Dynamical signatures of ‘phase transitions’: Chaos in finite clusters

Finite clusters of atoms or molecules, typically composed of about 50 particles (and often as few as 13 or even less) have proved to be useful prototypes of systems undergoing phase transitions. Analogues of the solid-liquid melting transition, surface melting, structural phase transitions and the glass transition have been observed in cluster systems. The methods of nonlinear dynamics can be applied to systems of this size, and these have helped elucidate the nature of the microscopic dynamics, which, as a function of internal energy (or ‘temperature’) can be in a solidlike, liquidlike, or even gaseous state. The Lyapunov exponents show a characteristic behaviour as a function of energy, and provide a reliable signature of the solid-liquid melting phase transition. The behaviour of such indices at other phase transitions has only partially been explored. These and related applications are reviewed in the present article.     

Catalytic Reduction of p‐Nitrophenol and Hexacyanoferrate (III) by Borohydride Using Green Synthesized Gold Nanoparticles

A simple and green approach for the synthesis of well‐stabilized gold nanoparticles (AuNPs) using gum Acacia (GA) is presented here. The gum acacia acts as the reductant and stabilizer. The synthesized gold nanoparticles were characterized by using ultraviolet visible (UV‐Vis), fourier transform infrared spectroscopy (FTIR), x‐ray diffraction (XRD), dynamic light scattering (DLS) and transmission electron microscopy (TEM) techniques. The UV‐Vis study revealed a distinct surface plasmon resonance at 520 – 550 nm, due to the formation of AuNPs. FTIR analysis showed the evidence that –OH groups present in the gum matrix were responsible in reducing the tetra chloroauric acid into AuNPs. XRD studies confirmed the formation of well crystalline nanoparticles with fcc structure and the particle size ranges from 4 – 29 nm, as indicated by TEM analysis. The synthesized gold nanoparticles exhibited homogeneous catalytic activity. The two model reactions studied were the reduction of p‐nitro phenol and the reduction of hexacyanoferrate (III) by borohydride ions. Both the reactions were monitored by UV‐Vis spectroscopy. The kinetic investigations were carried out for the AuNPs‐catalyzed reactions at different temperatures and different amount of catalyst.     

A facile and convenient synthesis of novel imidazo[1,2-b] isoxazoles and their Mannich bases as potential biodynamic agents

A series of novel imidazo[1,2-b]isoxazoles 3 and their Mannich bases 4–6 were synthesized via convenient reactions. The reaction of 3-aminoisoxazole 1 with substituted phenacyl bromides 2 in dry ethanol afforded the corresponding 6-methyl-3-aryl imidazo[1,2-b]isoxazoles 3 in good yields.Compounds 3 on treatment with 37% formaline and secondary amines furnished the corresponding novel Mannich bases viz., 6-methyl-3-aryl-2-(morpholine/pyrrolidin-1-yl/piperidin-1-yl)-methyl-imidazo[1,2-b]isoxazoles 4–6.     

A Convenient and Facile Synthesis of Isoxazolyl‐chromeno[4,3,2‐de]pyrimido[4,5‐h][1,6]napthyridinones

The ceric ammonium nitrate‐catalyzed synthesis of (E)‐5‐amino‐N‐(3‐methyl‐5‐styrylisoxazol‐4‐yl)‐2‐arylchromeno[4,3,2‐de][1,6]napthyridin‐4‐carboxamides 5 was simply achieved upon the one‐pot four‐component reaction of isoxazolyl cyanoacetamide 1 with malononitrile 2 , 2‐hydroxy acetophenone 3 , and aromatic aldehydes 4 in ethanol. Compounds 5 on heating with acetic anhydride underwent tandem N‐acetylation and cyclocondensation involving intramolecular cyclization to afford the title compounds (E)‐11‐methyl‐12‐(3‐methyl‐5‐styrylisoxazol‐4‐yl)‐2‐arylchromeno[4,3,2‐de][1,6]napthyridin‐13(12H)‐ones 6 in good yields. The chemical structures have been confirmed by analytical and spectral analyses.     

Interface-induced anisotropy and the nematic glass/gel state in jammed aqueous Laponite suspensions

Aqueous suspensions of Laponite, a system composed of disklike nanoparticles, are found to develop optical birefringence over several days, well after the suspensions solidified because of jamming. The optical anisotropy is particularly enhanced near the air-Laponite suspension interface over length scales of several millimeters, which is beyond 5 orders of magnitude larger than the particle length scale, suggestive of large-scale ordering influenced by the interface. The orientational order increases with time and is always greater for higher concentration of salt, higher concentration of Laponite, and higher temperatures of the suspension. Although weakly birefringent, Laponite suspensions covered by paraffin oil do not show any enhancement in optical anisotropy near the interface compared to that in the bulk. We suggest that the expedited structure formation near the air interface propagating progressively inside the sample is responsible for the observed behavior. We discuss the observed nematic ordering in the context of glass-like and gel-like microstructure associated with aqueous Laponite suspensions.     

Symmetry breaking in quantum chaotic systems

We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.     

Application of a momentum method to some rarefied gas flow problems

Zusammenfassung Eine Kombination der Lees-Methode und des Mott-Smith Ansatzes wird auf zwei Probleme der Couette-Strömung zwischen zwei Zylindern angewandt. Es werden Ausdrücke hergeleitet für das Moment im Fall, dass ein Zylinder rotiert, und für den Wärmefluss im Fall, dass beide Zylinder stationär sind, aber verschiedene Temperatur haben; diese Ausdrücke sind für alle Werte der Knudsenzahl gültig.     

Classical trajectory analysis in atom—triatom collisions: Continuous quantization and scaling behaviour

A method of analysing classical trajectory data, based on recently derived scaling principles, is applied to a model atom-triatom collinear collision system. Apart from the utility of the scaling idea in extending trajectory computations, the analysis of the scaling coefficients in terms of transition probabilities increases the scope of the classical scaling theory as a means of obtaining (at the very least) qualitative quantum-mechanical information from classical trajectories. As an useful adjunct, the method of continuous quantization is applied to generate approximate transition probabilities. These results are semiquantitative; thus a combination of classical scaling and continuous quantization affords a powerful means of modeling complex collision cases with a minimum of computational effort.