175 results
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2. A new modification into Quasi-Newton equation for solving unconstrained optimization problems.
- Author
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Hassan, Basim A., Taha, Mohammed W., Kadoo, Farah H., and Mohammed, Sulaiman Ibrahim
- Subjects
QUASI-Newton methods ,NUMERICAL analysis ,EQUATIONS - Abstract
One of the most common problems with quasi-Newton methods is how to select the suitable quasi-Newton equation while operating the algorithm. In this paper, a new modification Quasi-Newton equation is proposed based on recent quasi-Newton equation of the Biglari et.al. method. Theoretical analyses and numerical computations using standard functions, as well as comparison with Broyden-Fletcher-Goldfarb-Shanno (BFGS) show that the proposed new type is globally convergent and computationally efficient. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. On the proper derivation of the Floquet-based quantum classical Liouville equation and surface hopping describing a molecule or material subject to an external field.
- Author
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Chen, Hsing-Ta, Zhou, Zeyu, and Subotnik, Joseph E.
- Subjects
NUMERICAL analysis ,DEGREES of freedom ,EQUATIONS ,HOPS ,MOLECULES - Abstract
We investigate different approaches to derive the proper Floquet-based quantum–classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
4. Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation.
- Author
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Fukuchi, Tsugio
- Subjects
FINITE difference method ,NUMERICAL analysis ,INTERPOLATION ,EQUATIONS ,POISEUILLE flow - Abstract
In a previous paper, a calculation system for a high-accuracy, high-speed calculation of a one-dimensional (1D) Poisson equation based on the interpolation finite difference method was shown. Spatial high-order finite difference (FD) schemes, including a usual second-order accurate centered space FD scheme, are instantaneously derived on the equally spaced/unequally spaced grid points based on the definition of the Lagrange polynomial function. The upper limit of the higher order FD scheme is not theoretically limited but is studied up to the tenth order, following the previous paper. In the numerical analyses of the 1D Poisson equation published in the previous paper, the FD scheme setting method, SAPI (m), m = 2, 4, ..., 10, was defined. Due to specifying the value of m, the setting of FD schemes is uniquely defined. This concept is extended to the numerical analysis of two-dimensional Poisson equations. In this paper, we focus on Poiseuille flows passing through arbitrary cross sections as numerical calculation examples. Over regular and irregular domains, three types of FD methods—(i) forward time explicit method, (ii) time marching successive displacement method, and (iii) alternative direction implicit method—are formulated, and their characteristics of convergence and numerical calculation errors are investigated. The numerical calculation system of the 2D Poisson equation formulated in this paper enables high-accuracy and high-speed calculation by the high-order difference in an arbitrary domain. Especially in the alternative direction implicit method using the band diagonal matrix algorithm, convergence is remarkably accelerated, and high-speed calculation becomes possible. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
5. Special Second Order Stiff Delay Differential Equations Directly Solved by Using Variable Stepsize Variable Order Technique.
- Author
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Mohd Isa, Nora Baizura and Ishak, Fuziyah
- Subjects
DELAY differential equations ,MATHEMATICAL variables ,NUMERICAL solutions to differential equations ,NUMERICAL analysis ,EQUATIONS - Abstract
Less attention was made to solve special second order stiff delay differential equations (DDEs) directly. In this paper, the development of direct predictor-corrector variable stepsize variable order (DBVSVO) method is described to solve special second order stiff DDEs directly without reducing to first order equations. The predictor and corrector formulae is derived based on backward differentiation formulae (BDF) and represented in divided difference form. In order to achieve greater efficiency, the developed method is implemented using variable stepsize variable order (VSVO) technique. Numerical results are presented to show that the developed method is suitable for solving special second order stiff DDEs. For comparison purposes the same set of test examples are reduced to a system of the first order equations and solved using predictor-corrector variable stepsize variable order method based on backward differentiation formulae (BVSVO) method proposed by Mohd Isa et al. [1]. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
6. Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.
- Author
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Bardhan, Jaydeep P.
- Subjects
ELECTROSTATICS ,BOUNDARY element methods ,INTERPOLATION ,EQUATIONS ,NUMERICAL analysis - Abstract
The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
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7. Assigning signs to the electronic nonadiabatic coupling terms: The {H2,O} system as a case study.
- Author
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Vibók, Ágnes, Halász, Gábor J., Suhai, Sándor, and Baer, Michael
- Subjects
ELECTRONICS ,CASE studies ,COUPLING constants ,EQUATIONS ,MATHEMATICAL models ,NUMERICAL analysis - Abstract
This paper is devoted to a specific difficulty related to the electronic nonadiabatic coupling terms (NACT), namely, how to determine correctly their signs. It is well known that correct NACTs, including their signs, are crucial for any numerical treatment of the nuclear Schrödinger equation [see, i.e., A. Kuppermaan and R. Abrol, Adv. Chem. Phys. 124, 283 (2003)]. In most cases the derivation of the correct sign of the nonadiabatic coupling matrix (NACM) is done employing various continuity procedures. However, there are cases where these procedures do not suffice and for these cases we suggest to apply an additional procedure based on a mathematical lemma which asserts that the exponentiated line integral which yields the D matrix is invariant with respect to the initial point of the integration [M. Baer, J. Phys. Chem. A 104, 3181 (2000)]. In the numerical study we apply this lemma to determine the signs of the 3×3 NACM elements for the three excited states of the {H
2 ,O} system (some of these NACTs are presented here for the first time). It turns out that the ab initio treatment yields results from which one can form eight different 3×3 NACMs. However the application of this lemma (which does not require any significant additional numerical effort) reduces this number to two. The final selection is done by an enhanced numerical study which requires more accurate calculations. [ABSTRACT FROM AUTHOR]- Published
- 2005
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8. On Genocchi Operational Matrix of Fractional Integration for Solving Fractional Differential Equations.
- Author
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Abdulnasir Isah and Chang Phang
- Subjects
FRACTIONAL integrals ,MATHEMATICS ,POLYNOMIALS ,MATHEMATICAL analysis ,NUMERICAL analysis ,EQUATIONS ,ALGEBRA - Abstract
In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
9. Point-wise Integrated-RBF-based Discretisation of Differential Equations.
- Author
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Mai-Duy, Nam and Tran-Cong, Thanh
- Subjects
ELLIPTIC differential equations ,PARTIAL differential equations ,NUMERICAL analysis ,MATHEMATICAL analysis ,EQUATIONS - Abstract
This paper discusses a discretisation scheme which is based on point collocation and integrated radial basis function networks (IRBFNs) for the solution of elliptic differential equations (DEs). The use of IRBFNs to represent the field variable in a given DE gives several advantages over the case of using conventional RBFNs and polynomials. Some numerical examples are included for demonstration purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
10. Generalized solutions for the H1 model in ABS List of lattice equations.
- Author
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Da-jun Zhang and Hietarinta, Jarmo
- Subjects
SOLITONS ,NONLINEAR theories ,EQUATIONS ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
In this paper we discuss solutions in Casoratian form for H1, which is the simplest member in ABS list of lattice equations. By investigating the condition satisfied by the Casoratian basic column we propose a generalization, which yields solutions which are different form solitons. These solutions can be considered as limit solutions of solitons. Similar generalizations can apply to other lattice equations in ABS list, such as H2, H3 and Q1. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
11. A Reliable Vector-Valued Rational Interpolation and Its Existence Study.
- Author
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Xiaolin Zhu
- Subjects
INTERPOLATION ,APPROXIMATION theory ,NUMERICAL analysis ,ALGORITHMS ,EQUATIONS - Abstract
This paper presents a modified Thiele-Werner algorithm to construct a kind of reliable vector-valued rational interpolants (RVRIs) and then studies their existence. The reliability of this method means that if a solution of the basic vector-valued rational interpolation problem exists, the method given in this paper finds it. Then a method for testing the existence for RVRIs and some methods for dealing with unattainable points for RVRIs are given. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
12. The Stability of Spiral Waves.
- Author
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Amdjadi, Faridon and Wallace, Robert
- Subjects
DIFFUSION ,EQUATIONS ,ALGORITHMS ,NUMERICAL analysis ,SUPPLY & demand - Abstract
It is well known that the spiral wave solution of the reaction-diffusion equations is in the form of two qualitatively different classes of waves: rigidly rotating spirals or meandering spiral waves. The main objective of this paper is to study the stability of these waves. We develop an algorithm to deal with an operator dependent linearized system and to show that these waves are stable. This algorithm could be easily implemented. We also introduce a new approach for studying the dynamics change in the reaction diffusion system that obviates the need for tracing the path of spiral tip. Unlike tracing out the spiral tip which requires the intensive numerical procedures, our approach is easily implemented. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
13. On the dynamics of chaotic spiking-bursting transition in the Hindmarsh–Rose neuron.
- Author
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Innocenti, G. and Genesio, R.
- Subjects
CHAOS theory ,NEURONS ,NUMERICAL analysis ,EQUATIONS ,DYNAMICS - Abstract
The paper considers the neuron model of Hindmarsh–Rose and studies in detail the system dynamics which controls the transition between the spiking and bursting regimes. In particular, such a passage occurs in a chaotic region and different explanations have been given in the literature to represent the process, generally based on a slow-fast decomposition of the neuron model. This paper proposes a novel view of the chaotic spiking-bursting transition exploiting the whole system dynamics and putting in evidence the essential role played in the phenomenon by the manifolds of the equilibrium point. An analytical approximation is developed for the related crucial elements and a subsequent numerical analysis signifies the properness of the suggested conjecture. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
14. Molecular dynamics in the isothermal-isobaric ensemble: The requirement of a “shell” molecule. I. Theory and phase-space analysis.
- Author
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Uline, Mark J. and Corti, David S.
- Subjects
MOLECULAR dynamics ,BOUNDARY value problems ,STOCHASTIC processes ,NUMERICAL analysis ,EQUATIONS of motion ,EQUATIONS - Abstract
Current constant pressure molecular-dynamics (MD) algorithms are not consistent with the recent reformulation of the isothermal-isobaric (NpT) ensemble. The NpT ensemble partition function requires the use of a “shell” molecule to identify uniquely the volume of the system, thereby avoiding the redundant counting of configurations [e.g., G. J. M. Koper and H. Reiss, J. Phys. Chem. 100, 422 (1996); D. S. Corti, Phys. Rev. E, 64, 016128 (2001)]. So far, only the NpT Monte Carlo method has been updated to allow the system volume to be defined by a shell particle [D. S. Corti, Mol. Phys. 100, 1887 (2002)]. A shell particle has yet to be incorporated into MD simulations. The proper modification of the NpT MD algorithm is therefore the subject of this paper. Unlike Andersen’s method [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] where a piston of unknown mass serves to control the response time of volume fluctuations, the newly proposed equations of motion impose a constant external pressure via the introduction of a shell particle of known mass. Hence, the system itself sets the time scales for pressure and volume fluctuations. The new algorithm is subject to a number of fundamentally rigorous tests to ensure that the equations of motion sample phase space correctly. We also show that the Hoover NpT algorithm [W. G. Hoover, Phys. Rev. A. 31, 1695 (1985); 34, 2499 (1986)] does sample phase correctly, but only when periodic boundary conditions are employed. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
15. A practical treatment for the three-body interactions in the transcorrelated variational Monte Carlo method: Application to atoms from lithium to neon.
- Author
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Umezawa, Naoto, Tsuneyuki, Shinji, Ohno, Takahisa, Shiraishi, Kenji, and Chikyow, Toyohiro
- Subjects
MONTE Carlo method ,MATHEMATICAL models ,NUMERICAL analysis ,EQUATIONS ,LITHIUM ,NEON - Abstract
We suggest a practical solution to dealing with the three-body interactions in the transcorrelated variational Monte Carlo method (TC-VMC). In the TC-VMC method, which was suggested in our previous paper [N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003)], the Jastrow–Slater-type wave function is efficiently optimized through a self-consistent procedure by minimizing the variance of the local energy. The three-body terms in the transcorrelated self-consistent-field equation, which have been simply ignored in our previous works, are efficiently calculated by the Monte Carlo numerical integration. We found that our treatment for the three-body interactions is successful for atoms from Li to Ne. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
16. High-order accurate and high-speed calculation system of 1D Laplace and Poisson equations using the interpolation finite difference method.
- Author
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Fukuchi, Tsugio
- Subjects
FINITE difference method ,INTERPOLATION ,NUMERICAL calculations ,NUMERICAL analysis ,EQUATIONS ,LAPLACE transformation - Abstract
Among the methods of the numerical analysis of the physical phenomena of the continuum, the finite difference method (FDM) is the first examined method and has been established as a full numerical calculation system over the regular domain. However, there is a general perception that generality in numerical calculations cannot be expected over complex irregular domains. As using the FDM, the development of computational methods that are applicable over any irregular domain is considered to be a very important contemporary problem. In the FDM, there is a marked characteristic that the theory developed by the (spatial) one-dimensional (1D) problem is naturally applied to the 2D and 3D problems. The calculation method is called the interpolation FDM (IFDM). In this paper, attention is paid to 1D Laplace and Poisson equations, and the whole image of the IFDM using the algebraic polynomial interpolation method (APIM), the IFDM-APIM, is described. Based on the Lagrange interpolation function, the spatial difference schemes from 2nd order to 10th order including odd order are calculated and defined instantaneously over equally/unequally spaced grid points, then, high-order accurate and high-speed computations become possible. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
17. Kinetic laws at the collapse transition of a homopolymer.
- Author
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Kuznetsov, Yu. A., Timoshenko, E. G., and Dawson, K. A.
- Subjects
NUMERICAL analysis ,EQUATIONS ,GAUSSIAN processes ,POLYMERS ,SCALING laws (Nuclear physics) - Abstract
We present results from numerical analysis of the equations derived in the Gaussian self-consistent method for kinetics at the collapse transition of a homopolymer in dilute solution. The kinetic laws are obtained with and without hydrodynamics for different quench depths and viscosities of the solvent. Some of our earlier analytical estimates are confirmed, and new ones generated. Thus the first kinetic stage for small quenches is described by a power law decrease in time of the squared radius of gyration with the universal exponent αi=9/11 (7/11) with (without) hydrodynamics. We find the scaling laws of the characteristic time of the coarsening stage, τm∼Nγm, and the final relaxation time, τf∼Nγf, as a function of the degree of polymerization N. These exponents are equal to γm=3/2, γf=1 in the regime of strong hydrodynamic interaction, and γm=2, γf=5/3 without hydrodynamics. We regard this paper as the completion of our work on the collapse kinetics of a bead and spring model of a homopolymer, but discuss the possibility of studying more complex systems. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 1996
- Full Text
- View/download PDF
18. Thermal Analysis of Thin Plates Using the Finite Element Method.
- Author
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Er, G. K., Iu, V. P., and Liu, X. L.
- Subjects
FINITE element method ,NUMERICAL analysis ,THERMAL analysis ,MATHEMATICAL analysis ,EQUATIONS - Abstract
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
19. Application of the Two-grid Method to a Heat Radiation Problem.
- Author
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Jovanovic, B., Koleva, M. N., and Vulkov, L.
- Subjects
BOUNDARY value problems ,HEAT radiation & absorption ,RADIATION ,NONLINEAR systems ,EQUATIONS ,NUMERICAL analysis - Abstract
We consider a nonlinear elliptic boundary value problem, which describes a radiative heat transfer. This paper is concerned with the solution of the nonlinear system of equations arising from FEM approximations of the problem. We employ Newton’s method to develop a new version of the two-grid method originated from O. Axelson and J. Xu. Numerical results are given to a simple problem with exact solution and to a simplified version of the physical problem. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
20. A Study of the Robustness of Iterative Methods for Linear Systems.
- Author
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Diene, Oumar and Bhaya, Amit
- Subjects
NUMERICAL analysis ,EQUATIONS ,ROBUST control ,LINEAR systems ,ALGORITHMS ,ASTRONOMICAL perturbation ,ITERATIVE methods (Mathematics) - Abstract
Numerical methods are implemented in digital computers using finite precision arithmetics, in which real/complex numbers are represented by finite length words. This representation results in truncating/rounding off the numbers, which leads to numerical errors in the algorithms. The numerical errors can result in the loss of some properties of the numerical methods (for example, the orthogonality of the residues of the conjugate gradient), which, in turn, cause numerical instability. In this paper, a new model of the perturbations resulting from the use of finite precision arithmetic is proposed, based on a combination of the floating point model with the usual model of multiplicative perturbations at the input of a plant. This control perspective, applied to the classical problem of numerical perturbations due to finite precision, allows application of the well known small gain theorem of robust control theory in order to determine measures of the robustness or numerical stability of numerical algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
21. Numerical Approximation for a One-Dimensional Two-Phase Mixture Conservation Laws.
- Author
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Zeidan, D.
- Subjects
TWO-phase flow ,NUMERICAL analysis ,APPROXIMATION theory ,HYPERBOLIC spaces ,EQUATIONS - Abstract
An alternative to currently used two-phase flow equations is considered to resolve discontinuous solutions in gas-solid mixtures. The equations in the present paper are based on the theory of thermodynamically compatible systems of hyperbolic conservation laws. The conservative hyperbolic governing equations were solved using Godunov methods of centred-type. This solution is then employed in the source terms problem with Strang splitting technique to solve the general initial-value problem for the two-phase flow equations. Results are presented, demonstrating the accuracy of the numerical methods associated with of the proposed two-phase conservation laws. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
22. The Role of the Precise Definition of Stiffness in Designing Codes for the Solution of ODEs.
- Author
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Brugnano, Luigi, Mazzia, Francesca, and Trigiante, Donato
- Subjects
MATHEMATICS ,BOUNDARY value problems ,NUMERICAL analysis ,EQUATIONS ,CIPHERS - Abstract
The notion of stiffness, which originated in several applications of different nature, has dominated the activities related to the numerical treatment of differential problems in the last fifty years. Its definition has been, for a long time, not formally precise. The needs of applications, especially those rising in the construction of robust and general purpose codes, require nowadays a formally precise definition. In this paper, we review the evolution of such notion and we provide also with a precise definition that could be used practically. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
23. Applications of the Multi-Symplectic Euler-box Scheme.
- Author
-
Yushun Wang and Bin Wang
- Subjects
SYMPLECTIC geometry ,EULER angles ,EQUATIONS ,NUMERICAL analysis ,NONLINEAR statistical models - Abstract
In this paper, we investigate the multi-symplectic Euler-box scheme for Hamiltonian PDEs. We find that the multi-symplectic Euler-box scheme contains at least two classes of schemes which have the same spatial discrete and adjoint temporal discrete as each other. The two classes of schemes, though both are multi-symplectic, may have intrinsic different numerical properties. Some semi-discrete properties of the Euler-box scheme are also discussed. We apply the Euler-box scheme to some classical equations, e.g., the KdV equation, the Zakharov-Kuznetsov equation and the coupled nonlinear Schrödinger equation and derive some new efficient explicit or semi-explicit multi-symplectic schemes for those classical equations. Numerical comparison results on simulating the evolutions of solitons are presented to show the merits of the explicit multi-symplectic scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
24. Method for the Non-linear Identification of Aircraft Parameters by Testing Maneuvers.
- Author
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Boguslavskiy, I. A.
- Subjects
EQUATIONS ,STATISTICS ,NUMERICAL analysis ,APPROXIMATION theory ,ALGORITHMS ,INTERPOLATION ,EQUATIONS of motion ,LAGRANGE equations - Abstract
In this paper, we describe a variant of a solution for a common problem in applied statistics—we offer a variant method for estimating the parameters of a dynamic system, and observe its magnitudes, which statistically depend on the sequence of states of the system that are not observed. The method is realized by means of the multipolynomial approximations algorithm (the MPA algorithm). The method is validated by applying it to a problem of correction of finite sets of nominal experimental data on which nominal functions are constructed equationsby means of interpolation from the current states of the system. Nominal experimental data are presented on a finite set of points covering the domains of definition of the nominal functions. The nominal equations of motion of the dynamical system are defined by the nominal functions. In this paper, the concrete example of the nominal equations of motion correspond to the longitudinal motion of the aircraft similar of the F-l6 aircraft. The nominal functions are the calculated aerodynamic characteristics. The nominal experimental data are recorded by means of experiments in a wind-tunnel. The outcomes of measurements of the parameters of motion of the aircraft act on inputs for the MPA algorithm on a segment of real flight. The MPA algorithm defines a 32×1-vector of estimates of parameters, which are additive corrections to the nominal experimental data. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
25. Finite Element Analysis of Polycrystalline Deformation with the Rate-dependent Crystal Plasticity.
- Author
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Yoon, J. H., Huh, H., and Lee, Y. S.
- Subjects
FINITE element method ,MATHEMATICAL continuum ,EQUATIONS ,MATERIAL plasticity ,ALGORITHMS ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
Constitutive models for the crystal plasticity have the common objective which relates the behavior of microscopic single crystals in the crystallographic texture to the macroscopic continuum response. This paper presents the texture analysis of polycrystalline materials using the rate-dependent single crystal plasticity to develop a multi-scale description of the mechanism at the grain and aggregate levels. The texture analysis requires a numerical algorithm for integrating the constitutive equations. The implicit deformation gradient approach is employed to update the stresses and texture orientations as an integration algorithm. It considers elastic or plastic deformation gradient as the primary unknown variables and constructs the residual of the elastic and plastic velocity gradients as the governing equations. This algorithm is shown to be an efficient and robust algorithm in rather large time steps. The texture analysis of the asymmetric rolling process is also presented to show investigation of the effect of texture evolution based on the finite element analysis as a numerical example. The analysis result for texture evolution is investigated by comparing the pole figure before and after the asymmetric rolling process. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
26. Modeling and Simulation of Cell Growth in Injection Molding of Microcellular Plastics.
- Author
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Osorio, Andres, Lih-Sheng Turng, Ghosh, S., Castro, J.C., and Lee, J.K.
- Subjects
NUMERICAL analysis ,POLYMERS ,EQUATIONS ,GROWTH factors ,MOLDING of plastics - Abstract
This paper presents the numerical simulation for modeling non-isothermal cell growth during the post-filling stage of microcellular injection molding. The model combines two numerical techniques, namely, finite volume method to solve the transient equation of energy and finite difference method to solve continuity equation for computing the pressure field and a group of equations that describe the cell growth. The “unit-cell” model employed in this study takes into account the effects of injection and packing pressures, melt and mold temperatures, and material properties on the properties of polymer-gas solution and the cell growth. The numerical results in terms of cell size across the sprue diameter agree fairly well with the experimental observation for microcellular injection molded polyamide parts. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
27. Physics-based analytical model for ferromagnetic single electron transistor.
- Author
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Jamshidnezhad, K. and Sharifi, M. J.
- Subjects
FERROMAGNETIC materials ,SINGLE electron transistors ,MONTE Carlo method ,EQUATIONS ,NUMERICAL analysis - Abstract
A physically based compact analytical model is proposed for a ferromagnetic single electron transistor (FSET). This model is based on the orthodox theory and solves the master equation, spin conservation equation, and charge neutrality equation simultaneously. The model can be applied to both symmetric and asymmetric devices and does not introduce any limitation on the applied bias voltages. This feature makes the model suitable for both analog and digital applications. To verify the accuracy of the model, its results regarding a typical FSET in both low and high voltage regimes are compared with the existing numerical results. Moreover, the model's results of a parallel configuration FSET, where no spin accumulation exists in the island, are compared with the results obtained from a Monte Carlo simulation using SIMON. These two comparisons show that our model is valid and accurate. As another comparison, the model is compared analytically with an existing model for a double barrier ferromagnetic junction (having no gate). This also verifies the accuracy of the model. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
28. Comparative study of fractional Newell–Whitehead–Segel equation using optimal auxiliary function method and a novel iterative approach.
- Author
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Xin, Xiao, khan, Ibrar, Ganie, Abdul Hamid, Akgül, Ali, Bonyah, Ebenezer, Fathima, Dowlath, and Ali Yousif, Badria Almaz
- Subjects
CAPUTO fractional derivatives ,PARTIAL differential equations ,NUMERICAL analysis ,EQUATIONS ,COMPARATIVE studies - Abstract
This research explores the solution of the time-fractional Newell–Whitehead–Segel equation using two separate methods: the optimal auxiliary function method and a new iterative method. The Newell–Whitehead–Segel equation holds significance in modeling nonlinear systems, particularly in delineating stripe patterns within two-dimensional systems. Employing the Caputo fractional derivative operator, we address two case study problems pertaining to this equation through our proposed methods. Comparative analysis between the numerical results obtained from our techniques and an exact solution reveals a strong alignment. Graphs and tables illustrate this alignment, showcasing the effectiveness of our methods. Notably, as the fractional orders vary, the results achieved at different fractional orders are compared, highlighting their convergence toward the exact solution as the fractional order approaches an integer. Demonstrating both interest and simplicity, our proposed methods exhibit high accuracy in resolving diverse nonlinear fractional order partial differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Numerical study of the formation process of ferrofluid droplets.
- Author
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Liu, Jing, Yap, Yit Fatt, and Nguyen, Nam-Trung
- Subjects
NUMERICAL analysis ,MAGNETIC fluids ,DROPLETS ,MAGNETIC fields ,MATHEMATICAL models ,STRAINS & stresses (Mechanics) ,LIQUID-liquid interfaces ,EQUATIONS - Abstract
This paper numerically investigates the influence of a uniform magnetic field on the droplet formation process at a microfluidic flow focusing configuration. The mathematical model was formulated by considering the balance of forces such as interfacial tension, magnetic force, and viscous stress across the liquid/liquid interface. A linearly magnetizable fluid was assumed. The magnetic force acts as a body force where the magnetic permeability jumps across the interface. The governing equations were solved with finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the particle level set method. The code was validated with the equilibrium steady state of a ferrofluid droplet exposed to a uniform magnetic field. The evolution of the droplet formation in a flow focusing configuration was discussed. The paper mainly analyzes the effects of magnetic Bond number and the susceptibility on the velocity field and the droplet size. The droplet size increased with increasing magnetic strength and susceptibility. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
30. Random walks on the Comb model and its generalizations.
- Author
-
Arkhincheev, V. E.
- Subjects
DIFFUSION ,PROPERTIES of matter ,SOLUTION (Chemistry) ,SEPARATION (Technology) ,EQUATIONS ,NUMERICAL analysis ,MATHEMATICAL analysis ,RANDOM walks ,STOCHASTIC processes ,MATHEMATICAL physics - Abstract
Microscopic models with anomalous diffusion, which include the Comb model and its generalization for the finite width of the backbone, have been considered in this paper. The physical mechanisms of the subdiffusion random walks have been established. The first comes from the permanent return of the diffusing particle to the initial point of the diffusion due to “effective reducing” of the dimensionality of the considered system to the quasi-one-dimensional system. This physical mechanism has been obtained in the Comb model and in the model with a strip. The second mechanism of the subdiffusion is connected with random capture on the traps of diffusing particles and their ensuing random release from the traps. It has been shown that these different mechanisms of subdiffusion have been described by the different generalized diffusion equations of fractional order. The solutions of these different equations have been obtained, and the physical sense of the fractional order generalized equations has been discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
31. Supersymmetric fifth order evolution equations.
- Author
-
Tian, K. and Liu, Q. P.
- Subjects
SUPERSYMMETRY ,DIFFERENTIAL equations ,EQUATIONS ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
This paper considers supersymmetric fifth order evolution equations. Within the framework of symmetry approach, we give a list containing six equations, which are (potentially) integrable systems. Among these equations, the most interesting ones include a supersymmetric Sawada-Kotera equation and a novel supersymmetric fifth order KdV equation. For the latter, we supply some properties such as a Hamiltonian structures and a possible recursion operator. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
32. Gasdynamic agglomeration of aerosols. I. Acoustic waves.
- Author
-
Temkin, S.
- Subjects
AEROSOLS ,AGGLOMERATION (Materials) ,NUMERICAL integration ,NUMERICAL analysis ,EQUATIONS - Abstract
In this paper acoustic agglomeration of aerosols is studied in its simplest form, using a time-averaged form of the coalescence equations. An acoustic coagulation kernel is introduced that neglects all nonlinear effects, as well as particle interactions. Based on this model, it is shown that an acoustic frequency exists that optimizes the coalescence process. This optimum frequency does not have a unique value for all distributions, but for size distributions that are not too wide, it is given by ω[SUBopt] =1/τ*, where τ* is the relaxation time of a particle having a diameter corresponding to the mode count diameter of the initial size distribution function. The paper also includes the result of a numerical integration of the coalescence equations for typical aerosol distributions; which show their evolution under the influence of a sound wave. [ABSTRACT FROM AUTHOR]
- Published
- 1994
- Full Text
- View/download PDF
33. Second degree model of laser efficiency of a copper bromide laser.
- Author
-
Denev, N. P. and Iliev, I. P.
- Subjects
LASER research ,REGRESSION analysis ,NUMERICAL analysis ,PARAMETER estimation ,EQUATIONS - Abstract
The subject of this study is a CuBr laser. Due to its wide range of applications, it continues to be the object of scientific studies. For the first time, based on regression analysis, second degree regression parametric equations have been obtained in this paper, describing the behavior of laser efficiency in relation to 10 independent physical characteristics. The obtained relationships accounted for about 95% of the observed data. The predicted values have been checked against known experiment results. Correspondence is within 5%. Second degree terms which have the strongest influence on laser generation have been identified. Numerical experiments have been carried out in order to construct new laser sources with higher laser efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
34. Multiresolution Scheme for Incompressible Model of Three-phase Flow.
- Author
-
Louaked, M.
- Subjects
MULTIPHASE flow ,EQUATIONS ,UNSTEADY flow ,FLUID dynamics ,NUMERICAL analysis - Abstract
In this paper the analysis of incompressible three-phase flow systems is studied. A stable numerical method for the model equations based on the flux splitting approach is developed. A useable methodology for reducing the number of numerical flux computations in the multiphase equations is proposed. The multiresolution is based on the analysis of the solutions regularity according to various levels of resolution. Numerical predictions of transient flow problems in pipelines are compared to available experimental data. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
35. Numerical Solution of Laminar Incompressible Generalized Newtonian Fluids Flow.
- Author
-
Keslerová, R. and Kozel, K.
- Subjects
NUMERICAL analysis ,LAMINAR flow ,NEWTONIAN fluids ,BRANCHING processes ,EQUATIONS - Abstract
This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian (Newtonian and non-Newtonian) fluids in the branching channel. The mathematical model is the generalized system of Navier-Stokes equations. The right hand side of this system is defined by power-law model. The finite volume method combined with an artificial compressibility method is used for spatial discretization. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Numerical solution is divided into two parts, steady and unsteady. Steady state solution is achieved for t→∞ using steady boundary conditions and followed by steady residual behavior. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
36. Fully Discrete Scheme for the Equations Describing Unsaturated Flow in Porous Media with Dynamic Capillary Pressure.
- Author
-
Bodin, J. and Clopeau, T.
- Subjects
NUMERICAL analysis ,POROUS materials ,SATURATION vapor pressure ,EQUATIONS ,HEAT flux ,THERMODYNAMICS - Abstract
In this paper we present numerical results on the pseudoparabolic equation
(1) describing unsaturated flows in porous media with dynamic capillary pressure—saturation relationship, introduced in [2]–[6]. In the equation (1) τ is a positive constant, S is the wetting phase saturation, k is the hydraulic conductivity and P -div(k(S)(-P′∂S ∂t c (S)▿S+τ▿ )) = b∂S ∂t c is the static capillary pressure, μ the viscosity of the fluid and b a source term. In general, such models arise in a number of cases when non-equilibrium thermodynamics or extended non-equilibrium thermodynamics are used to compute the flux. [ABSTRACT FROM AUTHOR]- Published
- 2009
- Full Text
- View/download PDF
37. A TWO-SCALE FEM FORMULATION FOR HETEROGENEOUS MATERIALS.
- Author
-
IoniŢă, Axinte, Mas, Eric M., and Clements, Brad E.
- Subjects
INHOMOGENEOUS materials ,FINITE element method ,EQUATIONS ,MATHEMATICAL formulas ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
This article proposes a two-scale finite element approach for the dynamic response of heterogeneous materials. While common two-scale Finite Element Method (FEM) formulations consider the Representative Volume Element (RVE) much smaller than the finite element mesh, the present paper extends the formulation for the cases when RVE becomes comparable with the finite element in the mesh. The new two-scale equations and their FEM implementation, are presented together with an example. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
38. Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage.
- Author
-
Hayakawa, Kunio, Nakamura, Tamotsu, and Tanaka, Shigekazu
- Subjects
CARBIDES ,FINITE element method ,THERMODYNAMICS ,EQUATIONS ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix — WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
39. Comparison of methods for estimating continuous distributions of relaxation times.
- Author
-
Tuncer, Enis and Macdonald, J. Ross
- Subjects
- *
RELAXATION (Nuclear physics) , *NUMERICAL analysis , *ELECTRIC conductivity , *DIELECTRICS , *MATHEMATICAL functions , *EQUATIONS - Abstract
The nonparametric estimation of the distribution of relaxation-time approach is not as frequently used in the analysis of dispersed response of dielectric or conductive materials as are other immittance data analysis methods based on parametric curve fitting techniques. Nevertheless, such distributions can yield important information about the physical processes present in measured material. In this paper, we apply two quite different numerical inversion methods to estimate the distribution of relaxation times for glassy Li0.5La0.5TiO3 dielectric frequency-response data at 225 K. Both methods yield unique distributions that agree very closely with the actual exact one accurately calculated from the corrected bulk-dispersion Kohlrausch model established independently by means of parametric data fit using the corrected modulus formalism method. The obtained distributions are also greatly superior to those estimated using approximate function equations given in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
40. 2D Solitary Waves of Boussinesq Equation.
- Author
-
Choudhury, Jayanta and Christov, Christo I.
- Subjects
SOLITONS ,NONLINEAR theories ,EQUATIONS ,ALGORITHMS ,NUMERICAL analysis ,SPEED - Abstract
In this paper, the 2D stationary-propagating localized solutions of Boussinesq’s equation are investigated numerically. An algorithm for treating the bifurcation and finding a nontrivial solution is created. The scheme is validated employing different grid sizes and different size of the box that contains the solution. The results obtained show that there is pseudo-Lorentzian elongation of the scale of the solitons but it is only in the direction transverse to the propagation velocity. In longitudinal direction the scales are slightly contracted, so kind of “relative” contraction takes place. Results are shown graphically and discussed. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
41. A New Three-Level Rotated Implicit Method for Solving the Two-Dimensional Time Fractional Diffusion-Wave Equation.
- Author
-
Balasim, Alla Tareq and Mohd. Ali, Norhashidah Hj.
- Subjects
- *
DIFFUSION , *ITERATIVE methods (Mathematics) , *NUMERICAL analysis , *ITERATIVE decoding , *EQUATIONS - Abstract
Fractional diffusion-wave equation represents many physical phenomena in modeling diffusive processes, waves in fluid flow, and oil strata among others. The numerical solution of this equation is an important task and has been investigated extensively over the last several years. The main purpose of this paper is to formulate a new three time level method in solving the two dimensional time-fractional diffusion-wave equation based on a rotated finite difference approximation formula where the time fractional derivative is described by Caputo's derivative of order 1 <α < 2 . The developed scheme is derived from the standard implicit formula rotated 45° clockwise with respect to the standard mesh. Numerical example and comparison with the standard classical iterative method has been conducted in this study to test the effectiveness of the proposed method. We show that the proposed iterative method is superior to the standard iterative method in terms of iteration numbers and execution timings without having to jeopardize the accuracy of the solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
42. Stability of negative solitary waves for an integrable modified Camassa–Holm equation.
- Author
-
Jiuli Yin, Lixin Tian, and Xinghua Fan
- Subjects
SOLITONS ,EQUATIONS ,ALGEBRA ,QUINTIC equations ,NUMERICAL analysis - Abstract
In this paper, we prove that the modified Camassa–Holm equation is Painlevé integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
43. Existence of the weak solution of coupled time-dependent Ginzburg–Landau equations.
- Author
-
Shuhong Chen and Boling Guo
- Subjects
EQUATIONS ,ALGEBRA ,MATHEMATICS ,GALERKIN methods ,NUMERICAL analysis - Abstract
In this paper, we investigate the existence of weak solutions of the coupled time-dependent Ginzburg-Landau equations and establish the global existence of weak solutions to the equations by Galerkin method and compactness theory. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
44. Synchronizing Hindmarsh–Rose neurons over Newman–Watts networks.
- Author
-
Jalili, Mahdi
- Subjects
SYNCHRONIZATION ,TIME measurements ,EQUATIONS ,NUMERICAL analysis ,DIFFERENTIAL equations - Abstract
In this paper, the synchronization behavior of the Hindmarsh–Rose neuron model over Newman–Watts networks is investigated. The uniform synchronizing coupling strength is determined through both numerically solving the network’s differential equations and the master-stability-function method. As the average degree is increased, the gap between the global synchronizing coupling strength, i.e., the one obtained through the numerical analysis, and the strength necessary for the local stability of the synchronization manifold, i.e., the one obtained through the master-stability-function approach, increases. We also find that this gap is independent of network size, at least in a class of networks considered in this work. Limiting the analysis to the master-stability-function formalism for large networks, we find that in those networks with size much larger than the average degree, the synchronizing coupling strength has a power-law relation with the shortcut probability of the Newman–Watts network. The synchronization behavior of the network of nonidentical Hindmarsh–Rose neurons is investigated by numerically solving the equations and tracking the average synchronization error. The synchronization of identical Hindmarsh–Rose neurons coupled over clustered Newman–Watts networks, networks with dense intercluster connections but sparsely in intracluster linkage, is also addressed. It is found that the synchronizing coupling strength is influenced mainly by the probability of intercluster connections with a power-law relation. We also investigate the complementary role of chemical coupling in providing complete synchronization through electrical connections. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
45. Low-regularity solutions of the periodic Fornberg–Whitham equation.
- Author
-
Lixin Tian, Yuexia Chen, Xiuping Jiang, and Limeng Xia
- Subjects
EQUATIONS ,NUMERICAL analysis ,MATHEMATICAL physics ,PHYSICS ,ALGEBRA - Abstract
This paper studies low-regularity solutions of the periodic Fornberg–Whitham equation with initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic Fornberg–Whitham equation. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
46. A new explicit multisymplectic scheme for the regularized long-wave equation.
- Author
-
Jiaxiang Cai
- Subjects
EQUATIONS ,ITERATIVE methods (Mathematics) ,NUMERICAL analysis ,ALGORITHMS ,MATHEMATICAL analysis - Abstract
In this paper, we derive a new ten-point multisymplectic scheme for the regularized long-wave equation from its Bridges’ multisymplectic form. The new scheme is an explicit scheme in the sense that it does not need iteration. We discuss some properties of the new scheme. The performance and the efficiency of the new scheme are illustrated by solving several test examples. The obtained results are presented and compared with previous methods. Numerical results indicate that the multisymplectic scheme cannot only obtain satisfied solutions for the regularized long-wave equation but also keep three invariants of motion which are evaluated to determine the conservation properties of the algorithm very well. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
47. One- and two-dimensional modeling of argon K-shell emission from gas-puff Z-pinch plasmas.
- Author
-
Thornhill, J. W., Chong, Y. K., Apruzese, J. P., Davis, J., Clark, R. W., Giuliani Jr., J. L., Terry, R. E., Velikovich, A. L., Commisso, R. J., Whitney, K. G., Frese, M. H., Frese, S. D., Levine, J. S., Qi, N., Sze, H., Failor, B. H., Banister, J. W., Coleman, P. L., Coverdale, C. A., and Jones, B.
- Subjects
THERMODYNAMICS ,HIGH temperatures ,RADIATION ,EQUATIONS ,MATHEMATICAL analysis ,NUMERICAL analysis - Abstract
In this paper, a theoretical model is described and demonstrated that serves as a useful tool for understanding K-shell radiating Z-pinch plasma behavior. Such understanding requires a self-consistent solution to the complete nonlocal thermodynamic equilibrium kinetics and radiation transport in order to realistically model opacity effects and the high-temperature state of the plasma. For this purpose, we have incorporated into the MACH2 two-dimensional magnetohydrodynamic (MHD) code [R. E. Peterkin et al., J. Comput. Phys. 140, 148 (1998)] an equation of state, called the tabular collisional radiative equilibrium (TCRE) model [J. W. Thornhill et al., Phys. Plasmas 8, 3480 (2001)], that provides reasonable approximations to the plasma’s opacity state. MACH2 with TCRE is applied toward analyzing the multidimensional implosion behavior that occurred in Decade Quad (DQ) [D. Price et al., Proceedings of the 12th IEEE Pulsed Power Conference, Monterey, CA, edited by C. Stallings and H. Kirbie (IEEE, New York, 1999), p. 489] argon gas puff experiments that employed a 12 cm diameter nozzle with and without a central gas jet on axis. Typical peak drive currents and implosion times in these experiments were ∼6 MA and ∼230 ns. By using Planar Laser Induced Fluorescence measured initial density profiles as input to the calculations, the effect these profiles have on the ability of the pinch to efficiently produce K-shell emission can be analyzed with this combined radiation-MHD model. The calculated results are in agreement with the experimental result that the DQ central-jet configuration is superior to the no-central-jet experiment in terms of producing more K-shell emission. These theoretical results support the contention that the improved operation of the central-jet nozzle is due to the better suppression of instabilities and the higher-density K-shell radiating conditions that the central-jet configuration promotes. When we applied the model toward projecting argon K-shell yield behavior for Sandia National Laboratories’ ZR machine (∼25 MA peak drive currents, ∼100 ns implosion times) [D. McDaniel et al., Proceedings of the 5th International Conference on Dense Z-Pinches, Albuquerque, NM, 2002, edited by J. Davis, C. Deeney, and N. R. Pereira (American Institute of Physics, New York, 2002), Vol. 651, p. 23] for experiments that utilize the 12 cm diameter central-jet nozzle configuration, it predicts over 1 MJ of K-shell emission is attainable. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
48. Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation.
- Author
-
Yano, Ryosuke, Suzuki, Kojiro, and Kuroda, Hisayasu
- Subjects
NUMERICAL analysis ,DIATOMIC molecules ,DYNAMICS ,EQUATIONS ,CHEMICAL reactions ,DISSOCIATION (Chemistry) - Abstract
The direct description of chemical reactions by the Boltzmann equation still involves some difficulties in the kinetic theory. In this paper, we describe diatomic molecular dissociation due to transitions of vibrational quantum states resulting from inelastic collisions. These can be described by the Wang Chang-Uhlenbeck (WCU) equation. To avoid direct evaluation of the strong nonlinear collision kernel of the WCU equation, we used a kinetic equation. For accurate description of the dissociation process, we describe improvements we made to the conventional inelastic collision model (the so-called Morse model). Combining this inelastic collision model with the gas mixture model by Oguchi, we formulated a model for representing diatomic molecular dissociations. We validated this model by simulating a hypersonic shock layer with diatomic molecular dissociation. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
49. Robust discretizations versus increase of the time step for the Lorenz system.
- Author
-
Letellier, Christophe and Mendes, Eduardo M. A. M.
- Subjects
NUMERICAL analysis ,EQUATIONS ,LORENZ equations ,DIFFERENTIAL equations ,FINITE differences ,CALCULUS - Abstract
When continuous systems are discretized, their solutions depend on the time step chosen a priori. Such solutions are not necessarily spurious in the sense that they can still correspond to a solution of the differential equations but with a displacement in the parameter space. Consequently, it is of great interest to obtain discrete equations which are robust even when the discretization time step is large. In this paper, different discretizations of the Lorenz system are discussed versus the values of the discretization time step. It is shown that the sets of difference equations proposed are more robust versus increases of the time step than conventional discretizations built with standard schemes such as the forward Euler, backward Euler, or centered finite difference schemes. The nonstandard schemes used here are Mickens’ scheme and Monaco and Normand-Cyrot’s scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
50. Numerical comparison of Bhatnagar–Gross–Krook models with proper Prandtl number.
- Author
-
Mieussens, Luc and Struchtrup, Henning
- Subjects
EQUATIONS ,NUMERICAL analysis ,VISCOSITY ,FLUIDS ,COLLISIONS (Physics) ,KINETIC theory of matter ,FLUID dynamics ,PHYSICS - Abstract
While the standard Bhatnagar–Gross–Krook (BGK) model leads to the wrong Prandtl number, the BGK model with velocity dependent collision frequency as well as the ellipsoidal statistical BGK (ES-BGK) model can be adjusted to give its proper value of 2/3. In this paper, the BGK model with velocity dependent collision frequency is considered in some detail. The corresponding thermal conductivity and viscosity are computed from the Chapman–Enskog method, and several velocity-dependent collision frequencies are introduced which all give the proper Prandtl number. The models are tested for Couette flow, and the results are compared to solutions obtained with the ES-BGK model, and the direct simulation Monte Carlo method. The simulations rely on a numerical scheme that ensures positivity of solutions, conservation of moments, and dissipation of entropy. The advantages and disadvantages of the various BGK models are discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
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