Random oscillator with general Gaussian noise

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the energy of the oscillator grow as power-laws with time. We calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise. Our results are generalized to include dissipative effects and additive noise.     

Anharmonic Oscillator Driven by Additive Ornstein–Uhlenbeck Noise

We present an analytical study of a nonlinear oscillator subject to an additive Ornstein–Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or to a quasi-white noise (i.e., a noise with vanishingly small correlation time). Here, in contrast, we study the small dissipation case (we retain the inertial term) and consider a noise with finite correlation time. Our analysis is non perturbative and based on a recursive adiabatic elimination scheme a reduced effective Langevin dynamics for the slow action variable is obtained after averaging out the fast angular variable. In the conservative case, we show that the physical observables grow algebraically with time and calculate the associated anomalous scaling exponents and generalized diffusion constants. In the case of small dissipation, we derive an analytic expression of the stationary probability distribution function (PDF) which differs from the canonical Boltzmann–Gibbs distribution. Our results are in excellent agreement with numerical simulations.     

Induced Correspondence of a Local π‐Aromatic Sextet in Heteroannulenes: Synthesis and Characterization

Acid‐catalyzed [3+3] condensation reactions of two hitherto unknown tripyrrane moieties with pentafluorobenzaldehyde has led to the formation of new generation heteroannulene (4.1.4.1) and mutant heteroannulene (1.1.1.1.1.1). Inclusion of local π‐aromatic sextets, namely the N‐methyl pyrrole rings through β,β‐linkages and α,β‐linkages, has led to the isolation of first ever heteroannulenes cross‐conjugated at four points and two points respectively within the macrocycles.     

Green synthesis of water-dispersible silver nanoparticles at room temperature using green carambola (star fruit) extract

Journal of Sol-Gel Science and Technology - Silver nanoparticles (AgNPs) dispersible in water were synthesized at room temperature in the presence of carambola fruit extract at different pH. The...     

Polymer‐supported palladium: A hybrid system for multifunctional catalytic application

Polymer‐supported palladium was synthesized by applying a single‐step wet chemical synthesis route and the resultant composite material was characterized by means of various techniques. Infrared and UV–visible spectra provided information on the chemical structure of the polymer. Microscopy techniques showed the general morphology of the polymer. The oxidation state of palladium was determined using the X‐ray photoelectron spectroscopy method. The synthesized material was applied as a heterogeneous catalyst for the Heck coupling reaction and also as an electrocatalyst for the oxidation of cysteine.     

Kinetics and Mechanism of the Ligand Substitution Reaction of the Di-<Emphasis Type="Italic">μ</Emphasis>-hydroxobis(bipyridyl)dipalladium(II) Ion with some Bio-relevant Ligands

The interaction of di-μ-hydroxobis(bipyridyl)dipalladium(II) with the selected bio-relevant ligands: thioglycolic acid (HL¹), glutathione(HL²) and DL-penicillamine(HL³) has been studied spectrophotometrically in aqueous medium as a function of complex and ligand concentrations, pH, and temperature at constant ionic strength. Two consecutive reaction steps are observed: the first step is dependent on the incoming ligand concentration and the second step which is independent, is assigned to ring closure. The activation parameters, conductivity data and IR data obtained also support the proposed mechanism.     

Invariant Solutions of Inhomogeneous Universe with Electromagnetic Field in Lyra Geometry

The present study deals with the cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electro-magnetic field in Lyra geometry. Lie group analysis has been used to identify the generators (symmetries) that leave the given system of partial differential equations (field equations) invariant. With the help of canonical variables associated with these generators, the assigned system of partial differential equations is reduced to an ordinary differential equations whose simple solutions provide nontrivial solutions of the original system. They obtained a new class of invariant (similarity) solutions by considering the potentials of metric and displacement field are functions of coordinates t and x. The physical behavior of the derived models are also discussed.