universe using gravitational wave standard sirens. We simulate catalogues of standard sirens composed by massive black hole binaries whose gravitational radiation is detectable by eLISA, and which are likely to produce an electromagnetic counterpart observable by future surveys. The main issue for the identification of a counterpart resides in the capability of obtaining an accurate enough sky localisation with eLISA. This seriously challenges the capability of four-link (2 arm) configurations to successfully constrain the cosmological parameters. Conversely, six-link (3 arm) configurations have the potential to provide a test of the expansion of the universe up to z ∼ 8 which is complementary to other cosmological probes based on electromagnetic observations only. In particular, in the most favourable scenarios, they can provide a significant constraint on H{sub 0} at the level of 0.5%. Furthermore, (Ω{sub M}, Ω{sub Λ}) can be constrained to a level competitive with present SNIa results. On the other hand, the lack of massive black hole binary standard sirens at low redshift allows to constrain dark energy only at the level of few percent.
A simplified method of evaluating the stress wave environment of internal equipment
Colton, J. D.; Desmond, T. P.
1979-01-01
A simplified method called the transfer function technique (TFT) was devised for evaluating the stress wave environment in a structure containing internal equipment. The TFT consists of following the initial in-plane stress wave that propagates through a structure subjected to a dynamic load and characterizing how the wave is altered as it is transmitted through intersections of structural members. As a basis for evaluating the TFT, impact experiments and detailed stress wave analyses were performed for structures with two or three, or more members. Transfer functions that relate the wave transmitted through an intersection to the incident wave were deduced from the predicted wave response. By sequentially applying these transfer functions to a structure with several intersections, it was found that the environment produced by the initial stress wave propagating through the structure can be approximated well. The TFT can be used as a design tool or as an analytical tool to determine whether a more detailed wave analysis is warranted.
Character of GPR wave in air and processed method
International Nuclear Information System (INIS)
Shi Jianping; Zhang Zhiyong; Deng Juzhi
2009-01-01
The wave reflected by objects in the air is unavoidable because electromagnetic wave of GPR was send to all directions. There are three air reflection types: directly arrived wave, system ring and reflection wave. The directly arrived waves don't disturb the recognition of the reflections from earth because they affect the first short time of GPR trace record. But system ring and reflection from air are the mainly part of disturbs. The time and distance curve of reflection from air can be classified into two types: hyperbola type and line type. The reflection from air and from earth can be recognized by calculating the velocity of electromagnetic wave. Line type reflection can be filtered by background remove and 2-D filter; by comparing the migrated profiles with velocity in air and ground, the interpretation will become more exact. (authors)
Multiple (G /G)-expansion method and its applications to nonlinear ...
Indian Academy of Sciences (India)
to nonlinear evolution equations in mathematical physics ... recent years, due to the availability of symbolic computation systems like Mathematica ..... In this subsection we study the generalized shallow water wave (GSWW) equation [12,. 40],.
International Nuclear Information System (INIS)
Leaci, Paola
2015-01-01
Semicoherent all-sky searches over year-long observation times for continuous gravitational wave signals produce various thousands of potential periodic source candidates. Efficient methods able to discard false candidate events are crucial in order to put all the efforts into a computationally intensive follow-up analysis for the remaining most promising candidates (Shaltev et al 2014 Phys. Rev. D 89 124030). In this paper we present a set of techniques able to fulfill such requirements, identifying and eliminating false candidate events, reducing thus the bulk of candidate sets that need to be further investigated. Some of these techniques were also used to streamline the candidate sets returned by the Einstein@Home hierarchical searches presented in (Aasi J et al (The LIGO Scientific Collaboration and the Virgo Collaboration) 2013 Phys. Rev. D 87 042001). These powerful methods and the benefits originating from their application to both simulated and on detector data from the fifth LIGO science run are illustrated and discussed. (paper)
Interpretation of Piezocones in Silt, Using Cavity Expansion and Critical State Methods
DEFF Research Database (Denmark)
Bakmar, Christian LeBlanc; Randolph, M. F.
2008-01-01
was simulated using cylindrical cavity expansion in conjunction with a plasticity model formulated within the framework of critical state soil mechanics. The results readily explain the low cone tip resistance measured in silt sediments; this is a derived effect of the silt having a large slope of the critical...... state line, resulting in rather weak and compressible behaviour at high mean effective stresses....
International Nuclear Information System (INIS)
Passos, E.M.J. de
1976-01-01
The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt
Energy Technology Data Exchange (ETDEWEB)
Kromar, M; Trkov, A [Institut Jozef Stefan, Ljubljana (Yugoslavia); Pregl, G [Tehnishka Fakulteta Maribor Univ. (Yugoslavia)
1988-07-01
Nodal expansion method (NEM) is one of the advanced coarse-mesh methods based on integral form of few-group diffusion equation. NEM can be characterized by high accuracy and computational efficiency. Method was tested by development of computer code NEXT. Validation of the code was performed by calculation of 2-D and 3-D IAEA benchmark problem. NEXT was compared with codes based on other methods (finite differences, finite elements) and has been found to be accurate as well as fast. (author)
Kushibiki, Jun-ichi; Arakawa, Mototaka; Ohashi, Yuji; Suzuki, Kouji
2006-09-01
Experimental procedures and standard specimens for characterizing and evaluating TiO2-SiO2 ultra-low expansion glasses with periodic striae using the line-focus-beam (LFB) ultrasonic material characterization system are discussed. Two types of specimens were prepared, with specimen surfaces parallel and perpendicular to the striae plane using two different grades of glass ingots. The inhomogeneities of each of the specimens were evaluated at 225 MHz. It was clarified that parallel specimens are useful for accurately measuring velocity variations of leaky surface acoustic waves (LSAWs) excited on a water-loaded specimen surface associated with the striae. Perpendicular specimens are useful for obtaining periodicities in the striae for LSAW propagation perpendicular to the striae plane on a surface and for precisely measuring averaged velocities for LSAW propagation parallel to the striae plane. The standard velocity of Rayleigh-type LSAWs traveling parallel to the striae plane for the perpendicular specimens was numerically calculated using the measured velocities of longitudinal and shear waves and density. Consequently, a reliable standard specimen with an LSAW velocity of 3308.18 +/- 0.35 m/s at 23 degrees C and its temperature coefficient of 0.39 (m/s)/degrees C was obtained for a TiO2-SiO2 glass with a TiO2 concentration of 7.09 wt%. A basis for the striae analysis using this ultrasonic method was established.
Sumardiono, Siswo; Pudjihastuti, Isti; Jos, Bakti; Taufani, Muhammad; Yahya, Faad
2017-05-01
Modified cassava starch is very prospective products in the food industry. The main consideration of this study is the increasing volume of imported wheat and the demand for modified cassava starch industry. The purpose of this study is the assessing of lactic acid hydrolysis and microwave heating impact to the physicochemical and rheological properties of modified cassava starch, and test applications of modified cassava starch to coated peanut expansion quality. Experimental variables include the concentration of lactic acid (0.5% w/w, 1% w/w; 2% w/w), a time of hydrolysis (15, 30, 45 minutes), a time of microwave heating (1, 2, 3 hours). The research step is by dissolving lactic acid using aquadest in the stirred tank reactor, then added cassava starch. Hydrolysed cassava starch was then heated by microwave. Physicochemical properties and rheology of the modified cassava starch is determined by the solubility, swelling power, and test congestion. The optimum obtained results indicate that solubility, swelling power, congestion test, respectively for 19.75%; 24.25% and 826.10% in the hydrolysis treatment for 15 minutes, 1% w lactic acid and microwave heating 3 hours. The physicochemical and rheological properties of modified cassava starch have changed significantly when compared to the native cassava starch. Furthermore, these modified cassava starch are expected to be used for the substitution of food products.
A novel method for predicting the power outputs of wave energy converters
Wang, Yingguang
2018-03-01
This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.
Multipole expansion of acoustical Bessel beams with arbitrary order and location.
Gong, Zhixiong; Marston, Philip L; Li, Wei; Chai, Yingbin
2017-06-01
An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.
Method of γ expansions in the electronic theory of disordered alloys
International Nuclear Information System (INIS)
Masanskii, I.V.; Tokar', V.I.
1989-01-01
In the electronic theory of disordered alloys an expansion with respect to the parameter γ = exp( -1/ξ ), where ξ is the dimensionless correlation length of the single-electron Green's function, is proposed. This expansion makes it possible to take into account the presence in the alloy of short-range order and the effects of multiple scattering of the electrons by different sites. It is shown that in the case of sufficiently strong disorder γ is a small parameter of the coherent potential approximation, and the corrections to this approximation are found. It is also shown that in the framework of this approximation the equilibrium values of the parameters of the short-range order can be calculated
DEFF Research Database (Denmark)
Døssing, Mads; Aagaard Madsen, Helge; Bak, Christian
2012-01-01
The blade element momentum (BEM) method is widely used for calculating the quasi-steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now...... by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM....... In short, allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd....
Wei Wang; Wei Wang; Huiming Liu; Rongjin Huang; Rongjin Huang; Yuqiang Zhao; Chuangjun Huang; Shibin Guo; Yi Shan; Laifeng Li; Laifeng Li; Laifeng Li
2018-01-01
Thermal expansion and magnetostriction, the strain responses of a material to temperature and a magnetic field, especially properties at low temperature, are extremely useful to study electronic and phononic properties, phase transitions, quantum criticality, and other interesting phenomena in cryogenic engineering and materials science. However, traditional dilatometers cannot provide magnetic field and ultra-low temperature (<77 K) environment easily. This paper describes the design and ...
Directory of Open Access Journals (Sweden)
Donald C. Boone
2017-10-01
Full Text Available This computational research study will analyze the multi-physics of lithium ion insertion into a silicon nanowire in an attempt to explain the electrochemical kinetics at the nanoscale and quantum level. The electron coherent states and a quantum field version of photon density waves will be the joining theories that will explain the electron-photon interaction within the lithium-silicon lattice structure. These two quantum particles will be responsible for the photon absorption rate of silicon atoms that are hypothesized to be the leading cause of breaking diatomic silicon covalent bonds that ultimately leads to volume expansion. It will be demonstrated through the combination of Maxwell stress tensor, optical amplification and path integrals that a stochastic analyze using a variety of Poisson distributions that the anisotropic expansion rates in the <110>, <111> and <112> orthogonal directions confirms the findings ascertained in previous works made by other research groups. The computational findings presented in this work are similar to those which were discovered experimentally using transmission electron microscopy (TEM and simulation models that used density functional theory (DFT and molecular dynamics (MD. The refractive index and electric susceptibility parameters of lithiated silicon are interwoven in the first principle theoretical equations and appears frequently throughout this research presentation, which should serve to demonstrate the importance of these parameters in the understanding of this component in lithium ion batteries.
Hadron formation in a non-ideal quark gluon plasma using Mayer's method of cluster expansion
International Nuclear Information System (INIS)
Prasanth, J.P.; Bannur, Vishnu M.
2015-01-01
This work investigates the applicability of using the Mayer's cluster expansion method to derive the equation of state (EoS) of the quark-antiquark plasma. Dissociation of heavier hadrons in QGP is studied. The possibility of the existence of quarkonium after deconfinement at higher temperature than the critical temperature T > T c is investigated. The EoS has been studied by calculating second and third cluster integrals. The results are compared and discussed with available works. (author)
Levshin, Anatoli L.; Barmin, Mikhail P.; Moschetti, Morgan P.; Mendoza, Carlos; Ritzwoller, Michael H.
2012-01-01
The purpose of this study is to develop and test a modiﬁcation to a previous method of regional seismic event location based on Empirical Green’s Functions (EGFs) produced from ambient seismic noise. Elastic EGFs between pairs of seismic stations are determined by cross-correlating long ambient noise time-series recorded at the two stations. The EGFs principally contain Rayleigh- and Love-wave energy on the vertical and transverse components, respectively, and we utilize these signals between about 5 and 12 s period. The previous method, based exclusively on Rayleigh waves, may yield biased epicentral locations for certain event types with hypocentral depths between 2 and 5 km. Here we present theoretical arguments that show how Love waves can be introduced to reduce or potentially eliminate the bias. We also present applications of Rayleigh- and Love-wave EGFs to locate 10 reference events in the western United States. The separate Rayleigh and Love epicentral locations and the joint locations using a combination of the two waves agree to within 1 km distance, on average, but conﬁdence ellipses are smallest when both types of waves are used.
Energy Technology Data Exchange (ETDEWEB)
Rising, M. E.; Prinja, A. K. [Univ. of New Mexico, Dept. of Chemical and Nuclear Engineering, Albuquerque, NM 87131 (United States)
2012-07-01
A critical neutron transport problem with random material properties is introduced. The total cross section and the average neutron multiplicity are assumed to be uncertain, characterized by the mean and variance with a log-normal distribution. The average neutron multiplicity and the total cross section are assumed to be uncorrected and the material properties for differing materials are also assumed to be uncorrected. The principal component analysis method is used to decompose the covariance matrix into eigenvalues and eigenvectors and then 'realizations' of the material properties can be computed. A simple Monte Carlo brute force sampling of the decomposed covariance matrix is employed to obtain a benchmark result for each test problem. In order to save computational time and to characterize the moments and probability density function of the multiplication factor the polynomial chaos expansion method is employed along with the stochastic collocation method. A Gauss-Hermite quadrature set is convolved into a multidimensional tensor product quadrature set and is successfully used to compute the polynomial chaos expansion coefficients of the multiplication factor. Finally, for a particular critical fuel pin assembly the appropriate number of random variables and polynomial expansion order are investigated. (authors)
Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines
Directory of Open Access Journals (Sweden)
M. A. Banaja
2015-01-01
Full Text Available The equal width (EW equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW equation is obtained by using the method of lines (MOL based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the L2 and L∞ error norms. The results are found in good agreement with exact solution.
Experiments of Long-range Inspection Method in Straight Pipes using Ultrasonic Guided Waves
International Nuclear Information System (INIS)
Eom, H. S.; Lim, S. H.; Kim, J. H.; Joo, Y.S.
2006-02-01
This report describes experimental results of a long-range inspection method of pipes using ultrasonic guided waves. In chapter 2, theory of guided wave was reviewed. In chapter 3, equipment and procedures which were used in the experiments were described. Detailed specifications of the specimens described in chapter 4. In chapter 5, we analyzed characteristics of guided wave signals according to shapes and sizes of defects and presents results of various signal processing methods
DEFF Research Database (Denmark)
DING, YI; Wang, Peng; Goel, Lalit
2010-01-01
from long term planning point of view utilizing universal generating function (UGF) methods. The reliability models of wind farms and conventional generators are represented as the correspondin UGFs and the special operators for these UGFs are defined to evaluate the customer and the system...... reliabilities. The effect of transmission network on customer reliabilities is also considered in the system UGF. The power output models of wind turbine generators in a wind farm considering wind speed correlation and un-correlation are developed, respectively. A reliability-based reserve expansion method...
International Nuclear Information System (INIS)
Yue, Cong; Ren, Xingmin; Yang, Yongfeng; Deng, Wangqun
2016-01-01
This paper provides a precise and efficacious methodology for manifesting forced vibration response with respect to the time-variant linear rotational structure subjected to unbalanced excitation. A modified algorithm based on time step precise integration method and Magnus expansion is developed for instantaneous dynamic problems. The iterative solution is achieved by the ideology of transition and dimensional increment matrix. Numerical examples on a typical accelerating rotation system considering gyroscopic moment and mass unbalance force comparatively demonstrate the validity, effectiveness and accuracy with Newmark-β method. It is shown that the proposed algorithm has high accuracy without loss efficiency.
The finite product method in the theory of linear wave propagation
DEFF Research Database (Denmark)
Sorokin, Sergey; Chapman, John
2012-01-01
of the method are presented for several non-trivial examples, that of symmetric/anti-symmetric elastic waves in a layer and in a thin plate. In each case, the method gives a sequence of polynomial approximations to the dispersion relation of remarkable accuracy over a broad range of frequencies and wave numbers...
Directory of Open Access Journals (Sweden)
Chi Yaodan
2017-08-01
Full Text Available Crosstalk in wiring harness has been studied extensively for its importance in the naval ships electromagnetic compatibility field. An effective and high-efficiency method is proposed in this paper for analyzing Statistical Characteristics of crosstalk in wiring harness with random variation of position based on Polynomial Chaos Expansion (PCE. A typical 14-cable wiring harness was simulated as the object of research. Distance among interfering cable, affected cable and GND is synthesized and analyzed in both frequency domain and time domain. The model of naval ships wiring harness distribution parameter was established by utilizing Legendre orthogonal polynomials as basis functions along with prediction model of statistical characters. Detailed mean value, mean square error, probability density function and reasonable varying range of crosstalk in naval ships wiring harness are described in both time domain and frequency domain. Numerical experiment proves that the method proposed in this paper, not only has good consistency with the MC method can be applied in the naval ships EMC research field to provide theoretical support for guaranteeing safety, but also has better time-efficiency than the MC method. Therefore, the Polynomial Chaos Expansion method.
Producing accurate wave propagation time histories using the global matrix method
International Nuclear Information System (INIS)
Obenchain, Matthew B; Cesnik, Carlos E S
2013-01-01
This paper presents a reliable method for producing accurate displacement time histories for wave propagation in laminated plates using the global matrix method. The existence of inward and outward propagating waves in the general solution is highlighted while examining the axisymmetric case of a circular actuator on an aluminum plate. Problems with previous attempts to isolate the outward wave for anisotropic laminates are shown. The updated method develops a correction signal that can be added to the original time history solution to cancel the inward wave and leave only the outward propagating wave. The paper demonstrates the effectiveness of the new method for circular and square actuators bonded to the surface of isotropic laminates, and these results are compared with exact solutions. Results for circular actuators on cross-ply laminates are also presented and compared with experimental results, showing the ability of the new method to successfully capture the displacement time histories for composite laminates. (paper)
Chemical graph-theoretic cluster expansions
International Nuclear Information System (INIS)
Klein, D.J.
1986-01-01
A general computationally amenable chemico-graph-theoretic cluster expansion method is suggested as a paradigm for incorporation of chemical structure concepts in a systematic manner. The cluster expansion approach is presented in a formalism general enough to cover a variety of empirical, semiempirical, and even ab initio applications. Formally such approaches for the utilization of chemical structure-related concepts may be viewed as discrete analogues of Taylor series expansions. The efficacy of the chemical structure concepts then is simply bound up in the rate of convergence of the cluster expansions. In many empirical applications, e.g., boiling points, chromatographic separation coefficients, and biological activities, this rate of convergence has been observed to be quite rapid. More note will be made here of quantum chemical applications. Relations to questions concerning size extensivity of energies and size consistency of wave functions are addressed
Capacitive acoustic wave detector and method of using same
Yost, William T. (Inventor)
1994-01-01
A capacitor having two substantially parallel conductive faces is acoustically coupled to a conductive sample end such that the sample face is one end of the capacitor. A non-contacting dielectric may serve as a spacer between the two conductive plates. The formed capacitor is connected to an LC oscillator circuit such as a Hartley oscillator circuit producing an output frequency which is a function of the capacitor spacing. This capacitance oscillates as the sample end coating is oscillated by an acoustic wave generated in the sample by a transmitting transducer. The electrical output can serve as an absolute indicator of acoustic wave displacement.
International Nuclear Information System (INIS)
Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing
2009-01-01
In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.
A new time–space domain high-order finite-difference method for the acoustic wave equation
Liu, Yang; Sen, Mrinal K.
2009-01-01
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
A new time–space domain high-order finite-difference method for the acoustic wave equation
Liu, Yang
2009-12-01
A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.
Directory of Open Access Journals (Sweden)
H. O. Bakodah
2013-01-01
Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.
Localized atomic basis set in the projector augmented wave method
DEFF Research Database (Denmark)
Larsen, Ask Hjorth; Vanin, Marco; Mortensen, Jens Jørgen
2009-01-01
We present an implementation of localized atomic-orbital basis sets in the projector augmented wave (PAW) formalism within the density-functional theory. The implementation in the real-space GPAW code provides a complementary basis set to the accurate but computationally more demanding grid...
Cell detachment method using shock wave induced cavitation
Junge, L.; Junge, L.; Ohl, C.D.; Wolfrum, B.; Arora, M.; Ikink, R.
2003-01-01
The detachment of adherent HeLa cells from a substrate after the interaction with a shock wave is analyzed. Cavitation bubbles are formed in the trailing, negative pressure cycle following the shock front. We find that the regions of cell detachment are strongly correlated with spatial presence of
Energy Technology Data Exchange (ETDEWEB)
Cerda-Arias, Jose Luis
2012-07-01
Today's structure of power systems with competitive wholesale markets for electricity encourages the introduction of new agents and products, customers with self-generating capacity and the specialization of generators, network operators and power suppliers. Furthermore one has to take into account the variation of the fossil fuel prices in the world market, which even anticipates the closeness of its scarcity, the instability of the fulfilment of contracts, and the existence of import restrictions. In addition the implementation of policies aiming to control CO{sub 2} emissions, and efficient use of energy plus the advent of more efficient technologies have to be incorporated in new network expansion projects. These are forcing utilities and society to seek new forms of electric system expansion without affecting their economic growth. This expresses a challenge to sustain such a growth changing the vision for the power system and the required security of electricity supply, usually based on internal factors of the electric sector, without considering the connection between the current transmission and distribution networks, the uncertainties related to the competition in the electricity market and the effect of distributed generation units. The high penetration of distributed generation resources, based on renewable energy sources, is increasingly observed worldwide and it depends on the cost of the technologies, market design, and subsidies. On that account, it is necessary to find alternatives and offers to develop a sustainable strategic plan for power system expansion. Currently, efforts are oriented to develop planning models which consider the income of power generation based on renewable energy sources founded on these new requirements, bearing in mind the relationship between the competitive markets and the power system planning. In this Thesis a general planning method for the expansion of the power grids is proposed. This planning method should
Ashraf, M. A. M.; Kumar, N. S.; Yusoh, R.; Hazreek, Z. A. M.; Aziman, M.
2018-04-01
Site classification utilizing average shear wave velocity (Vs(30) up to 30 meters depth is a typical parameter. Numerous geophysical methods have been proposed for estimation of shear wave velocity by utilizing assortment of testing configuration, processing method, and inversion algorithm. Multichannel Analysis of Surface Wave (MASW) method is been rehearsed by numerous specialist and professional to geotechnical engineering for local site characterization and classification. This study aims to determine the site classification on soft and hard ground using MASW method. The subsurface classification was made utilizing National Earthquake Hazards Reduction Program (NERHP) and international Building Code (IBC) classification. Two sites are chosen to acquire the shear wave velocity which is in the state of Pulau Pinang for soft soil and Perlis for hard rock. Results recommend that MASW technique can be utilized to spatially calculate the distribution of shear wave velocity (Vs(30)) in soil and rock to characterize areas.
Analysis of efficient preconditioned defect correction methods for nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2014-01-01
Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow...... equations. We present new detailed fundamental analysis using finite-amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high-order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow...
Hsieh, Yi-Kai; Omura, Yoshiharu
2017-10-01
We investigate the properties of whistler mode wave-particle interactions at oblique wave normal angles to the background magnetic field. We find that electromagnetic energy of waves at frequencies below half the electron cyclotron frequency can flow nearly parallel to the ambient magnetic field. We thereby confirm that the gyroaveraging method, which averages the cyclotron motion to the gyrocenter and reduces the simulation from two-dimensional to one-dimensional, is valid for oblique wave-particle interaction. Multiple resonances appear for oblique propagation but not for parallel propagation. We calculate the possible range of resonances with the first-order resonance condition as a function of electron kinetic energy and equatorial pitch angle. To reveal the physical process and the efficiency of electron acceleration by multiple resonances, we assume a simple uniform wave model with constant amplitude and frequency in space and time. We perform test particle simulations with electrons starting at specific equatorial pitch angles and kinetic energies. The simulation results show that multiple resonances contribute to acceleration and pitch angle scattering of energetic electrons. Especially, we find that electrons with energies of a few hundred keV can be accelerated efficiently to a few MeV through the n = 0 Landau resonance.
Zou, Li; Tian, Shou-Fu; Feng, Lian-Li
2017-12-01
In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.
International Nuclear Information System (INIS)
Xia Liang; Chan, M.Y.; Deng Shiming
2008-01-01
A complete set of calculation method for steady-state equipment sensible heat ratio (SHR) for a direct expansion (DX) cooling coil has been developed and reported. The method was based on the fundamentals of energy conservation and heat and mass transfer taking place in the DX cooling coil, and was experimentally validated using an experimental DX A/C rig. With the method developed, the effect of refrigerant evaporating temperature at fixed inlet air conditions on equipment SHR has been theoretically analyzed. The validated method can be useful in further studying the inherent operating characteristics of a DX air conditioning (A/C) unit and in developing suitable control strategies for achieving higher energy efficiency and better indoor thermal environment
Approximated calculation of the vacuum wave function and vacuum energy of the LGT with RPA method
International Nuclear Information System (INIS)
Hui Ping
2004-01-01
The coupled cluster method is improved with the random phase approximation (RPA) to calculate vacuum wave function and vacuum energy of 2 + 1 - D SU(2) lattice gauge theory. In this calculating, the trial wave function composes of single-hollow graphs. The calculated results of vacuum wave functions show very good scaling behaviors at weak coupling region l/g 2 >1.2 from the third order to the sixth order, and the vacuum energy obtained with RPA method is lower than the vacuum energy obtained without RPA method, which means that this method is a more efficient one
Analysis of a plane stress wave by the moving least squares method
Directory of Open Access Journals (Sweden)
Wojciech Dornowski
2014-08-01
Full Text Available A meshless method based on the moving least squares approximation is applied to stress wave propagation analysis. Two kinds of node meshes, the randomly generated mesh and the regular mesh are used. The nearest neighbours’ problem is developed from a triangulation that satisfies minimum edges length conditions. It is found that this method of neighbours’ choice significantly improves the solution accuracy. The reflection of stress waves from the free edge is modelled using fictitious nodes (outside the plate. The comparison with the finite difference results also demonstrated the accuracy of the proposed approach.[b]Keywords[/b]: civil engineering, meshless method, moving least squares method, elastic waves
Development of fabrication method for thermal expansion difference irradiation temperature monitor
International Nuclear Information System (INIS)
Noguchi, Kouichi; Takatsudo, Hiroshi; Miyakawa, Shun-ichi; Kobori, Takahisa; Miyo, Toshimasa
1998-03-01
This report describes the development activities for the fabrication of the Thermal Expansion Difference irradiation temperature monitor (TED) at the Oarai Engineering Center (OEC)/PNC. TED is used for various irradiation tests in the experimental fast reactor JOYO. TED is the most accurate off-line temperature monitor used for irradiation examination. The TED is composed of a metallic sphere lid and either a stainless steel or nickel alloy container. Once the container is filled with sodium, the metallic sphere lid is sealed by using a resistance weld. This capsule is then loaded into a reactor. Once a TED is loaded into the JOYO reactor, the sodium inside the metallic container increases as a result of thermal expansion. The TED identifies the peak irradiation temperature of the reactor based on a formula correlating temperature to increment values. This formula is established specifically for the particular TED being used during a calibration process performed when the TED is fabricated. Initially the TED was developed by Argonne National Laboratory (ANL) in the United States, and was imported by PNC for use in the JOYO reactor. In 1992 PNC decided to fabricate TED domestically in order to ensure the stability of future supplies. Based on technical information provided by ANL, PNC began fabrication of a TED on an experimental basis. In addition, PNC endeavored to make the domestically produced TED more efficient. This involved improving the techniques used in the sodium filling and the metallic sphere welding processes. These quality control efforts led to PNC's development of processes enabling the capsules to be filled with sodium to nearly 100%. As a result, the accuracy of the temperature dispersion in the out-pile calibration test was improved from +/-10degC to +/-5degC. In 1996 the new domestically fabricated TED was attached to a JOYO irradiation rig. In March of 1997, irradiation of the rig was started on the 30th duty cycle operation, and should be
Directory of Open Access Journals (Sweden)
Zhong-ye Tian
2014-01-01
Full Text Available The seismic responses of a long-span cable-stayed bridge under uniform excitation and traveling wave excitation in the longitudinal direction are, respectively, computed. The numerical results show that the bridge’s peak seismic responses vary significantly as the apparent wave velocity decreases. Therefore, the traveling wave effect must be considered in the seismic design of long-span bridges. The bridge’s peak seismic responses do not vary monotonously with the apparent wave velocity due to the traveling wave resonance. A new traveling wave excitation method that can simplify the multisupport excitation process into a two-support excitation process is developed.
DEFF Research Database (Denmark)
Ibsen, Lars Bo
2008-01-01
Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many...... times smaller it remains very high. For example, whilst there is enough potential wave power off the UK to supply the electricity demands several times over, the economically recoverable resource for the UK is estimated at 25% of current demand; a lot less, but a very substantial amount nonetheless....
Energy Technology Data Exchange (ETDEWEB)
Tanabe, R.; Yasuda, K.; Yokoyama, R. (Tokyo Metropolitan Univ., Tokyo (Japan))
1992-05-20
To supply cheap, high-reliable and a planty of the electricity is an important task of the electric supply system because the requirement for the electricity is rapidly increased in Japan. In order to solve this problem, the authors of the paper are developing a most suitable practical method based on algorithm, according to which the generation expansion planning is divided into two problems: the optimal generation mix and the optimal generation construction process and the two problems are solved respectively. But there are some bad points in the method, for example, there are only approximative practical restriction of the capacity of single machine and the existing electric supply etc., because the optimal generation mix is determined on the basis of non-linear planning. So, in the present paper, the electric supply support system is practically constructed while proposing an unified generation expansion planning based on the dynamic programming that is possible to consider these restrictions strictly and the usefullness of the method is inspected. 12 refs., 7 figs., 5 tabs.
Failed fuel rod detection method by ultrasonic wave
International Nuclear Information System (INIS)
Takamatsu, Masatoshi; Muraoka, Shoichi; Ono, Yukio; Yasojima, Yujiro.
1990-01-01
Ultrasonic wave signals sent from an ultrasonic receiving element are supplied to an evaluation circuit by way of a gate. A table for gate opening and closing timings at the detecting position in each of the fuel rods in a fuel assembly is stored in a memory. A fuel rod is placed between an ultrasonic transmitting element and the receiving element to determine the positions of the transmitting element and the receiving element by positional sensors. The opening and closing timings at the positions corresponding to the result of the detection are read out from the table, and the gates are opened and closed by the timing. This can introduce the ultrasonic wave signals transmitted through a control rod always to the evaluation circuit passing through the gate. Accordingly, the state of failure of the fuel rod can be detected accurately. (I.N.)
Singular value decomposition methods for wave propagation analysis
Czech Academy of Sciences Publication Activity Database
Santolík, Ondřej; Parrot, M.; Lefeuvre, F.
2003-01-01
Roč. 38, č. 1 (2003), s. 10-1-10-13 ISSN 0048-6604 R&D Projects: GA ČR GA205/01/1064 Grant - others:Barrande(CZ) 98039/98055 Institutional research plan: CEZ:AV0Z3042911; CEZ:MSM 113200004 Keywords : wave propagation * singular value decomposition Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 0.832, year: 2003
Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method
Miyazaki, Yutaka; Tsuchiya, Takao
2012-07-01
The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
Characterization of non-Q wave infarction by radioisotopic methods
International Nuclear Information System (INIS)
Parodi, O.; Marzullo, P.; Marcassa, C.; Sambuceti, G.
1986-01-01
The syndrome of ''subendocardial infarction'' or ''non Q-wave infarction'', which has been defined only in terms of the presence of (ECG) electrocardiographic evidence of necrosis, has been shown to be poorly corelated with anatomical and pathomorphological findings. In a large number of patients who had been diagnosed as having this commonly described entity, the usefulness of a multiparametric approach was evaluated. The proper assessment of such patients may necessitate flow studies with T1-201, which is, however, a marker with known limitations: labelled microspheres; or Rb-82, a generator-produced positron emitter. Metabolic studies using fluoro-F-18-deoxyglucose or C-11 palmitate will defect impairment of fatty acid oxidation and residual glucose metabolism; wall motion studies will demonstrate impairment to a variable extent. The presence or absence of Q-waves does not distinguish between transmural and subendocardial infarction. The size and location of ST-T wave changes does not indicate the site of infarction. Patients with this syndrome exhibit a wide spectrum of wal motion abnormalities and usually have diffuse coronary lesions. Since conventional clinical investigations cannot be used to predict the presence and extent of necrosis, or its exact location, the studies performed should be directed toward the appropriate evaluation of perfusion and metabolic patterns. This emphasizes the important point that clinicians may investigate this syndrome by the use of the proper approach. (orig.)
An efficient wave extrapolation method for anisotropic media with tilt
Waheed, Umair bin
2015-03-23
Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source-dependent effective velocities for the elliptic medium using kinematic high-frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade-off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference-based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.
An efficient wave extrapolation method for anisotropic media with tilt
Waheed, Umair bin; Alkhalifah, Tariq Ali
2015-01-01
Wavefield extrapolation operators for elliptically anisotropic media offer significant cost reduction compared with that for the transversely isotropic case, particularly when the axis of symmetry exhibits tilt (from the vertical). However, elliptical anisotropy does not provide accurate wavefield representation or imaging for transversely isotropic media. Therefore, we propose effective elliptically anisotropic models that correctly capture the kinematic behaviour of wavefields for transversely isotropic media. Specifically, we compute source-dependent effective velocities for the elliptic medium using kinematic high-frequency representation of the transversely isotropic wavefield. The effective model allows us to use cheaper elliptic wave extrapolation operators. Despite the fact that the effective models are obtained by matching kinematics using high-frequency asymptotic, the resulting wavefield contains most of the critical wavefield components, including frequency dependency and caustics, if present, with reasonable accuracy. The methodology developed here offers a much better cost versus accuracy trade-off for wavefield computations in transversely isotropic media, particularly for media of low to moderate complexity. In addition, the wavefield solution is free from shear-wave artefacts as opposed to the conventional finite-difference-based transversely isotropic wave extrapolation scheme. We demonstrate these assertions through numerical tests on synthetic tilted transversely isotropic models.
A Method and an Apparatus for Generating a Phase-Modulated Wave Front of Electromagnetic Radiation
DEFF Research Database (Denmark)
2002-01-01
The present invention provides a method and a system for generating a phase-modulated wave front. According to the present invention, the spatial phase-modulation is not performed on the different parts of the wave front individually as in known POSLMs. Rather, the spatial phase-modulation of the...
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
The two-wave X-ray field calculated by means of integral-equation methods
International Nuclear Information System (INIS)
Bremer, J.
1984-01-01
The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendelloesung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented. (Auth.)
Kerimov, M. K.
2018-01-01
This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.
A coupled DEM-CFD method for impulse wave modelling
Zhao, Tao; Utili, Stefano; Crosta, GiovanBattista
2015-04-01
Rockslides can be characterized by a rapid evolution, up to a possible transition into a rock avalanche, which can be associated with an almost instantaneous collapse and spreading. Different examples are available in the literature, but the Vajont rockslide is quite unique for its morphological and geological characteristics, as well as for the type of evolution and the availability of long term monitoring data. This study advocates the use of a DEM-CFD framework for the modelling of the generation of hydrodynamic waves due to the impact of a rapid moving rockslide or rock-debris avalanche. 3D DEM analyses in plane strain by a coupled DEM-CFD code were performed to simulate the rockslide from its onset to the impact with still water and the subsequent wave generation (Zhao et al., 2014). The physical response predicted is in broad agreement with the available observations. The numerical results are compared to those published in the literature and especially to Crosta et al. (2014). According to our results, the maximum computed run up amounts to ca. 120 m and 170 m for the eastern and western lobe cross sections, respectively. These values are reasonably similar to those recorded during the event (i.e. ca. 130 m and 190 m respectively). In these simulations, the slope mass is considered permeable, such that the toe region of the slope can move submerged in the reservoir and the impulse water wave can also flow back into the slope mass. However, the upscaling of the grains size in the DEM model leads to an unrealistically high hydraulic conductivity of the model, such that only a small amount of water is splashed onto the northern bank of the Vajont valley. The use of high fluid viscosity and coarse grain model has shown the possibility to model more realistically both the slope and wave motions. However, more detailed slope and fluid properties, and the need for computational efficiency should be considered in future research work. This aspect has also been
Extended Krenciglowa-Kuo method and perturbation expansion of Q-box
International Nuclear Information System (INIS)
Shimizu, Genki; Otsuka, Takaharu; Takayanagi, Kazuo
2015-01-01
The Extended Krenciglowa-Kuo (EKK) method is a microscopic method to construct the energy-independent effective Hamiltonian H eff ; provided with an exact Q-box of the system, we can show which eigenstates are described by H eff given by the EKK method. In actual calculations, however, we can calculate the Q-box only up to a finite order in the perturbation theory. In this work, we examine the EKK method with the approximate Q-box, and show that the perturbative calculation of the Q-box does not harm the convergence properties of the EKK iterative method. (author)
A New Alternative in Urban Geophysics: Multi-Channel Analysis of Surface Waves (MASW) Method
International Nuclear Information System (INIS)
Ozcep, F.
2007-01-01
Geophysical studies are increasingly being applied to geotechnical investigations as they can identify soil properties and soil boundaries. Other advantage is that many of these methods are non-invasive and environment friendly. Soil stiffness is one of the critical material parameters considered during an early stage of most foundation construction. It is related directly to the stability of structural load, especially as it relates to possible earthquake hazard. Soil lacking sufficient stiffness for a given load can experience a significant reduction in strength under earthquake shaking resulting in liquefaction, a condition responsible for tremendous amounts of damage from earthquakes around the world The multichannel analysis of surface waves (MASW) method originated from the traditional seismic exploration approach that employs multiple (twelve or more) receivers placed along a linear survey line. Main advantage is its capability of recognizing different types of seismic waves based on wave propagation characteristics such as velocity and attenuation. The MASW method utilizes this capability to discriminate the fundamental-mode Rayleigh wave against all other types of surface and body waves generated not only from the active seismic source but also from the ambient site conditions. Dispersive characteristics of seismic waves are imaged from an objective 2-D wave field transformation. The present paper indicates results from MASW survey at different urban site in Turkey. MASW techniques will prove to be important tools for obtaining shear wave velocity and evaluating liquefaction potential, soil bearing capacity and soil amplification, etc. for future geophysical and geotechnical engineering community
International Nuclear Information System (INIS)
Ostachowicz, W; Kudela, P
2010-01-01
A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.
(G /G) -expansion method and its application to Sharma–Tasso ...
Indian Academy of Sciences (India)
Liaoning 110034, People's Republic of China. ∗. Corresponding ... The validity and advantage of the proposed method are illustrated by its ... competitive point of this method is that there is no need to set a restriction to the function fitted for G.
Two-Dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options
Ruijter, M.J.; Oosterlee, C.W.
2012-01-01
The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher
On analyticity of linear waves scattered by a layered medium
Nicholls, David P.
2017-10-01
The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.
SCATTERING OF SPIN WAVES BY MAGNETIC DEFECTS
Energy Technology Data Exchange (ETDEWEB)
Callaway, Joseph
1962-12-15
The scattering of spin waves by magnetic point defects is considered using a Green's function method. A partial wave expansion for the scattering amplitude is derived. An expression for the cross section is determined that includes the effect of resonant states. Application is made to the calculation of the thermal conductivity of an insulating ferromagnet. (auth)
Numerical simulation of electromagnetic wave propagation using time domain meshless method
International Nuclear Information System (INIS)
Ikuno, Soichiro; Fujita, Yoshihisa; Itoh, Taku; Nakata, Susumu; Nakamura, Hiroaki; Kamitani, Atsushi
2012-01-01
The electromagnetic wave propagation in various shaped wave guide is simulated by using meshless time domain method (MTDM). Generally, Finite Differential Time Domain (FDTD) method is applied for electromagnetic wave propagation simulation. However, the numerical domain should be divided into rectangle meshes if FDTD method is applied for the simulation. On the other hand, the node disposition of MTDM can easily describe the structure of arbitrary shaped wave guide. This is the large advantage of the meshless time domain method. The results of computations show that the damping rate is stably calculated in case with R < 0.03, where R denotes a support radius of the weight function for the shape function. And the results indicate that the support radius R of the weight functions should be selected small, and monomials must be used for calculating the shape functions. (author)
Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method
Directory of Open Access Journals (Sweden)
Sadaf Bibi
2014-03-01
Full Text Available Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme.
Directional spectrum of ocean waves from array measurements using phase/time/path difference methods
Digital Repository Service at National Institute of Oceanography (India)
Fernandes, A.A.; Sarma, Y.V.B.; Menon, H.B.
Wave direction has for the first time been consistently, accurately and unambiguously evaluated from array measurements using the phase/time/path difference (PTPD) methods of Esteva in case of polygonal arrays and Borgman in case of linear arrays...
Wave resistance calculation method combining Green functions based on Rankine and Kelvin source
Directory of Open Access Journals (Sweden)
LI Jingyu
2017-12-01
Full Text Available [Ojectives] At present, the Boundary Element Method(BEM of wave-making resistance mostly uses a model in which the velocity distribution near the hull is solved first, and the pressure integral is then calculated using the Bernoulli equation. However,the process of this model of wave-making resistance is complex and has low accuracy.[Methods] To address this problem, the present paper deduces a compound method for the quick calculation of ship wave resistance using the Rankine source Green function to solve the hull surface's source density, and combining the Lagally theorem concerning source point force calculation based on the Kelvin source Green function so as to solve the wave resistance. A case for the Wigley model is given.[Results] The results show that in contrast to the thin ship method of the linear wave resistance theorem, this method has higher precision, and in contrast to the method which completely uses the Kelvin source Green function, this method has better computational efficiency.[Conclusions] In general, the algorithm in this paper provides a compromise between precision and efficiency in wave-making resistance calculation.
Relativistic rise measurement by cluster counting method in time expansion chamber
International Nuclear Information System (INIS)
Rehak, P.; Walenta, A.H.
1979-10-01
A new approach to the measurement of the ionization energy loss for the charged particle identification in the region of the relativistic rise was tested experimentally. The method consists of determining in a special drift chamber (TEC) the number of clusters of the primary ionization. The method gives almost the full relativistic rise and narrower landau distribution. The consequences for a practical detector are discussed
Yanagihara, Kota; Kubo, Shin; Dodin, Ilya; Nakamura, Hiroaki; Tsujimura, Toru
2017-10-01
Geometrical Optics Ray-tracing is a reasonable numerical analytic approach for describing the Electron Cyclotron resonance Wave (ECW) in slowly varying spatially inhomogeneous plasma. It is well known that the result with this conventional method is adequate in most cases. However, in the case of Helical fusion plasma which has complicated magnetic structure, strong magnetic shear with a large scale length of density can cause a mode coupling of waves outside the last closed flux surface, and complicated absorption structure requires a strong focused wave for ECH. Since conventional Ray Equations to describe ECW do not have any terms to describe the diffraction, polarization and wave decay effects, we can not describe accurately a mode coupling of waves, strong focus waves, behavior of waves in inhomogeneous absorption region and so on. For fundamental solution of these problems, we consider the extension of the Ray-tracing method. Specific process is planned as follows. First, calculate the reference ray by conventional method, and define the local ray-base coordinate system along the reference ray. Then, calculate the evolution of the distributions of amplitude and phase on ray-base coordinate step by step. The progress of our extended method will be presented.
Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method
DEFF Research Database (Denmark)
Goo, Seongyeol; Wang, Semyung; Kook, Junghwan
2017-01-01
This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which...
A method of acoustic wave registration and determination their generation region
International Nuclear Information System (INIS)
Kozin, I.D.; Marchenko, M.V.
1998-01-01
Here is presented a method of acoustic wave registration with using of a synchronous LF broadcasting system. This method of detection and determination of underground nuclear explosion location is based on a registration of ionospheric disturbances induced by acoustic waves at the region of LF sign al reflection. The measuring complex created in the institute of the Ionosphere /1/ allows to register amplitude-frequency characteristics of composite signal from synchronous broadcasting net
Measuring longitudinal wave speed in solids: two methods and a half
International Nuclear Information System (INIS)
Fazio, C; Guastella, I; Sperandeo-Mineo, R M; Tarantino, G
2006-01-01
Three methods to analyse longitudinal wave propagation in metallic rods are discussed. Two of these methods also prove to be useful for measuring the sound propagation speed. The experimental results, as well as some interpretative models built in the context of a workshop on mechanical waves at the Graduate School for Pre-Service Physics Teacher Education, Palermo University, are described. Some considerations about observed modifications in trainee teachers' attitudes to utilizing physics experiments to build pedagogical activities are discussed
Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method
International Nuclear Information System (INIS)
Fan Engui
2002-01-01
A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)
International Nuclear Information System (INIS)
Ishikawa, Nobuyuki; Suzuki, Katsuo
1999-01-01
Having advantages of setting independently feedback characteristics such as disturbance rejection specification and reference response characteristics, two-degree-of-freedom (2DOF) control is widely utilized to improve the control performance. The ordinary design method such as model matching usually derives high-ordered feedforward element of 2DOF controller. In this paper, we propose a new design method for low order feedforward element which is based on Pade approximation of the denominator series expansion. The features of the proposed method are as follows: (1) it is suited to realize reference response characteristics in low frequency region, (2) the order of the feedforward element can be selected apart from the feedback element. These are essential to the 2DOF controller design. With this method, 2DOF reactor power controller is designed and its control performance is evaluated by numerical simulation with reactor dynamics model. For this evaluation, it is confirmed that the controller designed by the proposed method possesses equivalent control characteristics to the controller by the ordinary model matching method. (author)
Simulation of transients with space-dependent feedback by coarse mesh flux expansion method
International Nuclear Information System (INIS)
Langenbuch, S.; Maurer, W.; Werner, W.
1975-01-01
For the simulation of the time-dependent behaviour of large LWR-cores, even the most efficient Finite-Difference (FD) methods require a prohibitive amount of computing time in order to achieve results of acceptable accuracy. Static CM-solutions computed with a mesh-size corresponding to the fuel element structure (about 20 cm) are at least as accurate as FD-solutions computed with about 5 cm mesh-size. For 3d-calculations this results in a reduction of storage requirements by a factor 60 and of computing costs by a factor 40, relative to FD-methods. These results have been obtained for pure neutronic calculations, where feedback is not taken into account. In this paper it is demonstrated that the method retains its accuracy also in kinetic calculations, even in the presence of strong space dependent feedback. (orig./RW) [de
Chen, Zhongxian; Yu, Haitao; Wen, Cheng
2014-01-01
The goal of direct drive ocean wave energy extraction system is to convert ocean wave energy into electricity. The problem explored in this paper is the design and optimal control for the direct drive ocean wave energy extraction system. An optimal control method based on internal model proportion integration differentiation (IM-PID) is proposed in this paper though most of ocean wave energy extraction systems are optimized by the structure, weight, and material. With this control method, the heavy speed of outer heavy buoy of the energy extraction system is in resonance with incident wave, and the system efficiency is largely improved. Validity of the proposed optimal control method is verified in both regular and irregular ocean waves, and it is shown that IM-PID control method is optimal in that it maximizes the energy conversion efficiency. In addition, the anti-interference ability of IM-PID control method has been assessed, and the results show that the IM-PID control method has good robustness, high precision, and strong anti-interference ability. PMID:25152913
Chen, Zhongxian; Yu, Haitao; Wen, Cheng
2014-01-01
The goal of direct drive ocean wave energy extraction system is to convert ocean wave energy into electricity. The problem explored in this paper is the design and optimal control for the direct drive ocean wave energy extraction system. An optimal control method based on internal model proportion integration differentiation (IM-PID) is proposed in this paper though most of ocean wave energy extraction systems are optimized by the structure, weight, and material. With this control method, the heavy speed of outer heavy buoy of the energy extraction system is in resonance with incident wave, and the system efficiency is largely improved. Validity of the proposed optimal control method is verified in both regular and irregular ocean waves, and it is shown that IM-PID control method is optimal in that it maximizes the energy conversion efficiency. In addition, the anti-interference ability of IM-PID control method has been assessed, and the results show that the IM-PID control method has good robustness, high precision, and strong anti-interference ability.
Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations
Directory of Open Access Journals (Sweden)
Azizallah Alvandi
2017-06-01
Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.
Synthesis of Numerical Methods for Modeling Wave Energy Converter-Point Absorbers: Preprint
Energy Technology Data Exchange (ETDEWEB)
Li, Y.; Yu, Y. H.
2012-05-01
During the past few decades, wave energy has received significant attention among all ocean energy formats. Industry has proposed hundreds of prototypes such as an oscillating water column, a point absorber, an overtopping system, and a bottom-hinged system. In particular, many researchers have focused on modeling the floating-point absorber as the technology to extract wave energy. Several modeling methods have been used such as the analytical method, the boundary-integral equation method, the Navier-Stokes equations method, and the empirical method. However, no standardized method has been decided. To assist the development of wave energy conversion technologies, this report reviews the methods for modeling the floating-point absorber.
Action First--Understanding Follows: An Expansion of Skills-Based Training Using Action Method.
Martin, Colin
1988-01-01
This paper discusses the concept of training trainers in the skills they need to perform competently as trainers and how they follow their skills mastery with discussion on their new theoretical insight. Moreno's action method (psychodrama, sociodrama, sociometry, and role training) is the model used. (JOW)
International Nuclear Information System (INIS)
Sakai, Shiro; Arita, Ryotaro; Aoki, Hideo
2006-01-01
We propose a new quantum Monte Carlo method especially intended to couple with the dynamical mean-field theory. The algorithm is not only much more efficient than the conventional Hirsch-Fye algorithm, but is applicable to multiorbital systems having an SU(2)-symmetric Hund's coupling as well
Lancellotti, V.; Hon, de B.P.; Tijhuis, A.G.
2009-01-01
Linear embedding via Green's operators (LEGO) is a computational method in which the multiple scattering between adjacent objects - forming a large composite structure - is determined through the interaction of simple-shaped building domains, whose electromagnetic (EM) behavior is accounted for by
Hong, Youngjoon; Nicholls, David P.
2017-09-01
The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.
Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor
2010-01-01
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Jiang, Lijian
2010-08-01
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Real-space grid implementation of the projector augmented wave method
DEFF Research Database (Denmark)
Mortensen, Jens Jørgen; Hansen, Lars Bruno; Jacobsen, Karsten Wedel
2005-01-01
A grid-based real-space implementation of the projector augmented wave sPAWd method of Blöchl fPhys. Rev. B 50, 17953 s1994dg for density functional theory sDFTd calculations is presented. The use of uniform three-dimensional s3Dd real-space grids for representing wave functions, densities...... valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency...... is comparable to standard plane-wave methods, but the memory requirements are higher....
Spectral element method for wave propagation on irregular domains
Indian Academy of Sciences (India)
Yan Hui Geng
2018-03-14
Mar 14, 2018 ... Abstract. A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the ...
Spectral element method for wave propagation on irregular domains
Indian Academy of Sciences (India)
A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are ...
DEFF Research Database (Denmark)
Kinoshita, Koji; Parra, Elisa; Needham, David
2017-01-01
The dynamic adsorption of ionic surfactants at air-water interfaces have been less-well studied than that of the simpler non-ionics since experimental limitations on dynamic surface tension (DST) measurements create inconsistencies in their kinetic analysis. Using our newly designed "Micropipette...... interfacial area-expansion method", we have measured and evaluated both equilibrium and dynamic adsorption of a well-known anionic surfactant, sodium dodecyl sulphate (SDS), in the absence or presence of 100mM NaCl. Our focus was to determine if and to what extent the inclusion of a new correction parameter...... for the "ideal ionic activity", A±i, can renormalize both equilibrium and dynamic surface tension measurements and provide better estimates of the diffusion coefficient of ionic surfactants in aqueous media obtained from electroneutral models, namely extended Frumkin isotherm and Ward-Tordai adsorption models...
Application of the Most Likely Extreme Response Method for Wave Energy Converters: Preprint
Energy Technology Data Exchange (ETDEWEB)
Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang; Lawson, Michael
2016-07-01
Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based on spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.
International Nuclear Information System (INIS)
Lee, Joo Hee
2006-02-01
There is growing interest in developing pebble bed reactors (PBRs) as a candidate of very high temperature gas-cooled reactors (VHTRs). Until now, most existing methods of nuclear design analysis for this type of reactors are base on old finite-difference solvers or on statistical methods. But for realistic analysis of PBRs, there is strong desire of making available high fidelity nodal codes in three-dimensional (r,θ,z) cylindrical geometry. Recently, the Analytic Function Expansion Nodal (AFEN) method developed quite extensively in Cartesian (x,y,z) geometry and in hexagonal-z geometry was extended to two-group (r,z) cylindrical geometry, and gave very accurate results. In this thesis, we develop a method for the full three-dimensional cylindrical (r,θ,z) geometry and implement the method into a code named TOPS. The AFEN methodology in this geometry as in hexagonal geometry is 'robus' (e.g., no occurrence of singularity), due to the unique feature of the AFEN method that it does not use the transverse integration. The transverse integration in the usual nodal methods, however, leads to an impasse, that is, failure of the azimuthal term to be transverse-integrated over r-z surface. We use 13 nodal unknowns in an outer node and 7 nodal unknowns in an innermost node. The general solution of the node can be expressed in terms of that nodal unknowns, and can be updated using the nodal balance equation and the current continuity condition. For more realistic analysis of PBRs, we implemented em Marshak boundary condition to treat the incoming current zero boundary condition and the partial current translation (PCT) method to treat voids in the core. The TOPS code was verified in the various numerical tests derived from Dodds problem and PBMR-400 benchmark problem. The results of the TOPS code show high accuracy and fast computing time than the VENTURE code that is based on finite difference method (FDM)
Generalized separable expansion method of the two-body and the three-body scattering amplitudes
International Nuclear Information System (INIS)
Oryu, S.; Ishihara, T.
1976-01-01
A systematic method is proposed for obtaining new N-rank separable amplitudes of the two-body and the three-body equations. First of all, the authors start from the Amado equation which is modified from the three-body Faddeev equation by using the two-body Yamaguchi potential for the nucleon-nucleon interaction. It is well known that the Amado equation can be integrated on the real axis because the kernel has a logarithmic cut on the real axis. However, a separable three-body form factor which is regular on the real axis except for the cut has been found. (Auth.)
An energy recondensation method using the discrete generalized multigroup energy expansion theory
International Nuclear Information System (INIS)
Zhu Lei; Forget, Benoit
2011-01-01
Highlights: → Discrete-generalized multigroup method was implemented as a recondensation scheme. → Coarse group cross-sections were recondensed from core-level solution. → Neighboring effect of reflector and MOX bundle was improved. → Methodology was shown to be fully consistent when a flat angular flux approximation is used. - Abstract: In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially.
Application of the Exp-function method to the equal-width wave equation
International Nuclear Information System (INIS)
Biazar, J; Ayati, Z
2008-01-01
In this paper, the Exp-function method is used to find an exact solution of the equal-width wave (EW) equation. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving the EW equation.
Energy Technology Data Exchange (ETDEWEB)
Sidler, Rolf, E-mail: rsidler@gmail.com [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland); Carcione, José M. [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy); Holliger, Klaus [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)
2013-02-15
We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.
A maximal chromatic expansion method of mapping multichannel imagery into color space. [North Dakota
Juday, R. D.; Abotteen, R. A. (Principal Investigator)
1978-01-01
The author has identified the following significant results. A color film generation method that maximally expands the chromaticity and aligns Kauth brightness with the gray axis was presented. In comparison with the current LACIE film product, the new color film product has more contrast and more colors and appears to be brighter. The field boundaries in the new product were more pronounced than in the current LACIE product. The speckle effect was one problem in the new product. The yellowness speckle can be treated using an equation. This equation can be used to eliminate any speckle introduced by the greenness. This product leads logically toward another that will employ quantitative colorimetry which will account for some of the eye's perception of color stimuli.
MacGinnis, Matt; Chu, Howard; Youssef, George; Wu, Kimberley W; Machado, Andre Wilson; Moon, Won
2014-08-29
Orthodontic palatal expansion appliances have been widely used with satisfactory and, most often, predictable clinical results. Recently, clinicians have successfully utilized micro-implants with palatal expander designs to work as anchors to the palate to achieve more efficient skeletal expansion and to decrease undesired dental effects. The purpose of the study was to use finite element method (FEM) to determine the stress distribution and displacement within the craniofacial complex when simulated conventional and micro-implant-assisted rapid palatal expansion (MARPE) expansion forces are applied to the maxilla. The simulated stress distribution produced within the palate and maxillary buttresses in addition to the displacement and rotation of the maxilla could then be analyzed to determine if micro-implants aid in skeletal expansion. A three-dimensional (3D) mesh model of the cranium with associated maxillary sutures was developed using computed tomography (CT) images and Mimics modeling software. To compare transverse expansion stresses in rapid palatal expansion (RPE) and MARPE, expansion forces were distributed to differing points on the maxilla and evaluated with ANSYS simulation software. The stresses distributed from forces applied to the maxillary teeth are distributed mainly along the trajectories of the three maxillary buttresses. In comparison, the MARPE showed tension and compression directed to the palate, while showing less rotation, and tipping of the maxillary complex. In addition, the conventional hyrax displayed a rotation of the maxilla around the teeth as opposed to the midpalatal suture of the MARPE. This data suggests that the MARPE causes the maxilla to bend laterally, while preventing unwanted rotation of the complex. In conclusion, the MARPE may be beneficial for hyperdivergent patients, or those that have already experienced closure of the midpalatal suture, who require palatal expansion and would worsen from buccal tipping of the teeth
Advances in surface wave methods: Cascaded MASW-SASW
Westerhoff, R.S.; Brouwer, J.H.; Meekes, J.A.C.
2005-01-01
The application of the MASW method in areas that show strong lateral variations in subsurface properties is limited. Traditional SASW may yield a better lateral resolution but the dispersion curves (and thus the subsurface models) obtained with the method may be poor. The joint application of MASW
A Novel Grey Wave Method for Predicting Total Chinese Trade Volume
Directory of Open Access Journals (Sweden)
Kedong Yin
2017-12-01
Full Text Available The total trade volume of a country is an important way of appraising its international trade situation. A prediction based on trade volume will help enterprises arrange production efficiently and promote the sustainability of the international trade. Because the total Chinese trade volume fluctuates over time, this paper proposes a Grey wave forecasting model with a Hodrick–Prescott filter (HP filter to forecast it. This novel model first parses time series into long-term trend and short-term cycle. Second, the model uses a general GM (1,1 to predict the trend term and the Grey wave forecasting model to predict the cycle term. Empirical analysis shows that the improved Grey wave prediction method provides a much more accurate forecast than the basic Grey wave prediction method, achieving better prediction results than autoregressive moving average model (ARMA.
Non-overlapped P- and S-wave Poynting vectors and its solution on Grid Method
Lu, Yong Ming; Liu, Qiancheng
2017-01-01
Poynting vector represents the local directional energy flux density of seismic waves in geophysics. It is widely used in elastic reverse time migration (RTM) to analyze source illumination, suppress low-wavenumber noise, correct for image polarity and extract angle-domain common imaging gather (ADCIG). However, the P and S waves are mixed together during wavefield propagation such that the P and S energy fluxes are not clean everywhere, especially at the overlapped points. In this paper, we use a modified elastic wave equation in which the P and S vector wavefields are naturally separated. Then, we develop an efficient method to evaluate the separable P and S poynting vectors, respectively, based on the view that the group velocity and phase velocity have the same direction in isotropic elastic media. We furthermore formulate our method using an unstructured mesh based modeling method named the grid method. Finally, we verify our method using two numerical examples.
Non-overlapped P- and S-wave Poynting vectors and its solution on Grid Method
Lu, Yong Ming
2017-12-12
Poynting vector represents the local directional energy flux density of seismic waves in geophysics. It is widely used in elastic reverse time migration (RTM) to analyze source illumination, suppress low-wavenumber noise, correct for image polarity and extract angle-domain common imaging gather (ADCIG). However, the P and S waves are mixed together during wavefield propagation such that the P and S energy fluxes are not clean everywhere, especially at the overlapped points. In this paper, we use a modified elastic wave equation in which the P and S vector wavefields are naturally separated. Then, we develop an efficient method to evaluate the separable P and S poynting vectors, respectively, based on the view that the group velocity and phase velocity have the same direction in isotropic elastic media. We furthermore formulate our method using an unstructured mesh based modeling method named the grid method. Finally, we verify our method using two numerical examples.
Energy Technology Data Exchange (ETDEWEB)
Suthaker, N.; Tweedie, R. [Thurber Engineering Ltd., Edmonton, AB (Canada)
2009-07-01
Shear wave velocity measurements are an integral part of geotechnical studies for major structures and are an important tool in their design for site specific conditions such as site-specific earthquake response. This paper reported on a study in which shear wave velocities were measured at a proposed petrochemical plant site near Edmonton, Alberta. The proposed site is underlain by lacustrine clay, glacial till and upper Cretaceous clay shale and sandstone bedrock. The most commonly used methods for determining shear wave velocity include crosshole seismic tests, downhole seismic tests, and seismic cone penetration tests (SCPT). This paper presented the results of all 3 methods used in this study and provided a comparison of the various test methods and their limitations. The crosshole test results demonstrated a common trend of increasing shear wave velocity with depth to about 15 m, below which the velocities remained relatively constant. An anomaly was noted at one site, where the shear wave velocity was reduced at a zone corresponding to clay till containing stiff high plastic clay layers. The field study demonstrated that reasonable agreement in shear wave velocity measurements can be made using crosshole, downhole and seismic tests in the same soil conditions. The National Building Code states that the shear wave velocity is the fundamental method for determining site classification, thus emphasizing the importance of obtaining shear wave velocity measurements for site classification. It was concluded that an SCPT program can be incorporated into the field program without much increase in cost and can be supplemented by downhole or crosshole techniques. 5 refs., 2 tabs., 10 figs.
Multiquark masses and wave functions through modified Green's function Monte Carlo method
International Nuclear Information System (INIS)
Kerbikov, B.O.; Polikarpov, M.I.; Shevchenko, L.V.
1987-01-01
The Modified Green's function Monte Carlo method (MGFMC) is used to calculate the masses and ground-state wave functions of multiquark systems in the potential model. The previously developed MGFMC is generalized in order to treat systems containing quarks with inequal masses. The obtained results are presented with the Cornell potential for the masses and the wave functions of light and heavy flavoured baryons and multiquark states (N=6, 9, 12) made of light quarks
A Numerical Method for Blast Shock Wave Analysis of Missile Launch from Aircraft
Directory of Open Access Journals (Sweden)
Sebastian Heimbs
2015-01-01
Full Text Available An efficient empirical approach was developed to accurately represent the blast shock wave loading resulting from the launch of a missile from a military aircraft to be used in numerical analyses. Based on experimental test series of missile launches in laboratory environment and from a helicopter, equations were derived to predict the time- and position-dependent overpressure. The method was finally applied and validated in a structural analysis of a helicopter tail boom under missile launch shock wave loading.
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien
2016-09-01
The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.
Hofmann, Douglas C. (Inventor); Wilcox, Brian (Inventor)
2016-01-01
Bulk metallic glass-based strain wave gears and strain wave gear components. In one embodiment, a strain wave gear includes: a wave generator; a flexspline that itself includes a first set of gear teeth; and a circular spline that itself includes a second set of gear teeth; where at least one of the wave generator, the flexspline, and the circular spline, includes a bulk metallic glass-based material.
Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen
2018-06-01
In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.
Damage evaluation by a guided wave-hidden Markov model based method
Mei, Hanfei; Yuan, Shenfang; Qiu, Lei; Zhang, Jinjin
2016-02-01
Guided wave based structural health monitoring has shown great potential in aerospace applications. However, one of the key challenges of practical engineering applications is the accurate interpretation of the guided wave signals under time-varying environmental and operational conditions. This paper presents a guided wave-hidden Markov model based method to improve the damage evaluation reliability of real aircraft structures under time-varying conditions. In the proposed approach, an HMM based unweighted moving average trend estimation method, which can capture the trend of damage propagation from the posterior probability obtained by HMM modeling is used to achieve a probabilistic evaluation of the structural damage. To validate the developed method, experiments are performed on a hole-edge crack specimen under fatigue loading condition and a real aircraft wing spar under changing structural boundary conditions. Experimental results show the advantage of the proposed method.
An Improved Split-Step Wavelet Transform Method for Anomalous Radio Wave Propagation Modelling
Directory of Open Access Journals (Sweden)
A. Iqbal
2014-12-01
Full Text Available Anomalous tropospheric propagation caused by ducting phenomenon is a major problem in wireless communication. Thus, it is important to study the behavior of radio wave propagation in tropospheric ducts. The Parabolic Wave Equation (PWE method is considered most reliable to model anomalous radio wave propagation. In this work, an improved Split Step Wavelet transform Method (SSWM is presented to solve PWE for the modeling of tropospheric propagation over finite and infinite conductive surfaces. A large number of numerical experiments are carried out to validate the performance of the proposed algorithm. Developed algorithm is compared with previously published techniques; Wavelet Galerkin Method (WGM and Split-Step Fourier transform Method (SSFM. A very good agreement is found between SSWM and published techniques. It is also observed that the proposed algorithm is about 18 times faster than WGM and provide more details of propagation effects as compared to SSFM.
Gálvez-Coyt, Gonzalo; Muñoz-Diosdado, Alejandro; Peralta, José; Balderas-López, José; Angulo-Brown, Fernando
2012-06-01
Higuchi's method is a procedure that, if applied appropriately, can determine in a reliable way the fractal dimension D of time series; this fractal dimension permits to characterize the degree of correlation of the series. However, when analyzing some time series with Higuchi's method, there are oscillations at the right-hand side of the graph, which can cause a mistaken determination of the fractal dimension. In this work, an appropriate explanation is given to this type of behaviour. Using the seismogram as a time series and the properties of the P and S waves, it is possible to use the properties of Higuchi's method to previously detect the arrival of the earthquake shacking stage, some seconds in advance, approximately 30-35 s in the case of Mexico City. Thus, we propose the Higuchi's method to characterize and detect the P waves in order to estimate the strength of the forthcoming S waves.
Study of the method to estimate the hydraulic characteristics in rock masses by using elastic wave
International Nuclear Information System (INIS)
Katsu, Kenta; Ohnishi, Yuzo; Nishiyama, Satoshi; Yano, Takao; Ando, Kenichi; Yoshimura, Kimitaka
2008-01-01
In the area of radioactive waste repository, estimating radionuclide migration through the rock mass is an important factor for assessment of the repository. The purpose of this study is to develop a method to estimate hydraulic characteristics of rock masses by using elastic wave velocity dispersion. This method is based on dynamics poroelastic relations such as Biot and BISQ theories. These theories indicate relations between velocity dispersion and hydraulic characteristics. In order to verify the validity of these theories in crystalline rocks, we performed laboratory experiments. The results of experiments show the dependency of elastic wave velocity on its frequency. To test the applicability of this method to real rock masses, we performed in-situ experiment for tuff rock masses. The results of in-situ experiment show the possibility as a practical method to estimate the hydraulic characteristics by using elastic wave velocity dispersion. (author)
International Nuclear Information System (INIS)
Yun, Y.
2015-01-01
Thermal expansion of fuel pellet is an important property which limits the lifetime of the fuels in reactors, because it affects both the pellet and cladding mechanical interaction and the gap conductivity. By fitting a number of available measured data, recommended equations have been presented and successfully used to estimate thermal expansion coefficient of the nuclear fuel pellet. However, due to large scatter of the measured data, non-consensus data have been omitted in formulating the equations. Also, the equation is strongly governed by the lack of appropriate experimental data. For those reasons, it is important to develop theoretical methodologies to better describe thermal expansion behaviour of nuclear fuel. In particular, first-principles and molecular dynamics simulations have been certainly contributed to predict reliable thermal expansion without fitting the measured data. Furthermore, the two theoretical techniques have improved on understanding the change of fuel dimension by describing the atomic-scale processes associated with lattice expansion in the fuels. (author)
Three-dimensional stability of solitary kinetic Alfven waves and ion-acoustic waves
International Nuclear Information System (INIS)
Ghosh, G.; Das, K.P.
1994-01-01
Starting from a set of equations that lead to a linear dispersion relation coupling kinetic Alfven waves and ion-acoustic waves, three-dimensional KdV equations are derived for these waves. These equations are then used to investigate the three-dimensional stability of solitary kinetic Alfven waves and ion-acoustic waves by the small-k perturbation expansion method of Rowlands and Infeld. For kinetic Alfven waves it is found that there is instability if the direction of the plane-wave perturbation lies inside a cone, and the growth rate of the instability attains a maximum when the direction of the perturbation lies in the plane containing the external magnetic field and the direction of propagation of the solitary wave. For ion-acoustic waves the growth rate of instability attains a maximum when the direction of the perturbation lies in a plane perpendicular to the direction of propagation of the solitary wave. (Author)
Directory of Open Access Journals (Sweden)
Özkan Güner
2014-01-01
Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.
Time-dependent density-functional theory in the projector augmented-wave method
DEFF Research Database (Denmark)
Walter, Michael; Häkkinen, Hannu; Lehtovaara, Lauri
2008-01-01
We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we...
A cross-correlation method to search for gravitational wave bursts with AURIGA and Virgo
Bignotto, M.; Bonaldi, M.; Camarda, M.; Cerdonio, M.; Conti, L.; Drago, M.; Falferi, P.; Liguori, N.; Longo, S.; Mezzena, R.; Mion, A.; Ortolan, A.; Prodi, G. A.; Re, V.; Salemi, F.; Taffarello, L.; Vedovato, G.; Vinante, A.; Vitale, S.; Zendri, J. -P.; Acernese, F.; Alshourbagy, Mohamed; Amico, Paolo; Antonucci, Federica; Aoudia, S.; Astone, P.; Avino, Saverio; Baggio, L.; Ballardin, G.; Barone, F.; Barsotti, L.; Barsuglia, M.; Bauer, Th. S.; Bigotta, Stefano; Birindelli, Simona; Boccara, Albert-Claude; Bondu, F.; Bosi, Leone; Braccini, Stefano; Bradaschia, C.; Brillet, A.; Brisson, V.; Buskulic, D.; Cagnoli, G.; Calloni, E.; Campagna, Enrico; Carbognani, F.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cesarini, E.; Chassande-Mottin, E.; Clapson, A-C; Cleva, F.; Coccia, E.; Corda, C.; Corsi, A.; Cottone, F.; Coulon, J. -P.; Cuoco, E.; D'Antonio, S.; Dari, A.; Dattilo, V.; Davier, M.; Rosa, R.; Del Prete, M.; Di Fiore, L.; Di Lieto, A.; Emilio, M. Di Paolo; Di Virgilio, A.; Evans, M.; Fafone, V.; Ferrante, I.; Fidecaro, F.; Fiori, I.; Flaminio, R.; Fournier, J. -D.; Frasca, S.; Frasconi, F.; Gammaitoni, L.; Garufi, F.; Genin, E.; Gennai, A.; Giazotto, A.; Giordano, L.; Granata, V.; Greverie, C.; Grosjean, D.; Guidi, G.; Hamdani, S.U.; Hebri, S.; Heitmann, H.; Hello, P.; Huet, D.; Kreckelbergh, S.; La Penna, P.; Laval, M.; Leroy, N.; Letendre, N.; Lopez, B.; Lorenzini, M.; Loriette, V.; Losurdo, G.; Mackowski, J. -M.; Majorana, E.; Man, C. N.; Mantovani, M.; Marchesoni, F.; Marion, F.; Marque, J.; Martelli, F.; Masserot, A.; Menzinger, F.; Milano, L.; Minenkov, Y.; Moins, C.; Moreau, J.; Morgado, N.; Mosca, S.; Mours, B.; Neri, I.; Nocera, F.; Pagliaroli, G.; Palomba, C.; Paoletti, F.; Pardi, S.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Piergiovanni, F.; Pinard, L.; Poggiani, R.; Punturo, M.; Puppo, P.; Rapagnani, P.; Regimbau, T.; Remillieux, A.; Ricci, F.; Ricciardi, I.; Rocchi, A.; Rolland, L.; Romano, R.; Ruggi, P.; Russo, G.; Solimeno, S.; Spallicci, A.; Swinkels, B. L.; Tarallo, M.; Terenzi, R.; Toncelli, A.; Tonelli, M.; Tournefier, E.; Travasso, F.; Vajente, G.; van den Brand, J. F. J.; van der Putten, S.; Verkindt, D.; Vetrano, F.; Vicere, A.; Vinet, J. -Y.; Vocca, H.; Yvert, M.
2008-01-01
We present a method to search for transient gravitational waves using a network of detectors with different spectral and directional sensitivities: the interferometer Virgo and the bar detector AURIGA. The data analysis method is based on the measurements of the correlated energy in the network by
Wave propagation method as an accurate technique for effective refractive index retrieving
DEFF Research Database (Denmark)
Andryieuski, Andrei; Malureanu, Radu; Lavrinenko, Andrei
2009-01-01
An effective parameters retrieval method based on the wave propagation simulation is proposed and compared with the standard S-parameter procedure. The method is free from possible mistakes originated by the multiple branching of solutions in the S-parameter procedure and shows high accuracy. The...
Rayleigh-wave scattering by shallow cracks using the indirect boundary element method
International Nuclear Information System (INIS)
Ávila-Carrera, R; Rodríguez-Castellanos, A; Ortiz-Alemán, C; Sánchez-Sesma, F J
2009-01-01
The scattering and diffraction of Rayleigh waves by shallow cracks using the indirect boundary element method (IBEM) are investigated. The detection of cracks is of interest because their presence may compromise structural elements, put technological devices at risk or represent economical potential in reservoir engineering. Shallow cracks may give rise to scattered body and surface waves. These waves are sensitive to the crack's geometry, size and orientation. Under certain conditions, amplitude spectra clearly show conspicuous resonances that are associated with trapped waves. Several applications based on the scattering of surface waves (e.g. Rayleigh and Stoneley waves), such as non-destructive testing or oil well exploration, have shown that the scattered fields may provide useful information to detect cracks and other heterogeneities. The subject is not new and several analytical and numerical techniques have been applied for the last 50 years to understand the basis of multiple scattering phenomena. In this work, we use the IBEM to calculate the scattered fields produced by single or multiple cracks near a free surface. This method is based upon an integral representation of the scattered displacement fields, which is derived from Somigliana's identity. Results are given in both frequency and time domains. The analyses of the displacement field using synthetic seismograms and snapshots reveal some important effects from various configurations of cracks. The study of these simple cases may provide an archetype to geoscientists and engineers to understand the fundamental aspects of multiple scattering and diffraction by cracks
Vibration isolation design for periodically stiffened shells by the wave finite element method
Hong, Jie; He, Xueqing; Zhang, Dayi; Zhang, Bing; Ma, Yanhong
2018-04-01
Periodically stiffened shell structures are widely used due to their excellent specific strength, in particular for aeronautical and astronautical components. This paper presents an improved Wave Finite Element Method (FEM) that can be employed to predict the band-gap characteristics of stiffened shell structures efficiently. An aero-engine casing, which is a typical periodically stiffened shell structure, was employed to verify the validation and efficiency of the Wave FEM. Good agreement has been found between the Wave FEM and the classical FEM for different boundary conditions. One effective wave selection method based on the Wave FEM has thus been put forward to filter the radial modes of a shell structure. Furthermore, an optimisation strategy by the combination of the Wave FEM and genetic algorithm was presented for periodically stiffened shell structures. The optimal out-of-plane band gap and the mass of the whole structure can be achieved by the optimisation strategy under an aerodynamic load. Results also indicate that geometric parameters of stiffeners can be properly selected that the out-of-plane vibration attenuates significantly in the frequency band of interest. This study can provide valuable references for designing the band gaps of vibration isolation.
Chiral retrieval method based on right circularly polarized and left circularly polarized waves
International Nuclear Information System (INIS)
Martín, Ernesto; Muñoz, Juan; Margineda, José; Molina-Cuberos, Gregorio J; García-Collado, Ángel J
2014-01-01
The free-wave characterization of metamaterials is usually carried out by illuminating a sample with a linearly polarized plane electromagnetic wave. At points before and after the sample, sensors are introduced to measure the transverse components of the field, in order to compute the reflection and transmission coefficients related with the co- and cross-polar field components. Based on this information, retrieval algorithms allow parameters like rotation angle, effective chirality and refraction index to be calculated. Here we propose to use the transmission signals under illumination with plane circularly polarized waves, without sensing the reflection signal, to calculate the chirality parameter and the rotation angle due to the electromagnetic activity of the material. This new method, which allows a simpler characterization of a chiral slab, is applied to the study of metamaterials composed of both periodic and random distributions of metallic structures with chiral symmetry. The experimental results are contrasted with simulations and alternative measurements obtained using linearly polarized waves. (paper)
Burleyson, C. D.; Voisin, N.; Taylor, T.; Xie, Y.; Kraucunas, I.
2017-12-01
The DOE's Pacific Northwest National Laboratory (PNNL) has been developing the Building ENergy Demand (BEND) model to simulate energy usage in residential and commercial buildings responding to changes in weather, climate, population, and building technologies. At its core, BEND is a mechanism to aggregate EnergyPlus simulations of a large number of individual buildings with a diversity of characteristics over large spatial scales. We have completed a series of experiments to explore methods to calibrate the BEND model, measure its ability to capture interannual variability in energy demand due to weather using simulations of two distinct weather years, and understand the sensitivity to the number and location of weather stations used to force the model. The use of weather from "representative cities" reduces computational costs, but often fails to capture spatial heterogeneity that may be important for simulations aimed at understanding how building stocks respond to a changing climate (Fig. 1). We quantify the potential reduction in temperature and load biases from using an increasing number of weather stations across the western U.S., ranging from 8 to roughly 150. Using 8 stations results in an average absolute summertime temperature bias of 4.0°C. The mean absolute bias drops to 1.5°C using all available stations. Temperature biases of this magnitude translate to absolute summertime mean simulated load biases as high as 13.8%. Additionally, using only 8 representative weather stations can lead to a 20-40% bias of peak building loads under heat wave or cold snap conditions, a significant error for capacity expansion planners who may rely on these types of simulations. This analysis suggests that using 4 stations per climate zone may be sufficient for most purposes. Our novel approach, which requires no new EnergyPlus simulations, could be useful to other researchers designing or calibrating aggregate building model simulations - particularly those looking at
Algebraic method for constructing singular steady solitary waves: a case study
Clamond, Didier; Dutykh, Denys; Galligo, André
2016-07-01
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equation with surface tension, because it provides a tractable model that, at the same time, is not too simple, so interest in the method can be emphasized. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of physics. In capillary-gravity regime, there are two kinds of localized infinitely smooth travelling wave solutions-solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, then the `zoology' of solutions becomes much richer, and the main goal of this study is to provide a complete classification of such singular localized solutions using the methods of the effective algebraic geometry.
Overdetermined shooting methods for computing standing water waves with spectral accuracy
International Nuclear Information System (INIS)
Wilkening, Jon; Yu Jia
2012-01-01
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge–Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly
Application of numerical methods to the determination of molecular wave functions
International Nuclear Information System (INIS)
Douady, Jerome
1969-01-01
A simplified SCF Method is developed. The wave function of molecular systems and spin densities in the case of free radicals are computed from geometrical data. This method, including at the beginning a delocalization of electrons over all the molecular system, two methods which clear out bonding and anti-bonding interactions have been studied and programmed: a) overlap population analysis, b) localisation of molecular orbitals. These methods have been carried out in the case of organic compounds and free radicals. (author) [fr
Up-Wave and Autoregressive Methods for Short-Term Wave Forecasting for an Oscillating Water Column
Paparella, Francesco; Monk, Kieran; Winands, Victor; Lopes, M.F.P.; Conley, Daniel; Ringwood, John
2015-01-01
The real-time control of wave energy converters (WECs) requires the prediction of the wave elevation at the location of the device in order to maximize the power extracted from the waves. One possibility is to predict the future wave elevation by combining its past history with the spatial information coming from a sensor which measures the free surface elevation up-wave of the WEC. As an application example, this paper focuses on the prediction of the wave elevation inside the chamber of the...
Sorting method to extend the dynamic range of the Shack-Hartmann wave-front sensor
International Nuclear Information System (INIS)
Lee, Junwon; Shack, Roland V.; Descour, Michael R.
2005-01-01
We propose a simple and powerful algorithm to extend the dynamic range of a Shack-Hartmann wave-front sensor. In a conventional Shack-Hartmann wave-front sensor the dynamic range is limited by the f-number of a lenslet, because the focal spot is required to remain in the area confined by the single lenslet. The sorting method proposed here eliminates such a limitation and extends the dynamic range by tagging each spot in a special sequence. Since the sorting method is a simple algorithm that does not change the measurement configuration, there is no requirement for extra hardware, multiple measurements, or complicated algorithms. We not only present the theory and a calculation example of the sorting method but also actually implement measurement of a highly aberrated wave front from nonrotational symmetric optics
New method for rekindling the nonlinear solitary waves in Maxwellian complex space plasma
Das, G. C.; Sarma, Ridip
2018-04-01
Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main reason for this consideration is to exhibit the effects of dust charge fluctuations on acoustic modes evaluated by the use of a new method. A special method (G'/G) has been developed to yield the coherent features of nonlinear waves augmented through the derivation of a Korteweg-de Vries equation and found successfully the different nature of solitons recognized in space plasmas. Evolutions have shown with the input of appropriate typical plasma parameters to support our theoretical observations in space plasmas. All conclusions are in good accordance with the actual occurrences and could be of interest to further the investigations in experiments and satellite observations in space. In this paper, we present not only the model that exhibited nonlinear solitary wave propagation but also a new mathematical method to the execution.
Modeling of microwave applicators with an excitation through the wave guide using TLM method
Directory of Open Access Journals (Sweden)
Ranđelović Tijana
2005-01-01
Full Text Available In this paper, a real microwave applicator with a wave guide used to launch the energy from the source into the cavity is analyzed using 3D TLM method. In order to investigate the influence of the positions and number of feed wave guides to the number of the resonant modes inside the cavity, obtained results are compared with analytical results and results obtained by using TLM software with an impulse excitation as well. TLM method is applied to the both empty and loaded rectangular metallic cavity, and a very good agreement between simulated and experimental results is achieved.
The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2018-02-01
Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q
2013-03-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...
Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet
2017-11-01
In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.
DEFF Research Database (Denmark)
Ghadirian, Amin; Bredmose, Henrik; Schløer, Signe
2017-01-01
theory, that is, the most likely time history of inline force around a force peak of given value. The results of FORM and NewForce are linearly identical and show only minor deviations at second order. The FORM results are then compared to wave averaged measurements of the same criteria for crest height......In design of substructures for offshore wind turbines, the extreme wave loads which are of interest in Ultimate Limit States are often estimated by choosing extreme events from linear random sea states and replacing them by either stream function wave theory or the NewWave theory of a certain...... design wave height. As these wave theories super from limitations such as symmetry around the crest, other methods to estimate the wave loads are needed. In the present paper, the First Order Reliability Method, FORM, is used systematically to estimate the most likely extreme wave shapes. Two parameters...
Gao, Lingli; Pan, Yudi
2018-05-01
The correct estimation of the seismic source signature is crucial to exploration geophysics. Based on seismic interferometry, the virtual real source (VRS) method provides a model-independent way for source signature estimation. However, when encountering multimode surface waves, which are commonly seen in the shallow seismic survey, strong spurious events appear in seismic interferometric results. These spurious events introduce errors in the virtual-source recordings and reduce the accuracy of the source signature estimated by the VRS method. In order to estimate a correct source signature from multimode surface waves, we propose a mode-separated VRS method. In this method, multimode surface waves are mode separated before seismic interferometry. Virtual-source recordings are then obtained by applying seismic interferometry to each mode individually. Therefore, artefacts caused by cross-mode correlation are excluded in the virtual-source recordings and the estimated source signatures. A synthetic example showed that a correct source signature can be estimated with the proposed method, while strong spurious oscillation occurs in the estimated source signature if we do not apply mode separation first. We also applied the proposed method to a field example, which verified its validity and effectiveness in estimating seismic source signature from shallow seismic shot gathers containing multimode surface waves.
Vanel, Florence O.; Baysal, Oktay
1995-01-01
Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.
TSOS and TSOS-FK hybrid methods for modelling the propagation of seismic waves
Ma, Jian; Yang, Dinghui; Tong, Ping; Ma, Xiao
2018-05-01
We develop a new time-space optimized symplectic (TSOS) method for numerically solving elastic wave equations in heterogeneous isotropic media. We use the phase-preserving symplectic partitioned Runge-Kutta method to evaluate the time derivatives and optimized explicit finite-difference (FD) schemes to discretize the space derivatives. We introduce the averaged medium scheme into the TSOS method to further increase its capability of dealing with heterogeneous media and match the boundary-modified scheme for implementing free-surface boundary conditions and the auxiliary differential equation complex frequency-shifted perfectly matched layer (ADE CFS-PML) non-reflecting boundaries with the TSOS method. A comparison of the TSOS method with analytical solutions and standard FD schemes indicates that the waveform generated by the TSOS method is more similar to the analytic solution and has a smaller error than other FD methods, which illustrates the efficiency and accuracy of the TSOS method. Subsequently, we focus on the calculation of synthetic seismograms for teleseismic P- or S-waves entering and propagating in the local heterogeneous region of interest. To improve the computational efficiency, we successfully combine the TSOS method with the frequency-wavenumber (FK) method and apply the ADE CFS-PML to absorb the scattered waves caused by the regional heterogeneity. The TSOS-FK hybrid method is benchmarked against semi-analytical solutions provided by the FK method for a 1-D layered model. Several numerical experiments, including a vertical cross-section of the Chinese capital area crustal model, illustrate that the TSOS-FK hybrid method works well for modelling waves propagating in complex heterogeneous media and remains stable for long-time computation. These numerical examples also show that the TSOS-FK method can tackle the converted and scattered waves of the teleseismic plane waves caused by local heterogeneity. Thus, the TSOS and TSOS-FK methods proposed in
The Detection of Vertical Cracks in Asphalt Using Seismic Surface Wave Methods
International Nuclear Information System (INIS)
Iodice, M; Muggleton, J; Rustighi, E
2016-01-01
Assessment of the location and of the extension of cracking in road surfaces is important for determining the potential level of deterioration in the road overall and the infrastructure buried beneath it. Damage in a pavement structure is usually initiated in the tarmac layers, making the Rayleigh wave ideally suited for the detection of shallow surface defects. This paper presents an investigation of two surface wave methods to detect and locate top-down cracks in asphalt layers. The aim of the study is to compare the results from the well- established Multichannel Analysis of Surface Waves (MASW) and the more recent Multiple Impact of Surface Waves (MISW) in the presence of a discontinuity and to suggest the best surface wave technique for evaluating the presence and the extension of vertical cracks in roads. The study is conducted through numerical simulations alongside experimental investigations and it considers the cases for which the cracking is internal and external to the deployment of sensors. MISW is found to enhance the visibility of the reflected waves in the frequency wavenumber ( f-k ) spectrum, helping with the detection of the discontinuity. In some cases, by looking at the f-k spectrum obtained with MISW it is possible to extract information regarding the location and the depth of the cracking. (paper)
He, Yue-Jing; Hung, Wei-Chih; Syu, Cheng-Jyun
2017-12-01
The finite-element method (FEM) and eigenmode expansion method (EEM) were adopted to analyze the guided modes and spectrum of phase-shift fiber Bragg grating at five phase-shift degrees (including zero, 1/4π, 1/2π, 3/4π, and π). In previous studies on optical fiber grating, conventional coupled-mode theory was crucial. This theory contains abstruse knowledge about physics and complex computational processes, and thus is challenging for users. Therefore, a numerical simulation method was coupled with a simple and rigorous design procedure to help beginners and users to overcome difficulty in entering the field; in addition, graphical simulation results were presented. To reduce the difference between the simulated context and the actual context, a perfectly matched layer and perfectly reflecting boundary were added to the FEM and the EEM. When the FEM was used for grid cutting, the object meshing method and the boundary meshing method proposed in this study were used to effectively enhance computational accuracy and substantially reduce the time required for simulation. In summary, users can use the simulation results in this study to easily and rapidly design an optical fiber communication system and optical sensors with spectral characteristics.
A parallel orbital-updating based plane-wave basis method for electronic structure calculations
International Nuclear Information System (INIS)
Pan, Yan; Dai, Xiaoying; Gironcoli, Stefano de; Gong, Xin-Gao; Rignanese, Gian-Marco; Zhou, Aihui
2017-01-01
Highlights: • Propose three parallel orbital-updating based plane-wave basis methods for electronic structure calculations. • These new methods can avoid the generating of large scale eigenvalue problems and then reduce the computational cost. • These new methods allow for two-level parallelization which is particularly interesting for large scale parallelization. • Numerical experiments show that these new methods are reliable and efficient for large scale calculations on modern supercomputers. - Abstract: Motivated by the recently proposed parallel orbital-updating approach in real space method , we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue problems. In addition, we propose two new modified parallel orbital-updating methods. Compared to the traditional plane-wave methods, our methods allow for two-level parallelization, which is particularly interesting for large scale parallelization. Numerical experiments show that these new methods are more reliable and efficient for large scale calculations on modern supercomputers.
Directory of Open Access Journals (Sweden)
Z. EZZOUINE
2015-07-01
Full Text Available In this study, we present a newly designed electromagnetic dilatometer with micrometer accuracy for the measurement of the coefficient of thermal expansion of a solid in the 30 °C – 96 °C temperature range .The device has a graphical user interface to view real time data measurement. Iron and copper were subjected to temperature change in the thermal expansion experiment causing them to expand linearly. The voltage delivered in the electromagnetic dilatometer system, which includes the information about linear expansion and temperature change were transferred to a computer via a data acquisition card, presented by a program created in the LabVIEW environment, and the amount of linear expansion was detected in real time. The minimal change in length of the sample that can be resolved is 5µm, which yields the sensitivity comprised between 10-4 µm and 10-5 µm. In order to calibrate the electromagnetic dilatometer, thermal expansion coefficients of copper and Iron have been measured. By this technique, the thermal expansion coefficient can be determined with an acceptable accuracy. The present results appear also to agree well with those reported previously in the literature.
Laugel, Amélie; Menendez, Melisa; Benoit, Michel; Mattarolo, Giovanni; Mendez, Fernando
2013-04-01
Wave climate forecasting is a major issue for numerous marine and coastal related activities, such as offshore industries, flooding risks assessment and wave energy resource evaluation, among others. Generally, there are two main ways to predict the impacts of the climate change on the wave climate at regional scale: the dynamical and the statistical downscaling of GCM (Global Climate Model). In this study, both methods have been applied on the French coast (Atlantic , English Channel and North Sea shoreline) under three climate change scenarios (A1B, A2, B1) simulated with the GCM ARPEGE-CLIMAT, from Météo-France (AR4, IPCC). The aim of the work is to characterise the wave climatology of the 21st century and compare the statistical and dynamical methods pointing out advantages and disadvantages of each approach. The statistical downscaling method proposed by the Environmental Hydraulics Institute of Cantabria (Spain) has been applied (Menendez et al., 2011). At a particular location, the sea-state climate (Predictand Y) is defined as a function, Y=f(X), of several atmospheric circulation patterns (Predictor X). Assuming these climate associations between predictor and predictand are stationary, the statistical approach has been used to project the future wave conditions with reference to the GCM. The statistical relations between predictor and predictand have been established over 31 years, from 1979 to 2009. The predictor is built as the 3-days-averaged squared sea level pressure gradient from the hourly CFSR database (Climate Forecast System Reanalysis, http://cfs.ncep.noaa.gov/cfsr/). The predictand has been extracted from the 31-years hindcast sea-state database ANEMOC-2 performed with the 3G spectral wave model TOMAWAC (Benoit et al., 1996), developed at EDF R&D LNHE and Saint-Venant Laboratory for Hydraulics and forced by the CFSR 10m wind field. Significant wave height, peak period and mean wave direction have been extracted with an hourly-resolution at
Energy Technology Data Exchange (ETDEWEB)
Chen, Zaigao; Wang, Jianguo [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Northwest Institute of Nuclear Technology, P.O. Box 69-12, Xi' an, Shaanxi 710024 (China); Wang, Yue; Qiao, Hailiang; Zhang, Dianhui [Northwest Institute of Nuclear Technology, P.O. Box 69-12, Xi' an, Shaanxi 710024 (China); Guo, Weijie [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)
2013-11-15
Optimal design method of high-power microwave source using particle simulation and parallel genetic algorithms is presented in this paper. The output power, simulated by the fully electromagnetic particle simulation code UNIPIC, of the high-power microwave device is given as the fitness function, and the float-encoding genetic algorithms are used to optimize the high-power microwave devices. Using this method, we encode the heights of non-uniform slow wave structure in the relativistic backward wave oscillators (RBWO), and optimize the parameters on massively parallel processors. Simulation results demonstrate that we can obtain the optimal parameters of non-uniform slow wave structure in the RBWO, and the output microwave power enhances 52.6% after the device is optimized.
Nonlinear optimization method of ship floating condition calculation in wave based on vector
Ding, Ning; Yu, Jian-xing
2014-08-01
Ship floating condition in regular waves is calculated. New equations controlling any ship's floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship's displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.
Russell, C. T.; Strangeway, R. J.; Schwartz, S. J.
2017-12-01
The Magnetospheric Multiscale (MMS) spacecraft, with their state-of-the-art plasma and field instruments onboard, allow us to investigate electromagnetic waves at the bow shock and their association with small-scale disturbances in the shocked plasmas. Understanding these waves could improve our knowledge on the heating of electrons and ions across the shock ramp and the energy dissipation of supercritical shocks. We have found broad-band and narrow band waves across the shock ramp and slightly downstream. The broad-band waves propagate obliquely to the magnetic field direction and have frequencies up to the electron cyclotron frequency, while the narrow-band waves have frequencies of a few hundred Hertz, durations under a second, and are right-handed circularly polarized and propagate along the magnetic field lines. Both wave types are likely to be whistler mode with different generation mechanisms. When the solar wind pressure changes, MMS occasionally observed a pair of bow shocks when the magnetosphere was compressed and then expanded. We compare the wave observations under these two situations to understand their roles in the shock ramp as well as the upstream and downstream plasmas.
International Nuclear Information System (INIS)
Picolloto, A. M.; Mariucci, V. V. G.; Szpak, W.; Medina, A. N.; Baesso, M. L.; Astrath, N. G. C.; Astrath, F. B. G.; Bento, A. C.; Santos, A. D.; Moraes, J. C. S.
2013-01-01
The thermal wave method is applied for thermal properties measurement in fast endodontic cement (CER). This new formula is developed upon using Portland cement in gel and it was successfully tested in mice with good biocompatibility and stimulated mineralization. Recently, thermal expansion and setting time were measured, conferring to this material twice faster hardening than the well known Angelus Mineral trioxide aggregate (MTA) the feature of fast hardening (∼7 min) and with similar thermal expansion (∼12 μstrain/ °C). Therefore, it is important the knowledge of thermal properties like thermal diffusivity, conductivity, effusivity in order to match thermally the tissue environment upon its application in filling cavities of teeth. Photothermal radiometry technique based on Xe illumination was applied in CER disks 600 μm thick for heating, with prepared in four particle sizes (25, 38, 45, and 53) μm, which were added microemulsion gel with variation volumes (140, 150, 160, and 170) μl. The behavior of the thermal diffusivity CER disks shows linear decay for increase emulsion volume, and in contrast, thermal diffusivity increases with particles sizes. Aiming to compare to MTA, thermal properties of CER were averaged to get the figure of merit for thermal diffusivity as (44.2 ± 3.6) × 10 −3 cm 2 /s, for thermal conductivity (228 ± 32) mW/cm K, the thermal effusivity (1.09 ± 0.06) W s 0.5 /cm 2 K and volume heat capacity (5.2 ± 0.7) J/cm 3 K, which are in excellent agreement with results of a disk prepared from commercial MTA-Angelus (grain size < 10 μm using 57 μl of distilled water)
Picolloto, A. M.; Mariucci, V. V. G.; Szpak, W.; Medina, A. N.; Baesso, M. L.; Astrath, N. G. C.; Astrath, F. B. G.; Santos, A. D.; Moraes, J. C. S.; Bento, A. C.
2013-11-01
The thermal wave method is applied for thermal properties measurement in fast endodontic cement (CER). This new formula is developed upon using Portland cement in gel and it was successfully tested in mice with good biocompatibility and stimulated mineralization. Recently, thermal expansion and setting time were measured, conferring to this material twice faster hardening than the well known Angelus Mineral trioxide aggregate (MTA) the feature of fast hardening (˜7 min) and with similar thermal expansion (˜12 μstrain/ °C). Therefore, it is important the knowledge of thermal properties like thermal diffusivity, conductivity, effusivity in order to match thermally the tissue environment upon its application in filling cavities of teeth. Photothermal radiometry technique based on Xe illumination was applied in CER disks 600 μm thick for heating, with prepared in four particle sizes (25, 38, 45, and 53) μm, which were added microemulsion gel with variation volumes (140, 150, 160, and 170) μl. The behavior of the thermal diffusivity CER disks shows linear decay for increase emulsion volume, and in contrast, thermal diffusivity increases with particles sizes. Aiming to compare to MTA, thermal properties of CER were averaged to get the figure of merit for thermal diffusivity as (44.2 ± 3.6) × 10-3 cm2/s, for thermal conductivity (228 ± 32) mW/cm K, the thermal effusivity (1.09 ± 0.06) W s0.5/cm2 K and volume heat capacity (5.2 ± 0.7) J/cm3 K, which are in excellent agreement with results of a disk prepared from commercial MTA-Angelus (grain size < 10 μm using 57 μl of distilled water).
Energy Technology Data Exchange (ETDEWEB)
Picolloto, A. M.; Mariucci, V. V. G.; Szpak, W.; Medina, A. N.; Baesso, M. L.; Astrath, N. G. C.; Astrath, F. B. G.; Bento, A. C., E-mail: acbento@uem.br [Departamento de Física, Grupo de Espectroscopia Fotoacústica e Fototérmica, Universidade Estadual de Maringá – UEM, Av. Colombo 5790, 87020-900 Maringá, Paraná (Brazil); Santos, A. D.; Moraes, J. C. S. [Departamento de Física e Química, Universidade Estadual Paulista Júlio de Mesquita Filho – UNESP, Av. Brasil 56, 15385-000 Ilha Solteira, SP (Brazil)
2013-11-21
The thermal wave method is applied for thermal properties measurement in fast endodontic cement (CER). This new formula is developed upon using Portland cement in gel and it was successfully tested in mice with good biocompatibility and stimulated mineralization. Recently, thermal expansion and setting time were measured, conferring to this material twice faster hardening than the well known Angelus Mineral trioxide aggregate (MTA) the feature of fast hardening (∼7 min) and with similar thermal expansion (∼12 μstrain/ °C). Therefore, it is important the knowledge of thermal properties like thermal diffusivity, conductivity, effusivity in order to match thermally the tissue environment upon its application in filling cavities of teeth. Photothermal radiometry technique based on Xe illumination was applied in CER disks 600 μm thick for heating, with prepared in four particle sizes (25, 38, 45, and 53) μm, which were added microemulsion gel with variation volumes (140, 150, 160, and 170) μl. The behavior of the thermal diffusivity CER disks shows linear decay for increase emulsion volume, and in contrast, thermal diffusivity increases with particles sizes. Aiming to compare to MTA, thermal properties of CER were averaged to get the figure of merit for thermal diffusivity as (44.2 ± 3.6) × 10{sup −3} cm{sup 2}/s, for thermal conductivity (228 ± 32) mW/cm K, the thermal effusivity (1.09 ± 0.06) W s{sup 0.5}/cm{sup 2} K and volume heat capacity (5.2 ± 0.7) J/cm{sup 3} K, which are in excellent agreement with results of a disk prepared from commercial MTA-Angelus (grain size < 10 μm using 57 μl of distilled water)
International Nuclear Information System (INIS)
Jun-Mao, Wang; Miao, Zhang; Wen-Liang, Zhang; Rui, Zhang; Jia-Hua, Han
2008-01-01
We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified Benjamin–Bona–Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. (general)
A method to measure the diffusion coefficient by neutron wave propagation for limited samples
International Nuclear Information System (INIS)
Woznicka, U.
1986-03-01
A study has been made of the use of the neutron wave and pulse propagation method for measurement of thermal neutron diffusion parameters. Earlier works an homogenous and heterogeneous media are reviewed. A new method is sketched for the determination of the diffusion coefficient for samples of limited size. The principle is to place a relatively thin slab of the material between two blocks of a medium with known properties. The advantages and disadvantages of the method are discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation
Su, Bo; Tuo, Xianguo; Xu, Ling
2017-08-01
Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.
International Nuclear Information System (INIS)
Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar
2010-01-01
We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.
International Nuclear Information System (INIS)
Zhang Huiqun
2009-01-01
By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.
The development of efficient numerical time-domain modeling methods for geophysical wave propagation
Zhu, Lieyuan
This Ph.D. dissertation focuses on the numerical simulation of geophysical wave propagation in the time domain including elastic waves in solid media, the acoustic waves in fluid media, and the electromagnetic waves in dielectric media. This thesis shows that a linear system model can describe accurately the physical processes of those geophysical waves' propagation and can be used as a sound basis for modeling geophysical wave propagation phenomena. The generalized stability condition for numerical modeling of wave propagation is therefore discussed in the context of linear system theory. The efficiency of a series of different numerical algorithms in the time-domain for modeling geophysical wave propagation are discussed and compared. These algorithms include the finite-difference time-domain method, pseudospectral time domain method, alternating directional implicit (ADI) finite-difference time domain method. The advantages and disadvantages of these numerical methods are discussed and the specific stability condition for each modeling scheme is carefully derived in the context of the linear system theory. Based on the review and discussion of these existing approaches, the split step, ADI pseudospectral time domain (SS-ADI-PSTD) method is developed and tested for several cases. Moreover, the state-of-the-art stretched-coordinate perfect matched layer (SCPML) has also been implemented in SS-ADI-PSTD algorithm as the absorbing boundary condition for truncating the computational domain and absorbing the artificial reflection from the domain boundaries. After algorithmic development, a few case studies serve as the real-world examples to verify the capacities of the numerical algorithms and understand the capabilities and limitations of geophysical methods for detection of subsurface contamination. The first case is a study using ground penetrating radar (GPR) amplitude variation with offset (AVO) for subsurface non-aqueous-liquid (NAPL) contamination. The
A time reversal damage imaging method for structure health monitoring using Lamb waves
International Nuclear Information System (INIS)
Zhang Hai-Yan; Cao Ya-Ping; Sun Xiu-Li; Chen Xian-Hua; Yu Jian-Bo
2010-01-01
This paper investigates the Lamb wave imaging method combining time reversal for health monitoring of a metallic plate structure. The temporal focusing effect of the time reversal Lamb waves is investigated theoretically. It demonstrates that the focusing effect is related to the frequency dependency of the time reversal operation. Numerical simulations are conducted to study the time reversal behaviour of Lamb wave modes under broadband and narrowband excitations. The results show that the reconstructed time reversed wave exhibits close similarity to the reversed narrowband tone burst signal validating the theoretical model. To enhance the similarity, the cycle number of the excited signal should be increased. Experiments combining finite element model are then conducted to study the imaging method in the presence of damage like hole in the plate structure. In this work, the time reversal technique is used for the recompression of Lamb wave signals. Damage imaging results with time reversal using broadband and narrowband excitations are compared to those without time reversal. It suggests that the narrowband excitation combined time reversal can locate and determine the size of structural damage more precisely, but the cycle number of the excited signal should be chosen reasonably
Directory of Open Access Journals (Sweden)
Koichi Narahara
2012-01-01
Full Text Available Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs, together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.
Jia, Shouqing; La, Dongsheng; Ma, Xuelian
2018-04-01
The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.
International Nuclear Information System (INIS)
Hong, Ser Gi; Lee, Deokjung
2015-01-01
A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)
An extended Fourier modal method for plane-wave scattering from finite structures
Pisarenco, M.; Maubach, J.M.L.; Setija, I.D.; Mattheij, R.M.M.
2010-01-01
This paper extends the area of application of the Fourier modal method from periodic structures to aperiodic ones, in particular for plane-wave illumination at arbitrary angles. This is achieved by placing perfectly matched layers at the lateral sides of the computational domain and reformulating
Stress Wave Propagation in Soils Modelled by the Boundary Element Method
DEFF Research Database (Denmark)
Rasmussen, K. M.
This thesis deals with different aspects of the boundary element method (BEM) applied to stress wave propagation problems in soils. Among other things BEM formulations for coupled FEM and BEM, moving loads, direct BEM and indirect BEM are presented. For all the formulations both analytical...
A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data
Directory of Open Access Journals (Sweden)
Jingjing He
2017-09-01
Full Text Available This paper presents a systematic and general method for Lamb wave-based crack size quantification using finite element simulations and Bayesian updating. The method consists of construction of a baseline quantification model using finite element simulation data and Bayesian updating with limited Lamb wave data from target structure. The baseline model correlates two proposed damage sensitive features, namely the normalized amplitude and phase change, with the crack length through a response surface model. The two damage sensitive features are extracted from the first received S0 mode wave package. The model parameters of the baseline model are estimated using finite element simulation data. To account for uncertainties from numerical modeling, geometry, material and manufacturing between the baseline model and the target model, Bayesian method is employed to update the baseline model with a few measurements acquired from the actual target structure. A rigorous validation is made using in-situ fatigue testing and Lamb wave data from coupon specimens and realistic lap-joint components. The effectiveness and accuracy of the proposed method is demonstrated under different loading and damage conditions.
A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves
Liu, Li-qin; Liu, Ya-liu; Xu, Wan-hai; Li, Yan; Tang, You-gang
2018-03-01
The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship's manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.
Energy Technology Data Exchange (ETDEWEB)
Fusco, D [Messina Univ. (Italy). Instituto de Matematica
1979-01-01
The paper is concerned with a three-dimensional theory of non-linear magnetosonic waves in a turbulent plasma. A perturbation method is used that allows a transport equation, like Burgers equation but with a variable coefficient to be obtained.
Splendor and misery of the distorted wave method applied to heavy ions transfer reactions
International Nuclear Information System (INIS)
Mermaz, M.C.
1979-01-01
The success and failure of the Distorted Wave Method (DWM) applied to heavy ion transfer reactions are illustrated by few examples: one and multi-nucleon transfer reactions induced by 15 N and 18 O on 28 Si target nucleus performed on the vicinity of Coulomb barrier respectively at 44 and 56 MeV incident energy
The success of the distorted wave method at very high incident energy
International Nuclear Information System (INIS)
Barrette, J.; Berthier, B.; Gastebois, J.
1986-05-01
The one-proton and one-neutron direct surface transfer reactions induced by 793 MeV 16 O incident energy beam bombarding a 208 Pb target nucleus, are widely explained by two selection rules contained in the Dirtorted Wave Method formalism
International Nuclear Information System (INIS)
Wang Qi; Li Biao; Zhang Hongqing; Chen Yong
2005-01-01
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
Energy Technology Data Exchange (ETDEWEB)
Erlangga, Mokhammad Puput [Geophysical Engineering, Institut Teknologi Bandung, Ganesha Street no.10 Basic Science B Buliding fl.2-3 Bandung, 40132, West Java Indonesia puput.erlangga@gmail.com (Indonesia)
2015-04-16
Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, in case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.
2D XXZ model ground state properties using an analytic Lanczos expansion
International Nuclear Information System (INIS)
Witte, N.S.; Hollenberg, L.C.L.; Weihong Zheng
1997-01-01
A formalism was developed for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the t-expansion, and spin-wave theory and series expansion methods. It was found that far from the isotropic point all moment methods give essentially very similar results, but near the isotopic point the plaquette expansion is generally better than the others. 20 refs., 6 tabs
Directory of Open Access Journals (Sweden)
Mofza Algahtany
2016-10-01
Full Text Available Urban area expansion is one of the most critical types of worldwide change, and most urban areas are experiencing increased growth in population and infrastructure development. Urban change leads to many changes in the daily activities of people living within an affected area. Many studies have suggested that urbanization and crime are related. However, they focused particularly on land uses, types of land use, and urban forms, such as the physical features of neighbourhoods, roads, shopping centres, and bus stations. Understanding the correlation between urban area expansion and crime is very important for criminologists and urban planning decision-makers. In this study, we have used satellite images to measure urban expansion over a 10-year period and tested the correlations between these expansions and the number of criminal activities within these specific areas. The results show that there is a measurable relationship between urban expansion and criminal activities. Our findings support the crime opportunity theory as one possibility, which suggests that population density and crime are conceptually related. We found the correlations are stronger where there has been greater urban growth. Many other factors that may affect crime rate are not included in this paper, such as information on the spatial details of the population, city planning, economic considerations, the distance from the city centre, neighbourhood quality, and police numbers. However, this study will be of particular interest to those who aim to use remote sensing to study patterns of crime.
Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction.
Gilles, Luc; Vogel, Curtis R; Ellerbroek, Brent L
2002-09-01
We introduce a multigrid preconditioned conjugate-gradient (MGCG) iterative scheme for computing open-loop wave-front reconstructors for extreme adaptive optics systems. We present numerical simulations for a 17-m class telescope with n = 48756 sensor measurement grid points within the aperture, which indicate that our MGCG method has a rapid convergence rate for a wide range of subaperture average slope measurement signal-to-noise ratios. The total computational cost is of order n log n. Hence our scheme provides for fast wave-front simulation and control in large-scale adaptive optics systems.
Zou, Peng; Cheng, Jiubing
2017-01-01
-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using
International Nuclear Information System (INIS)
Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.; Cabot, William H.; Moin, Parviz; Olson, Britton J.; Rawat, Pradeep S.; Shankar, Santhosh K.; Sjoegreen, Bjoern; Yee, H.C.; Zhong Xiaolin; Lele, Sanjiva K.
2010-01-01
Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor-Green vortex, Shu-Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.
Zhang, Xiaoming; Qiang, Bo; Greenleaf, James
2011-02-01
The speed of the surface Rayleigh wave, which is related to the viscoelastic properties of the medium, can be measured by noninvasive and noncontact methods. This technique has been applied in biomedical applications such as detecting skin diseases. Static spherical indentation, which quantifies material elasticity through the relationship between loading force and displacement, has been applied in various areas including a number of biomedical applications. This paper compares the results obtained from these two methods on five gelatin phantoms of different concentrations (5%, 7.5%, 10%, 12.5% and 15%). The concentrations are chosen because the elasticity of such gelatin phantoms is close to that of tissue types such as skin. The results show that both the surface wave method and the static spherical indentation method produce the same values for shear elasticity. For example, the shear elasticities measured by the surface wave method are 1.51, 2.75, 5.34, 6.90 and 8.40kPa on the five phantoms, respectively. In addition, by studying the dispersion curve of the surface wave speed, shear viscosity can be extracted. The measured shear viscosities are 0.00, 0.00, 0.13, 0.39 and 1.22Pa.s on the five phantoms, respectively. The results also show that the shear elasticity of the gelatin phantoms increases linearly with their prepared concentrations. The linear regressions between concentration and shear elasticity have R(2) values larger than 0.98 for both methods. Copyright © 2010 Elsevier B.V. All rights reserved.