Varieties of dynamic multiscaling in fluid turbulence

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by different classes of bridge relations, which we derive. We check this explicitly by detailed numerical simulations of the Gledzer-Ohkitani-Yamada shell model for fluid turbulence. Our results can be generalized to any system in which both equal-time and time-dependent structure functions show multiscaling.     

A multisublattice magnetic phase induced by external field in a singlet magnet

The theory of magnetization in a longitudinal magnetic field is developed for an easy-plane multisublattice antiferromagnet with a singlet ground state and a strong single-ion anisotropy exceeding the magnitude of exchange interaction. The magnetic-field-induced phase transition from the singlet (magnetically dis-ordered) state to a multisublattice antiferromagnetic state represents a displacive magnetic phase transition. At T=0, this transition proceeds continuously and belongs to second-order phase transitions, while at T ≠0, the behavior changes to jumplike and the process becomes the first-order phase transition.     

Reactivity studies of carbon,phosphorus and sulfur‐based acyl sites with tertiary oximes in gemini surfactants

Kinetic studies of the reactions of tertiary oximes (monoisonitroso acetone; MINA and butane 2,3 dione monooxime; BDMO) with some carboxylate (p‐nitrophenyl acetate and p‐nitrophenyl benzoate), phosphate (p‐nitrophenyl diphenyl phosphate and bis (2,4‐dinitrophenyl) phosphate) and sulfonate (p‐nitrophenyl p‐toluene sulphonate) esters in gemini surfactants have been conducted. The observed first‐order rate constant versus surfactant profiles show micelle‐assisted bimolecular reactions involving interfacial ion exchange between bulk aqueous media and micellar pseudophase. Experimental results showed that MINA exhibited better nucleophilic activity towards ester cleavage than BDMO. Pseudophase model has been applied in order to determine micellar second‐order rate constants and binding constants. Copyright © 2013 John Wiley & Sons, Ltd.     

Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: Modeling and simulation

A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms.     

An efficient transient Navier–Stokes solver on compact nonuniform space grids

In this paper, we propose an implicit higher-order compact (HOC) finite difference scheme for solving the two-dimensional (2D) unsteady Navier–Stokes (N–S) equations on nonuniform space grids. This temporally second-order accurate scheme which requires no transformation from the physical to the computational plane is at least third-order accurate in space, which has been demonstrated with numerical experiments. It efficiently captures both transient and steady-state solutions of the N–S equations with Dirichlet as well as Neumann boundary conditions. The proposed scheme is likely to be very useful for the computation of transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variation. Numerical results are presented and compared with analytical as well as established numerical data. Excellent comparison is obtained in all the cases.     

Mesoporous aluminosilicate nanocage-catalyzed three-component coupling reaction: an expedient synthesis of α-aminophosphonates

Here we demonstrate for the first time the synthesis of α-aminophosphonates through the three-component coupling reaction of aldehydes, amines, and diethyl phosphite by using highly acidic 3D mesoporous aluminosilicate nanocage catalyst, which gave excellent yield with a high selectivity in a short reaction time due to its high acidity, 3D pores, and a huge space in the nanocages.     

Crystallization kinetics of linear polyethylene: The maximum in crystal growth rate-temperature dependence

This rapid communication reports a summary of the key findings of crystallization kinetics studies of unfractionated high density (linear) polyethylene at extremely large supercoolings. We report, for the first time, the maximum in crystal growth rate-crystallization temperature data for linear polyethylene, which has been sought by many researchers since the 1950s. The maximum growth rate was found to occur in the range of 70-75 °C with two separate methods. The kinetics studies were performed using a newly developed quench-crystallization technique based on depolarized reflection light microscopy that is capable of achieving enormously higher quench rates than existing methods. Typical onset crystallization temperatures accessed with this technique range from 40 to 90 °C. Bulk growth rates of crystals were obtained as the reciprocal of crystallization half times measured from the change in the depolarized light intensity upon direct crystallization from the melt. Separately, radial growth rates of spherulites were measured over a wide range of supercoolings. Secondary nucleation analysis of the crystal growth rates resulted in single linear fits extending into deep regime III, suggesting no change in mechanism of formation of the crystals at the largest supercoolings. The deeply quenched films, crystallized at temperatures below the maximum, contain non-impinged spherulites, capable of further crystallization.     

Lower bounds for adaptive locally decodable codes

An error‐correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan 12 showed that any such code C : {0, 1}ⁿ → Σ^m with a decoding algorithm that makes at most q probes must satisfy m = Ω((n/log |Σ|)^q/(q?1)). They assumed that the decoding algorithm is non‐adaptive, and left open the question of proving similar bounds for adaptive decoders. We show m = Ω((n/log |Σ|)^q/(q?1)) without assuming that the decoder is nonadaptive. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005