Phase transition in a self-gravitating planar gas

We consider a gas of Newtonian self-gravitating particles in two-dimensional space, finding a phase transition, with a high temperature homogeneous phase and a low temperature clumped one. We argue that the system is described in terms of a gas with fractal behaviour.     

Rapid and Efficient Synthesis of Imidazolines and Bisimidazolines Under Microwave and Ultrasonic Irradiation

Small assemblies of 2-imidazolines and bisimidazolines from appropriate nitriles and ethylenediamine with catalytic amounts of P₂S₅ employing a microwave assisted protocol were prepared. Sonication of this system also led to successful synthesis of 2-imidazolines and bisimidazolines. Another advantage of these systems is the ability to carry out large scale reactions.     

Multiplicatively and non-symmetric multiplicatively norm-preserving maps

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖ _X and ‖.‖ _Y denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖ _Y = ‖fg‖ _X , for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖ _X = ‖Tf Tg + α‖ _Y , f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,

Study of Salinity and pH Effects on Gelation Time of a Polymer Gel Using Central Composite Design Method

Experiments were conducted to investigate the main effects of salinity (NaCl) concentrations and pH factors and their interactions on the gelation time response of a polymer gel used in a water shutoff system in oil field reservoirs. Central composite design (CCD) was used to design experiments and a mathematical model building. The main advantage of CCD was to generate the quadratic mathematical model for the gelation time as functions of salinity and pH factors. Tests were limited and optimized by CCD points including low star (axial), low factorial, central, high factorial, and high star points. The evaluation of the data and the developed model were performed through the examination of graphical trend of residuals and a numerical approach. Analysis of variance (ANOVA) was used to estimate the amount of data variations from the model predictions. It was found that the model was significant at the 99% confidence against test data. The results showed that the gelation time was dependent more on pH than salinity. For low pH, the gelation time increased with increasing of the salinity, while for a high pH (>4) the relationship was inversed. The research shows that CCD can effectively be applied for the modeling of gelation time and finding an optimum condition to achieve maximum or minimum gelation time for different salinity and pH factors.     

Rheological and Mechanical Characterization of Multi-Walled Carbon Nanotubes/Polypropylene Nanocomposites

The rheology and morphology of multi-walled carbon nanotube (MWNT)/polypropylene (PP) nanocomposites prepared via melt blending was investigated. The minor phase content of MWNT varied between 0.25 and 8 wt%. From morphological studies using a scanning electron microscopy technique a good dispersion of carbon nanotubes in the PP matrix was observed. The rheological studies were performed by a capillary rheometer, and mechanical properties of the nanocomposites were studied using a tensile and flexural tester. Both PP and its nanocomposites showed non-Newtonian behavior. At low shear rates the addition of MWNT content causes an increase in viscosity; however, viscosity is less sensitive to addition of MWNT content at higher shear rates. Flow activation energy for the nanocomposites was calculated using an Arrhenius type equation. From this calculation it was concluded that the temperature sensitivity of nanocomposites was increased by increasing of nanotube content. An increase in tensile and flexural moduli and Izod impact strength was also observed by increasing the MWNT content. From rheological and mechanical tests it was concluded that the mechanical and rheological percolation threshold is at 1.5 wt%.     

Swelling and Gelation Time Behavior of Sulfonated Polyacrylamide/Chromium Triacetate Hydrogels

A hydrogel was prepared by crosslinking of aqueous solutions of sulfonated polyacrylamide/chromium triacetate for use in water shut-off operations in oil reservoirs. The effects of pH, salinity, retarder and temperature, as well as co-polymer and crosslinker concentration, on the gelation time were investigated. The results indicated that as temperature increased, gelation occurred more rapidly. The activation energy was measured as about 86 kJ/mol. The effects of initial pH and retarder on the gelation time were also examined. The results showed that addition of retarder and increasing of pH increased and decreased the gelation time, respectively. The increase of co-polymer concentration in solution increased the gel swelling. However, the increase of crosslinker concentration decreased the gel swelling. In the presence of electrolytes, the gel swelling decreased by about 80%. Finally, some usable practical recommendations are offered for the gelling systems in reservoirs.     

New Pool Boiling Heat Transfer in the Presence of Low-Frequency Vibrations Into a Vertical Cylindrical Heat Source

A vertical cylinder was applied as a heat source into a water pool; the vibrations were imposed into the heater with different heat fluxes, and the frequencies were adjusted at 10, 15, 20, and 25 Hz. An imaging system was employed to observe the produced bubbles around the cylindrical heat source. The results showed that the boiling heat transfer was enhanced under the vibrations with a shorter transient process, and the wall temperature also decreased. The best enhancement ratio was achieved at the frequency of 25 Hz and a heat flux value of 30 kW/m² as a consequence of imposed vibrations.     

Smarandache Vertices of the Graphs Associated to the Commutative Rings

Let R be a commutative ring with identity 1 ≠ 0. A nonzero element a in R is said to be a Smarandache zero-divisor if there exist three different nonzero elements x, y, and b (≠ a) in R such that ax = ab = by = 0, but xy ≠ 0. We will generalize this notion to the Smarandache vertex of an arbitrary simple graph and characterize the Smarandache zero-divisors of commutative rings (resp. with respect to an ideal) via their associated zero-divisor graphs. We illustrate them with examples and prove some interesting results about them.     

Slant Submanifolds of Almost Contact Metric 3-Structure Manifolds

In this paper we introduce the notion of slant submanifold of an almost contact metric 3-structure manifold. We give some examples and characterize these submanifolds. Moreover, Sasakian slant submanifolds of an almost contact 3-structure manifold are defined and studied. We also establish a sharp inequality including the squared mean curvature and Ricci curvature of a Sasakian slant submanifold.