The Experts below are selected from a list of 10647 Experts worldwide ranked by ideXlab platform

Changyou Wang - One of the best experts on this subject based on the ideXlab platform.

  • Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells
    Chinese Annals of Mathematics Series B, 2019
    Co-Authors: Fanghua Lin, Changyou Wang
    Abstract:

    This is in the sequel of authors’ paper [Lin, F. H., Pan, X. B. and Wang, C. Y., Phase transition for potentials of high dimensional wells, Comm. Pure Appl. Math. , 65 (6), 2012, 833-888] in which the authors had set up a program to verify rigorously some formal statements associated with the multiple component phase transitions with higher dimensional wells. The main goal here is to establish a regularity theory for minimizing maps with a rather non-Standard Boundary Condition at the sharp interface of the transition. The authors also present a proof, under simplified geometric assumptions, of existence of local smooth gradient flows under such constraints on interfaces which are in the motion by the mean-curvature. In a forthcoming paper, a general theory for such gradient flows and its relation to Keller-Rubinstein-Sternberg’s work (in 1989) on the fast reaction, slow diffusion and motion by the mean curvature would be addressed.

  • harmonic maps in connection of phase transitions with higher dimensional potential wells
    arXiv: Analysis of PDEs, 2018
    Co-Authors: Changyou Wang
    Abstract:

    This is in the sequel of authors' paper \cite{LPW} in which we had set up a program to verify rigorously some formal statements associated with the multiple component phase transitions with higher dimensional wells. The main goal here is to establish a regularity theory for minimizing maps with a rather non-Standard Boundary Condition at the sharp interface of the transition. We also present a proof, under simplified geometric assumptions, of existence of local smooth gradient flows under such constraints on interfaces which are in the motion by the mean-curvature. In a forthcoming paper, a general theory for such gradient flows and its relation to Keller-Rubinstein-Sternberg's work \cite{KRS1, KRS2} on the fast reaction, slow diffusion and motion by the mean curvature would be addressed.

Gert Heinrich - One of the best experts on this subject based on the ideXlab platform.

  • Polymer adsorption in finite range surface potentials: Planar and spherical adsorbing surfaces
    The Journal of Chemical Physics, 2009
    Co-Authors: A. I. Chervanyov, Gert Heinrich
    Abstract:

    We analytically solve the problem of the reversible adsorption of Gaussian polymers onto the planar and spherical surfaces in the presence of the square well attractive potential. By making use of the obtained exact solution of the Edwards equation, we calculate the end density and surface excess of the polymers at the planar and spherical substrates. We derive the exact equation that determines the surface bound states that give rise to the dominant contributions to the polymer surface excess. In the case of the spherical substrate, the exact expression for the polymer surface excess is obtained in the remarkably simple form of a quadratic function of the radius of the substrate. Using the calculated polymer surface excesses, we obtain the adsorption-desorption diagrams of the polymers adsorbed onto the spherical and planar surface in terms of the introduced “effectiveness” of the adsorption potential. By performing the analogous calculation based of the Standard Boundary Condition approach, we demonstra...

Ruxandra Stavre - One of the best experts on this subject based on the ideXlab platform.

  • Asymptotic analysis of a thin rigid stratified elastic plate – viscous fluid interaction problem
    Applicable Analysis, 2016
    Co-Authors: Irina Malakhova-ziablova, Grigory Panasenko, Ruxandra Stavre
    Abstract:

    A three-dimensional model for the interaction of a thin stratified rigid plate and a viscous fluid layer is considered. This problem depends on a small parameter which is the ratio of the thickness of the plate and that of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate’s Young’s modulus is of order , i.e. it is great, while its density is of order 1. At the solid–fluid interface, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is proved for the partial sums of the asymptotic expansion. The limit problem contains a non-Standard Boundary Condition for the Stokes equations. The existence, uniqueness, and regularity of its solution are proved. The asymptotic analysis is applied to the partial asymptotic dimension redu...

  • Asymptotic analysis of a thin rigid stratified elastic plate – viscous fluid interaction problem
    Applicable Analysis, 2016
    Co-Authors: Irina Malakhova-ziablova, Grigory Panasenko, Ruxandra Stavre
    Abstract:

    A three-dimensional model for the interaction of a thin stratified rigid plate and a viscous fluid layer is considered. This problem depends on a small parameter $\varepsilon$ which is the ratio of the thickness of the plate and that of the fluid layer. The right-hand side functions are 1-periodic with respect to the tangential variables of the plate. The plate’s Young’s modulus is of order $\varepsilon^{-3}$, i.e. it is great, while its density is of order 1. At the solid–fluid interface, the velocity and the normal stress are continuous. The variational analysis of this model (including the existence, uniqueness of the solution and its regularity) is provided. An asymptotic expansion of the solution is constructed and justified. The error estimate is proved for the partial sums of the asymptotic expansion. The limit problem contains a non-Standard Boundary Condition for the Stokes equations. The existence, uniqueness, and regularity of its solution are proved. The asymptotic analysis is applied to the partial asymptotic dimension reduction of the solid phase and the derivation of the asymptotically exact junction Conditions between two-dimensional and three-dimensional models of the plate.

Hassan Sidibé - One of the best experts on this subject based on the ideXlab platform.

A. I. Chervanyov - One of the best experts on this subject based on the ideXlab platform.

  • Polymer adsorption in finite range surface potentials: Planar and spherical adsorbing surfaces
    The Journal of Chemical Physics, 2009
    Co-Authors: A. I. Chervanyov, Gert Heinrich
    Abstract:

    We analytically solve the problem of the reversible adsorption of Gaussian polymers onto the planar and spherical surfaces in the presence of the square well attractive potential. By making use of the obtained exact solution of the Edwards equation, we calculate the end density and surface excess of the polymers at the planar and spherical substrates. We derive the exact equation that determines the surface bound states that give rise to the dominant contributions to the polymer surface excess. In the case of the spherical substrate, the exact expression for the polymer surface excess is obtained in the remarkably simple form of a quadratic function of the radius of the substrate. Using the calculated polymer surface excesses, we obtain the adsorption-desorption diagrams of the polymers adsorbed onto the spherical and planar surface in terms of the introduced “effectiveness” of the adsorption potential. By performing the analogous calculation based of the Standard Boundary Condition approach, we demonstra...