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Yirang Yuan - One of the best experts on this subject based on the ideXlab platform.

  • modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system
    Applied Mathematics and Mechanics-english Edition, 2013
    Co-Authors: Yirang Yuan, Tongjun Sun, Yunxin Liu
    Abstract:

    A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative Commutation Rule of difference operators, multiplicative Commutation Rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l2 norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

  • modified characteristic finite difference fractional step method for moving boundary value problem of percolation coupled system
    Applied Mathematics and Mechanics-english Edition, 2012
    Co-Authors: Yirang Yuan, Tongjun Sun
    Abstract:

    For the coupled system with moving boundary values of multilayer dynamics of fluids in porous media, a characteristic finite difference fractional step scheme applicable to the parallel arithmetic is put forward. Some techniques, such as the change of regions, the calculus of variations, the piecewise threefold quadratic interpolation, the multiplicative Commutation Rule of difference operators, the decomposition of high order difference operators, and the prior estimates, are adopted. The optimal order estimates in the l2 norm are derived to determine the error in the approximate solution. This numerical method has been successfully used to simulate the flow of migration-accumulation of the multilayer percolation coupled system. Some numerical results are well illustrated in this paper.

  • the upwind finite difference method for moving boundary value problem of coupled system
    Acta Mathematica Scientia, 2011
    Co-Authors: Yirang Yuan
    Abstract:

    Abstract Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. The upwind finite difference schemes applicable to parallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as change of variables, calculus of variations, multiplicative Commutation Rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. The estimates in l 2 norm are derived to determine the error in the approximate solution. This method was already applied to the numerical simulation of migration-accumulation of oil resources.

Tongjun Sun - One of the best experts on this subject based on the ideXlab platform.

  • modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system
    Applied Mathematics and Mechanics-english Edition, 2013
    Co-Authors: Yirang Yuan, Tongjun Sun, Yunxin Liu
    Abstract:

    A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative Commutation Rule of difference operators, multiplicative Commutation Rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l2 norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

  • modified characteristic finite difference fractional step method for moving boundary value problem of percolation coupled system
    Applied Mathematics and Mechanics-english Edition, 2012
    Co-Authors: Yirang Yuan, Tongjun Sun
    Abstract:

    For the coupled system with moving boundary values of multilayer dynamics of fluids in porous media, a characteristic finite difference fractional step scheme applicable to the parallel arithmetic is put forward. Some techniques, such as the change of regions, the calculus of variations, the piecewise threefold quadratic interpolation, the multiplicative Commutation Rule of difference operators, the decomposition of high order difference operators, and the prior estimates, are adopted. The optimal order estimates in the l2 norm are derived to determine the error in the approximate solution. This numerical method has been successfully used to simulate the flow of migration-accumulation of the multilayer percolation coupled system. Some numerical results are well illustrated in this paper.

Steven Kenneth Kauffmann - One of the best experts on this subject based on the ideXlab platform.

  • 120 Marine Parade
    2012
    Co-Authors: Steven Kenneth Kauffmann
    Abstract:

    Unambiguous quantization from the maximum classical correspondence that is self-consistent: the slightly stronger canonical Commutation Rule Dirac misse

  • Unambiguous Quantization from the Maximum Classical Correspondence that Is Self-consistent: The Slightly Stronger Canonical Commutation Rule Dirac Missed
    Foundations of Physics, 2011
    Co-Authors: Steven Kenneth Kauffmann
    Abstract:

    Dirac’s identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets to embrace only the Cartesian components of the phase space vector. Dirac’s canonical Commutation Rule fails to determine the order of noncommuting factors within quantized classical dynamical variables, but does imply the quantum/classical correspondence of Poisson brackets between any linear function of phase space and the sum of an arbitrary function of only configuration space with one of only momentum space. Since every linear function of phase space is itself such a sum, it is worth checking whether the assumption of quantum/classical correspondence of Poisson brackets for all such sums is still self-consistent. Not only is that so, but this slightly stronger canonical Commutation Rule also unambiguously determines the order of noncommuting factors within quantized dynamical variables in accord with the 1925 Born-Jordan quantization surmise, thus replicating the results of the Hamiltonian path integral, a fact first realized by E.H. Kerner. Born-Jordan quantization validates the generalized Ehrenfest theorem, but has no inverse, which disallows the disturbing features of the poorly physically motivated invertible Weyl quantization, i.e., its unique deterministic classical “shadow world” which can manifest negative densities in phase space.

  • unambiguous quantization from the maximum classical correspondence that is self consistent the slightly stronger canonical Commutation Rule dirac missed
    viXra, 2009
    Co-Authors: Steven Kenneth Kauffmann
    Abstract:

    Dirac’s identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets to embrace only the Cartesian components of the phase space vector. Dirac’s canonical Commutation Rule fails to determine the order of noncommuting factors within quantized classical dynamical variables, but does imply the quantum/classical correspondence of Poisson brackets between any linear function of phase space and the sum of an arbitrary function of only configuration space with one of only momentum space. Since every linear function of phase space is itself such a sum, it is worth checking whether the assumption of quantum/classical correspondence of Poisson brackets for all such sums is still self-consistent. Not only is that so, but this slightly stronger canonical Commutation Rule also unambiguously determines the order of noncommuting factors within quantized dynamical variables in accord with the 1925 Born-Jordan quantization surmise, thus replicating the results of the Hamiltonian path integral, a fact first realized by E. H. Kerner. Born-Jordan quantization validates the generalized Ehrenfest theorem, but has no inverse, which disallows the disturbing features of the poorly physically motivated invertible Weyl quantization, i.e., its unique deterministic classical “shadow world” which can manifest negative densities in phase space. Introduction The canonical Commutation Rule and the Heisenberg equation of motion both give concrete expression to Dirac’s profound discovery that (−i/h) times the commutator bracket is the quantum analog of the classical Poisson bracket, and together serve to incorporate both the correspondence principle and the uncertainty principle into orthodox operator quantum dynamics. Dirac’s 1925 version of the canonical Commutation Rule is well-known, however, to be too weak to determine the ordering of noncommuting factors that in principle can

Yunxin Liu - One of the best experts on this subject based on the ideXlab platform.

  • modified characteristic finite difference fractional step method for moving boundary value problem of nonlinear percolation system
    Applied Mathematics and Mechanics-english Edition, 2013
    Co-Authors: Yirang Yuan, Tongjun Sun, Yunxin Liu
    Abstract:

    A fractional step scheme with modified characteristic finite differences running in a parallel arithmetic is presented to simulate a nonlinear percolation system of multilayer dynamics of fluids in a porous medium with moving boundary values. With the help of theoretical techniques including the change of regions, piecewise threefold quadratic interpolation, calculus of variations, multiplicative Commutation Rule of difference operators, multiplicative Commutation Rule of difference operators, decomposition of high order difference operators, induction hypothesis, and prior estimates, an optimal order in l2 norm is displayed to complete the convergence analysis of the numerical algorithm. Some numerical results arising in the actual simulation of migration-accumulation of oil resources by this method are listed in the last section.

Kundu Anjan - One of the best experts on this subject based on the ideXlab platform.

  • Exact Bethe ansatz solution of a nonlinear quantum field model in quasi-two dimensions linked to the Landau–Lifshitz equation
    The Author. Published by Elsevier B.V., 2016
    Co-Authors: Kundu Anjan
    Abstract:

    AbstractIntegrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang–Baxter integrability is proved for the model by finding a new kind of Commutation Rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau–Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras

  • Exact Bethe ansatz solution for a quantum field model of interacting scalar fields in quasi-two dimensions
    2016
    Co-Authors: Kundu Anjan
    Abstract:

    Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang-Baxter integrability is proved for the model by finding a new kind of Commutation Rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau-Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras.Comment: 16 pages, no figur