Search results for "Critical point"
showing 10 items of 228 documents
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
Three solutions for a two-point boundary value problem with the prescribed mean curvature equation
2015
The existence of at least three classical solutions for a parametric ordinary Dirichlet problem involving the mean curvature operator are established. In particular, a variational approach is proposed and the main results are obtained simply requiring the sublinearity at zero of the considered nonlinearity.
Thermodynamic properties of a liquid–vapor interface in a two-component system
2010
Abstract We report a complete set of thermodynamic properties of the interface layer between liquid and vapor two-component mixtures, using molecular dynamics. The mixtures consist of particles which have identical masses and diameters and interact with a long-range Lennard-Jones spline potential. The potential depths in dimensionless units for like interactions is 1 (for component 1) and 0.8 (for component 2). The surface excess entropy decreases when the temperature increases, so the surface has a negative excess heat capacity. This is a consequence of the fact that the surface tension decreases to zero at the critical point, proportional to ( T C , i − T ) 2 ν . The surface entropy decre…
On the effect of pressure on the phase transition of polymer blends and polymer solutions: Oligostyrene–n-alkane systems
2001
Critical temperatures of some binary solutions of weakly interacting low molecular weight polystyrenes dissolved in linear alkanes (oligoethylenes) were measured over the range 0.1 to 100 MPa. While (dT/dP)crit along the upper critical solution (UCS) locus for a “typical blend” is positive, and for the “ typical solution” can be either positive or negative (but is usually negative), there is no essential difference between blend and solution. Rather, the difference in sign is a consequence of the location of the hypercritical point (that point in (T,P)crit space where (dT/dP)crit changes sign, [(dT/dP)crit = 0 and (d2T/dP2)crit>0], also called the double critical point, DCP), which is norma…
Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
2021
We look for solutions to the Schr\"{o}dinger-Poisson-Slater equation $$- \Delta u + \lambda u - \gamma (|x|^{-1} * |u|^2) u - a |u|^{p-2}u = 0 \quad \text{in} \quad \mathbb{R}^3, $$ which satisfy \begin{equation*} \int_{\mathbb{R}^3}|u|^2 \, dx = c \end{equation*} for some prescribed $c>0$. Here $ u \in H^1(\mathbb{R}^3)$, $\gamma \in \mathbb{R},$ $ a \in \mathbb{R}$ and $p \in (\frac{10}{3}, 6]$. When $\gamma >0$ and $a > 0$, both in the Sobolev subcritical case $p \in (\frac{10}{3}, 6)$ and in the Sobolev critical case $p=6$, we show that there exists a $c_1>0$ such that, for any $c \in (0,c_1)$, the equation admits two solutions $u_c^+$ and $u_c^-$ which can be characterized respectively…
On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations
2016
In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.
Multiple periodic solutions for Hamiltonian systems with not coercive potential
2010
Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems. © 2009 Elsevier Inc. All rights reserved.
Characterization of the pressure induced Ringwoodite toMg-perovskite and Mg-wüstite phase transition by Catastrophe Theory
2010
The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electro…
2011
In order to characterize the pressure-induced decomposition of ringwoodite (c-Mg2SiO4), the topological analysis of the electron density q(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree– Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite -> Mg-perovskite + periclase) occurring at the transition zone–lower…
Thermodynamic study on phase equilibrium of epoxy resin/thermoplastic blends
2008
Abstract The experimental phase diagrams (cloud point curves) of three series of epoxy/thermoplastic blends, namely, epoxy/polystyrene (PS), epoxy/poly(ether sulfone) (PES), and epoxy/poly(ether imide) (PEI) as a function of molar mass and composition have been analysed from a thermodynamic point of view. A model based on the Flory–Huggins lattice theory considering the concentration dependence of the interaction parameter as predicted by Koningsveld was employed to determine the equilibrium compositions, and concentration and temperature dependent interaction parameters. Binodal, spinodal, and critical point data have been computed and show good agreement with experimental data.