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  • 1
    Electronic Resource
    Electronic Resource
    Burgers' equation with high Reynolds number (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 1853-1855 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Burgers' equation, involving very high Reynolds numbers, is numerically solved by using a new approach based on the distributed approximating functional for representing spatial derivatives of the velocity field. For moderately large Reynolds numbers, this simple approach can provide very high accuracy while using a small number of grid points. In the case where the Reynolds number ≥105, the exact solution is not available and a discrepancy exists in the literature. Our results clarify the behavior of the solution under these conditions. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869305
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  • 2
    Electronic Resource
    Electronic Resource
    Moderately dense gas quantum kinetic theory: Transport coefficient expressions (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 3066-3078 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Expressions for the transport coefficients of a moderately dense gas are obtained, based on a recently derived density corrected quantum Boltzmann equation. Linearization of the equations determining the pair correlation and the "free'' singlet density operators about local equilibrium is discussed first. The rate of change of the pair correlations is treated as dynamic effects for pairs of particles relaxing to local equilibrium via a relaxation time model arising from interactions with "third particles.'' In contrast, the singlet density operator satisfies a Boltzmann equation with binary collisions. Spatially inhomogeneous corrections to the collision superoperator are included. Contributions to the transport coefficients arise from the perturbation from local equilibrium through fluxes associated with kinetic, collisional and, for the thermal conductivity, potential energy mechanisms. A comparison is made between the classical limit of the transport coefficient expressions obtained here and the classical expressions previously derived from the Boltzmann equation with the nonlocal collision corrections of Green and Bogoliubov. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472176
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  • 3
    Electronic Resource
    Electronic Resource
    Moderately dense gas quantum kinetic theory: Aspects of pair correlations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 3057-3065 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A recently formulated density corrected quantum Boltzmann equation emphasizes the need to explicitly include pair correlations and the conversion of kinetic energy to potential energy as important effects in the kinetic theory of moderately dense gases. This paper first considers an appropriate evolution equation for the pair correlations which includes their decay via interactions with other particles in the gas. The molecular description is given of such a gas close to local thermal equilibrium, together with expressions for the associated hydrodynamic variables. Wigner functions are used to uniquely separate macroscopic and microscopic properties. An accompanying paper solves the combination of linearized Boltzmann and correlated pair equations to obtain expressions for the transport coefficients. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472167
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  • 4
    Electronic Resource
    Electronic Resource
    Distributed approximating functional approach to the Fokker–Planck equation: Time propagation (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 3239-3246 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Fokker–Planck equation is solved by the method of distributed approximating functionals via forward time propagation. Numerical schemes involving higher-order terms in Δt are discussed for the time discretization. Three typical examples (a Wiener process, an Ornstein–Uhlenbeck process, and a bistable diffusion model) are used to test the accuracy and reliability of the present approach, which provides solutions that are accurate up to ten significant figures while using a small number of grid points and a reasonably large time increment. Two sets of solutions for the bistable system, one computed using the eigenfunction expansion of a preceding paper and the other using the present time-dependent treatment, agree to no fewer than five significant figures. It is found that the distributed approximating functional method, while simple in its implementation, yields the most accurate numerical solutions yet available for the Fokker–Planck equation. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474674
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  • 5
    Electronic Resource
    Electronic Resource
    Equal reaction rates for all recombination pathways (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 1463-1466 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Formal collision theory indicates that the absolute termolecular recombination reaction rate can be expressed in a form associated either with direct or indirect mechanisms for the recombination. Moreover, the same exact rate constant can be calculated using either of the four mechanisms. These results are to be contrasted to the rate constants standardly calculated by approximate methods. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473294
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  • 6
    Electronic Resource
    Electronic Resource
    Distributed approximating functional approach to the Fokker–Planck equation: Eigenfunction expansion (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 5216-5224 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The distributed approximating functional method is applied to the solution of the Fokker–Planck equations. The present approach is limited to the standard eigenfunction expansion method. Three typical examples, a Lorentz Fokker–Planck equation, a bistable diffusion model and a Henon–Heiles two-dimensional anharmonic resonating system, are considered in the present numerical testing. All results are in excellent agreement with those of established methods in the field. It is found that the distributed approximating functional method yields the accuracy of a spectral method but with a local method's simplicity and flexibility for the eigenvalue problems arising from the Fokker–Planck equations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473520
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  • 7
    Electronic Resource
    Electronic Resource
    Discrete singular convolution for the solution of the Fokker–Planck equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 8930-8942 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper introduces a discrete singular convolution algorithm for solving the Fokker–Planck equation. Singular kernels of the Hilbert-type and the delta type are presented for numerical computations. Various sequences of approximations to the singular kernels are discussed. A numerical algorithm is proposed to incorporate the approximation kernels for physical applications. Three standard problems, the Lorentz Fokker–Planck equation, the bistable model and the Henon–Heiles system, are utilized to test the accuracy, reliability, and speed of convergency of the present approach. All results are in excellent agreement with those of previous methods in the field. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478812
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  • 8
    Electronic Resource
    Electronic Resource
    An application of distributed approximating functional-wavelets to reactive scattering (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 7065-7069 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A newly developed distributed approximating functional (DAF)-wavelet, the Dirichlet–Gabor DAF-wavelet (DGDW), is applied in a calculation of the state-to-state reaction probabilities for the three-dimensional (3-D) (J=0)H+H2 reaction, using the time-independent wave-packet reactant-product decoupling (TIWRPD) method. The DGDWs are reconstructed from a rigorous mathematical sampling theorem, and are shown to be DAF-wavelet generalizations of both the sine discrete variable representation (sinc-DVR) and the Fourier distributed approximating functionals (DAFs). An important feature of the generalized sinc-DVR representation is that the grid points are distributed at equally spaced intervals and the kinetic energy matrix has a banded, Toeplitz structure. Test calculations show that, in accordance with mathematical sampling theory, the DAF-windowed sinc-DVR converges much more rapidly and to higher accuracy with bandwidth, 2W+1. The results of the H+H2 calculation are in very close agreement with the results of previous TIWRPD calculations, demonstrating that the DGDW representation is an accurate and efficient representation for use in FFT wave-packet propagation methods, and that, more generally, the theory of wavelets and related techniques have great potential for the study of molecular dynamics. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476125
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  • 9
    Electronic Resource
    Electronic Resource
    Chain relations of reduced distribution functions and their associated correlation functions (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 706-714 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: For a closed system, the integration (trace in the quantum case) over one particle of a reduced distribution function is related to the reduced distribution function of one lower order. The particular details of this "chain" relation depend sensitively on the detailed manner in which the reduced distribution functions are defined, specifically their normalization. Correlation functions are defined in terms of reduced distribution functions, which fixes the normalization of the correlation functions and, provided they exist, their associated chain relations. Chain relations for the correlation functions are shown to exist for normalizations of generic type but not for normalizations of specific type. The normalization requirement is shown, in general, to prevent the direct association of correlation functions with physical clusters, which is commonly assumed in the literature. These relations are illustrated for an ideal gas of monomers and dimers. The effect of taking the thermodynamic limit on the chain relations for this system is discussed. This illustrates how the thermodynamic limit generally destroys the chain relations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475430
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  • 10
    Electronic Resource
    Electronic Resource
    Numerical solutions of incompressible Euler and Navier-Stokes equations by efficient discrete singular convolution method (2000)
    Springer
    Acta mechanica Sinica 16 (2000), S. 223-239 
    Details
    ISSN: 1614-3116
    Keywords: incompressible flows ; periodic boundary ; DSC method ; fourth-order Runge-Kutta method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract An efficient discrete singular convolution (DSC) method is introduced to the numerical solutions of incompressible Euler and Navier-Stokes equations with periodic boundary conditions. Two numerical tests of two-dimensional Navier-Stokes equations with periodic boundary conditions and Euler equations for doubly periodic shear layer flows are carried out by using the DSC method for spatial derivatives and fourth-order Runge-Kutta method for time advancement, respectively. The computational results show that the DSC method is efficient and robust for solving the problems of incompressible flows, and has the potential of being extended to numerically solve much broader problems in fluid dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02487664
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