The Experts below are selected from a list of 15 Experts worldwide ranked by ideXlab platform

H. G. Miller - One of the best experts on this subject based on the ideXlab platform.

  • Determining the Tsallis parameter via maximum entropy.
    Physical review. E Statistical nonlinear and soft matter physics, 2015
    Co-Authors: J. M. Conroy, H. G. Miller
    Abstract:

    The nonextensive entropic measure proposed by Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On the other hand, from a phenomenological viewpoint, there are instances in which q cannot be treated as a constant. We present two distinct approaches for determining q depending on the form of the Equations of Constraint for the particular system. In the first case the Equations of Constraint for the operator O can be written as Tr(F(q)O)=C, where C may be an explicit function of the distribution function F. We show that in this case one can solve an equivalent maxent problem which yields q as a function of the corresponding Lagrange multiplier. As an illustration the exact solution of the static generalized Fokker-Planck Equation (GFPE) is obtained from maxent with the Tsallis enropy. As in the case where C is a constant, if q is treated as a variable within the maxent framework the entropic measure is maximized trivially for all values of q. Therefore q must be determined from existing data. In the second case an additional Equation of Constraint exists which cannot be brought into the above form. In this case the additional Equation of Constraint may be used to determine the fixed value of q.

  • MAXENT and the Tsallis Parameter
    arXiv: Statistical Mechanics, 2014
    Co-Authors: J. M. Conroy, H. G. Miller
    Abstract:

    The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On the other hand, from a phenomenological viewpoint, there are instances in which q cannot be treated as a constant. We present two distinct approaches for determining q depending on the form of the Equations of Constraint for the particular system. In the first case the Equations of Constraint for an operator O can be written as $Tr[F^{q}O]=C$, where C may be an explicit function of the distribution function, F. In this case one can solve an equivalent MAXENT problem which yields q as a function of the corresponding Lagrange Multiplier. As an illustration the exact solutions to the static Generalized Fokker-Planck Equation (GFP) are obtained from MAXENT. As in the case where C is a constant if q is treated as a variable within the MAXENT framework, the entropic measure is maximized for all values of q trivially. Therefore q must be determined from existing data. In the second case an additional Equation of Constraint exists which cannot be brought into the above form. In this case the additional Equation of Constraint may be used to determine the fixed value of q.

P. Long - One of the best experts on this subject based on the ideXlab platform.

  • Two-body Dirac Equation of Constraint dynamics for covariant interactions
    Bulletin of the American Physical Society, 1995
    Co-Authors: H. Crater, P. Long
    Abstract:

    Past work has led to explicit Schrodinger-like forms of the two-body Dirac Equations of Constraint dynamics for combined scalar, timelike vector, and spacelike vector interactions and applications to QED and quark model calculations of the meson spectrum. The authors find generalizations of those forms to include combined scalar, timelike vector, spacelike vector, pseudoscalar, time-like pseudovector, spacelike pseudovector, polar tensor and axial tensor interactions and discuss their Schrodinger-like forms useful for applications.

J. M. Conroy - One of the best experts on this subject based on the ideXlab platform.

  • Determining the Tsallis parameter via maximum entropy.
    Physical review. E Statistical nonlinear and soft matter physics, 2015
    Co-Authors: J. M. Conroy, H. G. Miller
    Abstract:

    The nonextensive entropic measure proposed by Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On the other hand, from a phenomenological viewpoint, there are instances in which q cannot be treated as a constant. We present two distinct approaches for determining q depending on the form of the Equations of Constraint for the particular system. In the first case the Equations of Constraint for the operator O can be written as Tr(F(q)O)=C, where C may be an explicit function of the distribution function F. We show that in this case one can solve an equivalent maxent problem which yields q as a function of the corresponding Lagrange multiplier. As an illustration the exact solution of the static generalized Fokker-Planck Equation (GFPE) is obtained from maxent with the Tsallis enropy. As in the case where C is a constant, if q is treated as a variable within the maxent framework the entropic measure is maximized trivially for all values of q. Therefore q must be determined from existing data. In the second case an additional Equation of Constraint exists which cannot be brought into the above form. In this case the additional Equation of Constraint may be used to determine the fixed value of q.

  • MAXENT and the Tsallis Parameter
    arXiv: Statistical Mechanics, 2014
    Co-Authors: J. M. Conroy, H. G. Miller
    Abstract:

    The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On the other hand, from a phenomenological viewpoint, there are instances in which q cannot be treated as a constant. We present two distinct approaches for determining q depending on the form of the Equations of Constraint for the particular system. In the first case the Equations of Constraint for an operator O can be written as $Tr[F^{q}O]=C$, where C may be an explicit function of the distribution function, F. In this case one can solve an equivalent MAXENT problem which yields q as a function of the corresponding Lagrange Multiplier. As an illustration the exact solutions to the static Generalized Fokker-Planck Equation (GFP) are obtained from MAXENT. As in the case where C is a constant if q is treated as a variable within the MAXENT framework, the entropic measure is maximized for all values of q trivially. Therefore q must be determined from existing data. In the second case an additional Equation of Constraint exists which cannot be brought into the above form. In this case the additional Equation of Constraint may be used to determine the fixed value of q.

H. Crater - One of the best experts on this subject based on the ideXlab platform.

  • Two-body Dirac Equation of Constraint dynamics for covariant interactions
    Bulletin of the American Physical Society, 1995
    Co-Authors: H. Crater, P. Long
    Abstract:

    Past work has led to explicit Schrodinger-like forms of the two-body Dirac Equations of Constraint dynamics for combined scalar, timelike vector, and spacelike vector interactions and applications to QED and quark model calculations of the meson spectrum. The authors find generalizations of those forms to include combined scalar, timelike vector, spacelike vector, pseudoscalar, time-like pseudovector, spacelike pseudovector, polar tensor and axial tensor interactions and discuss their Schrodinger-like forms useful for applications.

T. P. Tovstik - One of the best experts on this subject based on the ideXlab platform.

  • On the frequency spectrum of free vibrations of membranes and plates in contact with a fluid
    Vestnik St. Petersburg University: Mathematics, 2016
    Co-Authors: D. N. Ivanov, N. V. Naumova, V. S. Sabaneev, P. E. Tovstik, T. P. Tovstik
    Abstract:

    A parallelepiped-shaped container, which is completely filled with a perfect incompressible fluid, is considered. The container is covered with an elastic lid, which is modeled by a membrane or a constant-thickness plate. The other faces of the container are nondeformable. The frequency spectrum of small free vibrations of the lid has been obtained taking into account the apparent mass of the fluid the movement of which is assumed to be potential. The main specific feature of the problem formulation is that the volume of the fluid under the cover remains unchanged in the course of vibrations. As a result, the shape of the deflection of the lid should satisfy the Equation of Constraint, which follows from the condition of preservation of the volume of the fluid under the lid.