The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform

Thomas Jordan - One of the best experts on this subject based on the ideXlab platform.

  • Phase Transitions for Suspension Flows
    Communications in Mathematical Physics, 2013
    Co-Authors: Godofredo Iommi, Thomas Jordan
    Abstract:

    This paper is devoted to studying the thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the Pressure Function. We establish conditions for the Pressure Function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the Pressure has countably many phase transitions.

  • Phase transitions for suspension flows
    Communications in Mathematical Physics, 2013
    Co-Authors: Godofredo Iommi, Thomas Jordan
    Abstract:

    This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the Pressure Function. We establish conditions for the Pressure Function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the Pressure has countably many phase transitions.

Wolf Val Pinczewski - One of the best experts on this subject based on the ideXlab platform.

  • Menisci in a wedge and a slit for incomplete wetting conditions
    Journal of Colloid and Interface Science, 1999
    Co-Authors: M Kagan, Wolf Val Pinczewski
    Abstract:

    Abstract This paper presents a closed form analytical solution to the augmented Young–Laplace equation for the meniscus profile in two-dimensional wedge- and slit-shaped capillaries. The solution is valid for conditions of complete and incomplete wetting and for any form of the disjoining Pressure Function.

  • Meniscus and contact angle in an eye-shaped capillary
    Journal of colloid and interface science, 1998
    Co-Authors: M Kagan, Wolf Val Pinczewski
    Abstract:

    Abstract This paper presents an approximate analytical solution to the augmented Young–Laplace equation for the meniscus profile in an eye-shaped capillary. The solution is valid for nonmonotonic forms of the disjoining Pressure Function and shows the relationship between the meniscus profile, contact angle, and disjoining Pressure. The expression derived for the contact angle reduces to the widely used Deryaguin–Frumkin formula.

  • Meniscus in a Narrow Slit
    Journal of Colloid and Interface Science, 1996
    Co-Authors: M Kagan, Wolf Val Pinczewski
    Abstract:

    Abstract This note presents a closed-form analytical solution to the augmented Young–Laplace equation for the meniscus profile in a narrow slit. The solution is valid for any monotonic form of the disjoining Pressure Function.

Godofredo Iommi - One of the best experts on this subject based on the ideXlab platform.

  • Phase Transitions for Suspension Flows
    Communications in Mathematical Physics, 2013
    Co-Authors: Godofredo Iommi, Thomas Jordan
    Abstract:

    This paper is devoted to studying the thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the Pressure Function. We establish conditions for the Pressure Function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the Pressure has countably many phase transitions.

  • Phase transitions for suspension flows
    Communications in Mathematical Physics, 2013
    Co-Authors: Godofredo Iommi, Thomas Jordan
    Abstract:

    This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the Pressure Function. We establish conditions for the Pressure Function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the Pressure has countably many phase transitions.

  • The Lyapunov spectrum as the Newton method
    Physica A: Statistical Mechanics and its Applications, 2012
    Co-Authors: Godofredo Iommi
    Abstract:

    Abstract For a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton–Raphson method applied to the derivative of the Pressure Function.

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

  • Menisci in a wedge and a slit for incomplete wetting conditions
    Journal of Colloid and Interface Science, 1999
    Co-Authors: M Kagan, Wolf Val Pinczewski
    Abstract:

    Abstract This paper presents a closed form analytical solution to the augmented Young–Laplace equation for the meniscus profile in two-dimensional wedge- and slit-shaped capillaries. The solution is valid for conditions of complete and incomplete wetting and for any form of the disjoining Pressure Function.

  • Meniscus and contact angle in an eye-shaped capillary
    Journal of colloid and interface science, 1998
    Co-Authors: M Kagan, Wolf Val Pinczewski
    Abstract:

    Abstract This paper presents an approximate analytical solution to the augmented Young–Laplace equation for the meniscus profile in an eye-shaped capillary. The solution is valid for nonmonotonic forms of the disjoining Pressure Function and shows the relationship between the meniscus profile, contact angle, and disjoining Pressure. The expression derived for the contact angle reduces to the widely used Deryaguin–Frumkin formula.

  • Meniscus in a Narrow Slit
    Journal of Colloid and Interface Science, 1996
    Co-Authors: M Kagan, Wolf Val Pinczewski
    Abstract:

    Abstract This note presents a closed-form analytical solution to the augmented Young–Laplace equation for the meniscus profile in a narrow slit. The solution is valid for any monotonic form of the disjoining Pressure Function.

Mariusz Urbański - One of the best experts on this subject based on the ideXlab platform.

  • TRANSVERSALITY FAMILY OF EXPANDING RATIONAL SEMIGROUPS
    Advances in Mathematics, 2013
    Co-Authors: Hiroki Sumi, Mariusz Urbański
    Abstract:

    Abstract We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a d -parameter family of such semigroups satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the Pressure Function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the Pressure Function is greater than 2 , then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient conditions for a family to satisfy the transversality conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with the transversality condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the Pressure Function and is less than 2 . We also show that a family of small perturbations of the Sierpinski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the Pressure Function, which is equal to the similarity dimension. Combining the arguments on the transversality condition, thermodynamical formalisms and potential theory, we show that for each a ∈ C with | a | ≠ 0 , 1 , the family of small perturbations of the semigroup generated by { z 2 , a z 2 } satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.

  • Transversality Family of Expanding Rational Semigroups
    arXiv: Dynamical Systems, 2011
    Co-Authors: Hiroki Sumi, Mariusz Urbański
    Abstract:

    This paper deals with both complex dynamical systems and conformal iterated Function systems. We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a $d$-parameter family of such semigroups satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the Pressure Function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the Pressure Function is greater than 2, then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient conditions for a family to satisfy the transversality conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with transversality condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the Pressure Function and is less than 2. We also show that a family of small perturbations of Sierpi\'nski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the Pressure Function, which is equal to the similarity dimension. Combining the arguments on the transversality condition, thermodynamical formalisms and potential theory, we show that for each complex number $a$ with $|a|\neq 0,1$, the family of small perturbations of the semigroup generated by ${z^{2}, az^2} $ satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.