Regularity of renormalized solutions in the Boltzmann equation with long‐range interactions

It is well‐established that renormalized solutions of the Boltzmann equation enjoy some kind of regularity, or at least compactness, in the velocity variable when the angular collision kernel is nonintegrable. However, obtaining explicit estimates in convenient and natural functional settings proves rather difficult. In this work, we derive a velocity smoothness estimate from the a priori control of the renormalized dissipation. As a direct consequence of our result, we show that, in the presence of long‐range interactions, any renormalized solution F(t, x, v) to the Boltzmann equation satisfies locally ${\textstyle{F \over {1 + F}}} \in W_{t,x,v}^{s,p}$ for every $1 \le p \le {\textstyle{D \over {D - 1}}}$ and for some s > 0 depending on p. We also provide an application of this new estimate to the hydrodynamic limit of the Boltzmann equation without cutoff. © 2012 Wiley Periodicals, Inc.     

Succinimide sulfonic acid (SuSA): an efficient and recyclable catalyst for the chemoselective <Emphasis Type="Italic">N</Emphasis>-Boc protection of amines

Abstract  

Succinimide sulfonic acid (SuSA) as a stable reagent is easily prepared by the reaction of succinimide with neat chlorosulfonic acid. This compound is able to catalyze the chemoselective conversion of amines to their corresponding N-Boc protected derivatives with (Boc)₂O. All reactions were performed under mild conditions, giving the desired products in good to high yields.     

Zwitterionic Salts from the Reaction of Symmetrical and Unsymmetrical (thio)Barbituric Acids with 2‐Pyridinecarbaldehyde under Solvent‐free Condition

A simple and efficient synthesis for the preparation of unusual charge‐separated pyridinium (thio)barbiturate zwitterion derivatives was achieved via a one‐pot reaction of (thio)barbituric acid derivatives and 2‐pyridinecarbaldehyde under solvent‐free condition and also in methanol under refluxing. The structure of the compounds was confirmed by ¹H NMR, ¹³C NMR, FT‐IR, mass and X‐ray analysis. The mechanism of the formation is discussed. Instead, no related pyridinium zwitterion was afforded from the reaction between dimedone and 2‐pyridinecarbaldehyde under the same conditions and its xanthene derivative was obtained.     

Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers

Using the method of multiple scales, an extensive frequency response and subharmonic resonance analysis of the equations of motion governing the nonlinear flexural vibrations of piezoelectrically actuated microcantilevers is performed. Such comprehensive understanding of the nonlinear response and subharmonics analysis of these microcantilevers is, indeed, justified by the applications of piezoelectrically actuated microcantilevers that are increasingly becoming popular in many science and engineering areas including scanning force microscopy, biosensors, and microactuators. Along this line, the method of multiple scales is used to derive the 2× and 3× subharmonic resonances appearing in nonlinear flexural vibrations of a piezoelectrically actuated microcantilever. An experimental examination is performed in order to verify the analytical results. The analytical and experimental results yield the same system response for the fundamental frequency. In addition, the experimental results demonstrate the presence of subharmonic resonances that are supported by numerical simulations of the equations of motion. The experimental mode shapes of these subharmonic frequencies are also measured and compared with fundamental frequency.     

Ekman layers of rotating fluids: The case of general initial data

In this paper we describe the weak solutions of the Navier‐Stokes equations with a large Coriolis term as the Rossby and the Ekman numbers go to zero in a special domain with various boundary conditions. This work extends the results (in the case of well‐prepared initial data) in [19, 30]. © 2000 John Wiley & Sons, Inc.     

VTF to arrhenius crossover in temperature dependence of conductivity in (PEG)xNH4ClO4 polymer electrolyte

We have studied the temperature variation of conductivity and ¹H NMR linewidth of (PEG)_xNH₄ClO₄ (x = 20, 30, 46, 100, 200, & 1000) polymer electrolyte systems. The temperature dependence of the conductivity shows two distinct behaviors, the low temperature VTF dependence crossing over to Arrhenius dependence at higher temperatures. The departure from the VTF behavior is found to be composition dependent. NMR spectra indicate the presence of large fractions of crystalline regions that start to melt around the crossover temperature. We understand the deviation from the VTF behavior as a consequence of this crystalline to elastomer transition. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1201–1209, 1998     

The clean and mild synthesis,crystal structure,and intra-molecular hydrogen bond study of substituted new 4,8-dihydropyrano[3,2-b]-pyrans containing chlorokojic acid moiety

Research on Chemical Intermediates - A safe, green and convenient process was developed for the synthesis of a novel group of 4,8-dihydropyrano[3,2-b]-pyrans by dialkyl acetylenedicarboxylates and...     

Dynamics of an electrified confined planar jet in a zero gravity environment

Meccanica - The present work deals with temporal electro-aerodynamics instability properties of an inviscid confined planar jet in a zero gravity environment and the existence of electric field....