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.     

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.     

Discrepancy between subcritical and fast rupture roughness: a cumulant analysis

Rough crack fronts in a sheet of paper, obtained during a creep experiment, do not follow true scaling laws. Local roughness exponents are estimated using the first order cumulant, a quantity recently introduced in the turbulence literature [J. Delour, J. F. Muzy, and A. Arneodo, Eur. Phys. J. B 23, 243 (2001)10.1007/s100510170074]. Using a large data set (102 fronts), we find a significant difference in local roughness between the slow (subcritical) and the fast growth regime.     

Companding to improve cochlear-implant speech recognition in speech-shaped noise

Nonlinear sensory and neural processing mechanisms have been exploited to enhance spectral contrast for improvement of speech understanding in noise. The "companding" algorithm employs both two-tone suppression and adaptive gain mechanisms to achieve spectral enhancement. This study implemented a 50-channel companding strategy and evaluated its efficiency as a front-end noise suppression technique in cochlear implants. The key parameters were identified and evaluated to optimize the companding performance. Both normal-hearing (NH) listeners and cochlear-implant (CI) users performed phoneme and sentence recognition tests in quiet and in steady-state speech-shaped noise. Data from the NH listeners showed that for noise conditions, the implemented strategy improved vowel perception but not consonant and sentence perception. However, the CI users showed significant improvements in both phoneme and sentence perception in noise. Maximum average improvement for vowel recognition was 21.3 percentage points (p<0.05) at 0 dB signal-to-noise ratio (SNR), followed by 17.7 percentage points (p<0.05) at 5 dB SNR for sentence recognition and 12.1 percentage points (p<0.05) at 5 dB SNR for consonant recognition. While the observed results could be attributed to the enhanced spectral contrast, it is likely that the corresponding temporal changes caused by companding also played a significant role and should be addressed by future studies.     

Selectivity in Garratt-Braverman cyclization: an experimental and computational study

Bispropargyl sulfones equipped with aromatic rings of dissimilar nature were synthesized. Under basic conditions, these sulfones isomerized to the bisallenic sulfones, creating a competitive scenario between two alternate Garratt-Braverman (GB) cyclization pathways. The observed product distribution ruled out the involvement of any ionic intermediate and supported the diradical mechanism with greater involvement of the electron-rich aromatic ring via the more nucleophilic radical. DFT-based calculations supported the diradical mechanism along with the observed selectivity.