• Title, Summary, Keyword: critical point theory

Search Result 174, Processing Time 0.036 seconds

A Calculation for the Viscosity of Fluid at the Critical Point

  • Kim, Won-Soo;Chair, Tong-Seek
    • Bulletin of the Korean Chemical Society
    • /
    • v.23 no.11
    • /
    • pp.1524-1526
    • /
    • 2002
  • It is very difficult to measure the fluid viscosity at the critical point, there are seldom found experimental values of fluid viscosity at the critical point. Few theories can explain the critical viscosity quantitatively. A theory of viscosity previously proposed by authors10 is applied to the fluid at the critical point. This theory can be simplified as a simple form with no adjustable parameters, allowing for easy calculation. Viscosities at the critical point for some substances have been calculated, and calculated results are satisfactory when compared with the observed values.

CRITICAL POINTS RESULT FOR THE C1,1 FUNCTIONAL AND THE RELATIVE CATEGORY THEORY

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.21 no.4
    • /
    • pp.437-445
    • /
    • 2008
  • We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

  • PDF

PERIODIC SOLUTIONS FOR THE NONLINEAR HAMILTONIAN SYSTEMS

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
    • /
    • v.17 no.3
    • /
    • pp.331-340
    • /
    • 2009
  • We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

  • PDF

LIMIT RELATIVE CATEGORY THEORY APPLIED TO THE CRITICAL POINT THEORY

  • Jung, Tack-Sun;Choi, Q-Heung
    • Bulletin of the Korean Mathematical Society
    • /
    • v.46 no.2
    • /
    • pp.311-319
    • /
    • 2009
  • Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

A Study on the Abnormal Behavior of the Viscosity near the Critical Point

  • Kim, Won-Soo;Pak, Hyung-Suk;Chair, Tong-Seek
    • Bulletin of the Korean Chemical Society
    • /
    • v.10 no.4
    • /
    • pp.372-374
    • /
    • 1989
  • The new viscosity theory is applied to the abnormal behavior of the viscosity near the critical point. This theory suggests that the viscosity is equal to the product of the absolute pressure(kinetic pressure + internal pressure) and the collision time. We can find this abnormal behavior to be due to the large collision time near the critical point. The agreements between theoriticals and experimentals of the critical enhancement are satisfactory.

  • PDF

HAMILTONIAN SYSTEM WITH THE SUPERQUADRATIC NONLINEARITY AND THE LIMIT RELATIVE CATEGORY THEORY

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
    • /
    • v.22 no.3
    • /
    • pp.471-489
    • /
    • 2014
  • We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

THE INDEX FOR A TOPOLOGICAL DEGREE THEORY FOR DENSELY DENIED OPERATORS OF TYPE ${S_+}_O,L$ IN BANACH SPACES

  • Kartsatos, Athanassios G.;Skrypnik, Igor V.
    • Journal of the Korean Mathematical Society
    • /
    • v.37 no.6
    • /
    • pp.901-913
    • /
    • 2000
  • This is a summary of results involving the development of a theory of an index of an isolated critical point for densely defined nonlinear operators of type (S(sub)+)(sub)0,L. This index theory is associated with a degree theory, for such operators, whch has been recently developed by the authors.

  • PDF

ASYMPTOTICALLY LINEAR BEAM EQUATION AND REDUCTION METHOD

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
    • /
    • v.19 no.4
    • /
    • pp.481-493
    • /
    • 2011
  • We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.