Existence of solutions for the anti-plane stress for a new class of “strain-limiting” elastic bodies

The main purpose of this study is to establish the existence of a weak solution to the anti-plane stress problem on V-notch domains for a class of recently proposed new models that could describe elastic materials in which the stress can increase unboundedly while the strain yet remains small. We shall also investigate the qualitative properties of the solution that is established. Although the equations governing the deformation that are being considered share certain similarities with the minimal surface problem, the boundary conditions and the presence of an additional model parameter that appears in the equation and its specific range makes the problem, as well as the result, different from those associated with the minimal surface problem.     

Modeling of the microwave drying process of aqueous dielectrics

We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz Field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.     

Further remarks on simple flows of fluids with pressure-dependent viscosities

Recently Suslov and Tran (2008) [1] claimed to have found an error in one of the solutions given in the paper by Hron (2001) et al. [2] concerning the flows of fluids with pressure-dependent viscosities. We show that their arguments are related to the question of the continuity of the pressure, and we show that the original solution, although it is not a classical one, can be interpreted as a solution in a generalized sense. Mathematical and physical implications of such generalizations are briefly discussed. The discussion in the paper highlights the importance of recognizing what is meant by a “solution” to a partial differential equation, whether by a solution we mean a classical solution, a weak solution, or a solution in some other sense.     

Enantioselective solvent-free Robinson annulation reactions

The enantioselective cyclization of the prochiral cyclic substrates1 to7 and26, can be carried out in theneat using S-proline as catalyst. The substrates18 to22 and27 could not be cyclized with S-proline but could be cyclized with a mixture of S-phenylalanine and d-camphorsulphonic acid. The enantioselective cyclization of prochiral acyclic triones45 and47 and also the racemic tricarbonyl compounds54 to57 could also be carried out in theneat using S-proline as catalyst. The optically active enediones obtained in the above cyclizations could also be obtained directly from 1,3-diones or 2-hydroxymethylene cycloalkanones in a one-pot reaction with methyl vinyl ketone (MVK) and S-proline in the absence of solvents.¹³C NMR studies of the one-pot synthesis ofS-11 andS-14 reveal that the annulations involve initial formation of an acid-base complex followed by a Michael reaction and then an enantioselective cyclization. Such enantioselective cyclizations probably occur on the surface of S-proline crystals.     

A note on unsteady unidirectional flows of a non-Newtonian fluid

Exact solutions are established for a class of unsteady unidirectional flows of an in compressible second grade fluid wherein inertial effects are not ignored. Amongst the several interesting flows which belong to this class are the flow due to a rigid plate oscillating in its own direction, the flow between two rigid boundaries one of which is suddenly started and the time-periodic Poiseuille flow due to an oscillating pressure gradient.