Scaling Equation

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

E. Kogan - One of the best experts on this subject based on the ideXlab platform.

  • Poor man's Scaling: anisotropic Kondo and Coqblin--Schrieffer models
    Journal of Physics Communications, 2018
    Co-Authors: E. Kogan
    Abstract:

    We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive Scaling Equation to the second order for such a model. We show how the Scaling Equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general Scaling Equation. We introduce the anisotropic Coqblin--Schrieffer model, apply the general method to derive Scaling Equation for that model for the power law DOS, and integrate the derived Equation analytically.

  • Poor man's Scaling Equation for the anisotropic modified Coqblin--Schrieffer model
    2018
    Co-Authors: E. Kogan
    Abstract:

    We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive Scaling Equation to the second order for such a model. We show how the Scaling Equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general Scaling Equation. We introduce the anisotropic Coqblin--Schrieffer model, apply the general method to derive Scaling Equation for that model for the power law DOS, and integrate the derived Equation analytically.

  • Poor man's Scaling Equation for the anisotropic Coqblin--Schrieffer model
    arXiv: Mesoscale and Nanoscale Physics, 2018
    Co-Authors: E. Kogan
    Abstract:

    We derive the poor man's Scaling Equation to the second order for a general anisotropic model, describing embedded into a gas of itinerant electrons a point scatterer, with its own degrees of freedom. We show how the obtained previously Scaling Equations for anisotropic $s-d$ exchange model follow from it. We apply the general Scaling Equation to the anisotropic Coqblin--Schrieffer model. We solve analytically thus obtained poor man Scaling Equation for that model for the particular case $N=2$. We find the phase, which corresponds to the isotropic Coqblin--Schrieffer model with infinitely strong exchange interaction (the Kondo phase) and the phase with finitely strong Ising interaction.

  • Poor man's Scaling: Kondo and generalized Coqblin--Schrieffer models
    2018
    Co-Authors: E. Kogan
    Abstract:

    We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive Scaling Equation to the second order for such a model. We show how the Scaling Equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general Scaling Equation. We introduce the anisotropic Coqblin--Schrieffer model, apply the general method to derive Scaling Equation for that model for the power law DOS, and integrate the derived Equation analytically.

  • Poor man's Scaling: Kondo and the Coqblin--Schrieffer models
    2018
    Co-Authors: E. Kogan
    Abstract:

    We discuss Kondo effect for a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, and derive Scaling Equation to the second order for such a model. We show how the Scaling Equation for the spin-anisotropic Kondo model with the power law density of states (DOS) for itinerant electrons follows from the general Scaling Equation. We introduce the anisotropic Coqblin--Schrieffer model, apply the general method to derive Scaling Equation for that model for the power law DOS, and integrate the derived Equation analytically.

Xiaoyun Zhang - One of the best experts on this subject based on the ideXlab platform.

  • generalized Scaling of spontaneous imbibition data for strongly water wet systems
    Journal of Petroleum Science and Engineering, 1997
    Co-Authors: Ma Shouxiang, Norman Robert Morrow, Xiaoyun Zhang
    Abstract:

    Mass transfer between fractures and matrix blocks is critical to oil recovery by waterflooding in fractured reservoirs. A Scaling Equation has been used for rate of oil recovery by spontaneous imbibition and presented their results as oil recovery vs. dimensionless time. Many conditions apply to this Scaling Equation, including identical core sample shapes and fluid viscosity ratios. Recent investigation by experiment of these two factors has resulted in a more generalized Scaling Equation for strongly water-wet systems with a general definition of characteristic length and a viscosity ratio term included in the definition of dimensionless time. In this paper, published data on oil recovery by imbibition have been analyzed and correlated through application of the new definition. These data sets were for different porous media, core dimensions, boundary conditions, and oil and water viscosities. All of the systems were strongly water-wet. The generalized correlation was fitted closely by an empirical mass transfer function with the new definition of dimensionless time as the only parameter.

  • Generalized Scaling Of Spontaneous Imbibition Data For Strongly Water-Wet Systems
    Technical Meeting Petroleum Conference of The South Saskatchewan Section, 1995
    Co-Authors: Norman Robert Morrow, Xiaoyun Zhang
    Abstract:

    Mass transfer between fractures and matrix blocks is critical to oil recovery by waterflooding in fractured reservoirs. A Scaling Equation has been used for rate of oil recovery by spontaneous imbibition and presented their results as oil recovery vs. dimensionless time. Many conditions apply to this Scaling Equation, including identical core sample shapes and fluid viscosity ratios. Recent investigation by experiment of these two factors has resulted in a more generalized Scaling Equation for strongly water-wet systems with a general definition of characteristic length and a viscosity ratio term included in the definition of dimensionless time. In this paper, published data on oil recovery by imbibition have been analyzed and correlated through application of the new definition. These data sets were for different porous media, core dimensions, boundary conditions, and oil and water viscosities. All of the systems were strongly water-wet. The generalized correlation was fitted closely by an empirical mass transfer function with the new definition of dimensionless time as the only parameter. © 1997 Elsevier Science B.V.

Francesco Parisen Toldin - One of the best experts on this subject based on the ideXlab platform.

  • the critical Equation of state of the three dimensional o n universality class n 4
    Nuclear Physics, 2005
    Co-Authors: Agostino Butti, Francesco Parisen Toldin
    Abstract:

    Abstract We determine the Scaling Equation of state of the three-dimensional O ( N ) universality class, for N = 5 , 6 , 32 , 64 . The N = 5 model is relevant for the SO ( 5 ) theory of high- T c superconductivity, while the N = 6 model is relevant for the chiral phase transition in two-color QCD with two flavors. We first obtain the critical exponents and the small-field, high-temperature, expansion of the effective potential (Helmholtz free energy) by analyzing the available perturbative series, in both fixed-dimension and e-expansion schemes. Then, we determine the critical Equation of state by using a systematic approximation scheme, based on polynomial representations valid in the whole critical region, which satisfy the known analytical properties of the Equation of state, take into account the Goldstone singularities at the coexistence curve and match the small-field, high-temperature, expansion of the effective potential. This allows us also to determine several universal amplitude ratios. We also compare our approximate solutions with those obtained in the large-N expansion, up to order 1 / N , finding good agreement for N ≳ 32 .

  • The Scaling Equation of state of the 3-D O(4) universality class
    Journal of High Energy Physics, 2003
    Co-Authors: Francesco Parisen Toldin, Andrea Pelissetto, Ettore Vicari
    Abstract:

    We determine the Scaling Equation of state of the three-dimensional O(4) universality class, which is relevant for the finite-temperature transition of quantum chromodynamics with two light flavors. We first consider the small-field expansion of the effective potential (Helmholtz free energy). Then, we apply a systematic approximation scheme based on polynomial parametric representations that are valid in the whole critical regime, satisfy the correct analytic properties (Griffiths' analyticity), take into account the Goldstone singularities at the coexistence curve, and match the small-field expansion of the effective potential. From the approximate representations of the Equation of state, we obtain estimates of several universal amplitude ratios.

Hyoung Jin Choi - One of the best experts on this subject based on the ideXlab platform.

  • generalized yield stress Equation for electrorheological fluids
    Journal of Colloid and Interface Science, 2013
    Co-Authors: Ke Zhang, Myung S Jhon, Ying Dan Liu, Hyoung Jin Choi
    Abstract:

    A new generalized yield stress Scaling Equation for electrorheological (ER) fluids was developed by introducing the critical electric field (Ec) and material parameter. This Equation can be used to describe the dependency of the yield stress on an electric field not only for conventional ER suspensions with a change in slope from 2.0 to 1.5, but also for giant ER fluids with a change in slope from 2.0 to 1.0. The yield stress data obtained from different ER fluid systems with different material parameters was collapsed onto a single curve for the entire range of electric field strengths using the proper Scaling method proposed in this study.

  • yield stress analysis of 1d calcium and titanium precipitate based giant electrorheological fluids
    Colloid and Polymer Science, 2013
    Co-Authors: Ying Dan Liu, Yuchuan Cheng, Hyoung Jin Choi
    Abstract:

    1D calcium and titanium composite nanorods synthesized were applied as electrorheological (ER) active materials with extremely high static yield stresses, i.e., giant ER effect. The yield stress of this giant ER fluid was analyzed using a new universal yield stress Scaling Equation in the form of the modified Bessel functions with two different limiting behaviors in a low and high electric field region. The universal yield stress Equation collapsed the yield stress data onto a single curve.

  • new analysis of yield stress on giant electrorheological fluids
    Colloid and Polymer Science, 2012
    Co-Authors: Sesha Hari Vemuri, Myung S Jhon, Ke Zhang, Hyoung Jin Choi
    Abstract:

    A new universal yield stress Scaling Equation is proposed to accurately model experimental data for giant electrorheological (GER) fluids. This new Equation expressed in modified Bessel function predicts both regions of polarization effect predominant in the low electric field strength applied and polar molecule-dominating GER behavior, as well as collapses the experimental data of yield stress in a single line for a broad range of electric field strengths.