ITSTUDIES ON THE EFFECT OF UREA ON THE COMPATIBILITY OF PMMA/PVC MIXTURES IN DMF BY A DILUTE- SOLUTION VISCOMETRY METHOD

The interaction between poly(methymethacrylate) (PMMA) and poly(vinyl chloride) (PVC) has been studied indilute urea solutions of dimethylformamide (DMF) at 28℃ using a dilute solution viscometry method. The results show thatthe polymer mixtures are compatible in DMF solution in the absence of urea. The influence of urea addition on the degree ofcompatibility of the polymer mixtures has been studied in terms of the compatibility parameters (△b_m and △[η]_m). It wasfound that the compatibility of the polymer mixtures is decreased with increasing urea addition, passing through a minimumat 0.5 M urea.     

Phase mismatch effects on the dynamics of a semilinear photorefractive oscillator with reflection-type gratings

This paper describes the effect of pump waves misalignement on the performance of the semilinear photorefractive coherent oscillator with the reflection gratings. The oscillation intensity and its modulation frequency are calculated numerically for different misalignement angles, coupling strengths and pump intensity ratios. It is shown that a small angular detuning of the pump wave, less than one milliradian, extends the range of pump ratios and the range of coupling strengths for which a non-degenerate oscillation occurs. The results of experiments with the BaTiO₃-based semilinear oscillator are in qualitative agreement with the calculated data.     

Classification of finite Morse index solutions for Hénon type elliptic equation -\Delta u = |x|^{\alpha } u_{+}^{p}

In this paper we investigate the non-autonomous elliptic equations \(-\Delta u = |x|^{\alpha } u_{+}^{p}\) in \( \mathbb{R }^{N}\) and in \( \mathbb{R }_+^{N}\) with the Dirichlet boundary condition, with \(N \ge 2\) , \(p>1\) and \(\alpha >-2\) . We consider the weak solutions with finite Morse index and obtain some classification results.     

Effects of angular pump mismatch for the semi-linear oscillator

We investigate, analytically and numerically, the influence of an angular mismatch of counter-propagating pump beams on the threshold of oscillation for the photorefractive semi-linear oscillator driven by non-local non-linear response. Our analysis includes the frequency degenerate and non-degenerate regimes within a wide range of the variable input parameters—the coupling strength, the pump ratio, and the feedback mirror reflectivity. The limiting case of mirrorless oscillation is considered as well. The main outcome of our studies is the possibility of strong reduction of the oscillation threshold owing to the angular mismatch. Furthermore, increasing the mismatch induces pronounced bifurcations of the oscillation parameters, including transitions between degenerate and non-degenerate oscillation modes. The main findings are verified by direct simulations of the dynamic equations.     

VISCOMETRIC STUDY OF POLY(METHYL METHACRYLATE) AND POLYSTYRENE BLENDS IN DIFFERENT SOLVENTS

The intermolecular interaction between poly(methyl methacrylate) (PMMA) and polystyrene (PS) intetrahydrofuran (THF) and N,N'-dimethyl formamide (DMF) solvents was studied at 28℃ using a dilute solution viscometrymethod. Solvent is believed to play a key role in characterizing the viscosity behavior of the polymer solution. The intrinsicviscosity and viscosity interaction parameter were experimentally measured for the binary (solvent/polymer) and for theternary systems in two solvents. The compatibility of the polymer mixture was discussed in terms of the sign of △b_m. Theresults show that the compatibility of PMMA/PS blend in DMF is larger than that in THF.     

Hardy and Cowling–Price theorems associated with the Jacobi–Cherednik operator

This paper is devoted to the proof of Hardy and Cowling–Price type theorems for the Fourier transform tied to the Jacobi–Cherednik operator.     

A priori estimates for superlinear and subcritical elliptic equations: the Neumann boundary condition case

We consider here solutions of a nonlinear Neumann elliptic equation Δu +?f (x, u) =?0 in Ω, ?u/?ν =?0 on ?Ω, where Ω is a bounded open smooth domain in ${\mathbb{R}^N, N\geq2}$ and f satisfies super-linear and subcritical growth conditions. We prove that L ^∞?bounds on solutions are equivalent to bounds on their Morse indices.     

Equilibrium and dynamics of Langmuir monolayers when the interface is a selective solvent: Polystyrene-b-poly(t-butyl acrylate) block copolymers

The surface pressure of monolayers of insoluble diblock copolymers has been measured. One of the blocks is made of poly(t-butyl acrylate) (PtBA), and the other one by polystyrene (PS). The interface is a good solvent for PtBA, while it is a poor solvent for PS. For the sake of comparison, monolayers of a PtBA homopolymer (good solvent conditions) and of poly(4-hydroxy styrene) (P4HS) (poor solvent conditions) have been also measured. It has been found that the relative length of the blocks plays an important role on the shape of the surface pressure Pi versus surface concentration Gamma curves and also on the shape of the equilibrium compressibility versus Gamma curves. However, it does not affect the maximum value of Pi reached at high Gamma's. Surprisingly, the ellipsometric thickness of the copolymer monolayers is almost independent of the relative length of the blocks. The dynamics of the monolayers has been studied by step compression and by surface-light scattering techniques. When M(w,PtBA) > M(w,PS) single exponential relaxations are observed. However, stretched exponentials are obtained for M(w,PS) > or = M(w,PtBA). The relaxation times decrease with increasing Gamma for all the copolymers studied. This is the behavior usually found for poor solvent conditions (P4HS) and opposite to that found for homopolymers under good solvent conditions [PtBA, poly(vinylacetate)]. This means that the solvent quality of the interface does not determine the pressure dependence of tau. The elasticity modulus of the monolayers in the kilohertz range takes values that are similar to those of the high-frequency limit of the relaxation experiments. This means that the relaxation processes have characteristic frequencies below 1 Hz.     

On heat transfer effects of a viscous fluid squeezed and extruded between two parallel plates

The unsteady squeezing and extrusion of a viscous fluid between two parallel plates of constant temperature is examined. The dimensionless extrusion parameter,=U/V, is introduced to represent the effects of the extrusion on the squeezing velocities. The squeezing parameter=VH/, represents the effect of the inertial forces on heat and fluid flow characteristics. It is found that increasing the extrusion parameter will increase both the velocity and the heat transfer rates to the viscous fluid. Increasing the squeezing parameter had also decreased the fluid velocity and enhanced heat transfer rates. Increasing the viscous effects or the Eckert number E=U²/c_p (T_E – T_s) heated the fluid and consequently decreased the heat transfer rates. Different velocity profiles, temperature profiles, and Nusselt numbers against various dimensionless groups are drawn.