A correspondence principle connecting IBVPs of wave propagation and heat conduction

A wave-heat correspondence principle is established by utilizing previous operational relations of van der Pol and Bremmer. By the suggested procedure, heat conduction problems can be solved by using an auxiliary wave-propagation problem in conjunction with the correspondence principle. A check on this procedure was provided by solving a mixed BVP of transient heat flow. The present correspondence principle is particularly useful in dealing with IBVPs involving wedge-shaped domains, and characteristic lengths.     

Stereoselective ring closure of 6-[[(methylamino)carbonyl]oxy]-2H-pyran-3(6H)-ones. Formation of the 5H-pyrano[3,2-d]oxazole-2,6-dione ring system

The stereospecific formation of the 5H-pyrano[3,2-d]oxazole-2,6-dione ring system from 2,2-disubstituted-6-[[(methylamino)carbonyl]oxy]-2H-pyran-3(6H)-one via an enolization at C-5 is presented. The outcome of the same reaction in the case of 2-monosubstituted 2H-pyran-3(6H)-ones is also discussed.     

Solid-phase synthesis of an oxalic acid amide library

Monoamides of oxalic acid are of interest as bioisosteric replacements for phosphate groups in the design of new enzyme inhibitors. Here, we have demonstrated the use of oxalic acid as a linker to the Wang resin to synthesize individual or libraries of phosphate biosteres. The highly reactive resin-bound acid chloride reacts with arylamines to yield resin-bound N-aryloxamic acids (oxanilic acids). This methodology is especially useful for the rapid synthesis of 2-(oxalylamino)benzoic acids (OBAs), because it can be utilized for library synthesis and eliminates the intermediate purification step necessary in solution-phase reactions. The products are cleaved off the resin with trifluoroacetic acid in dichloromethane in good yields.     

Synchronized EPI phase contrast velocimetry in a mixing reactor

Notwithstanding its widespread use in cardiovascular and functional MRI studies, Echo Planar Imaging (EPI) has only recently been subjected to systematic validation studies. Most velocity measurement studies employing such ultrafast MRI methods involve the use of phantoms characterized by rigid or deformable solid motion. The current implementation involves a rotating phantom (angular velocity up to 10.5 rpm) with a superimposed swirling liquid flow (with axial velocities ranging between 0.145 and 0.27 cm/s) of water doped with copper sulfate. The standard implementation of single-shot EPI with phase contrast velocity encoding allows the complete mapping of the Eulerian velocity field in slices perpendicular to the rotation axis following a subtractive procedure requiring the synchronized acquisition of each velocity component on each selected transverse slice during two revolutions of the rotor. The image acquisition time is 100 ms (per velocity component) at each 64 x 64 slice. In addition to acquiring full-field velocity data for future direct comparisons with other techniques, EPI is employed here for the first time to reconstruct the three-dimensional flow field between the blades of a partitioned pipe mixer.     

An illustration of sliding contact at any constant speed on highly elastic half-spaces

A rigid smooth indentor slides at a constant speed on a compressibleisotropic neo-Hookean half-space that is subjected to pre-stressaligned with the surface and sliding direction. A dynamic steady-slidingsituation of plane strain is treated as the superposition ofcontact-triggered infinitesimal deformations superposed uponfinite deformations due to pre-stress. The neo-Hookean materialbehaves for small strains as a linear elastic solid with Poisson'sratio 1 : 4. Exact solutions are presented for both deformationsand, for a range of acceptable pre-stress values, the infinitesimalcomponent exhibits the typical non-isotropy induced by pre-stress,and several critical speeds. In view of the unilateral constraintsof contact, these speeds serve to define the sliding speed rangesfor which physically acceptable solutions arise. A Rayleighspeed is the upper bound for subsonic sliding, and transonicsliding can occur only at a single speed. For the generic parabolicindentor, contact zone traction continuity is lost at the zoneleading edge for trans- and supersonic sliding. For pre-stresslevels that fall outside the acceptable range, either a negativePoisson effect occurs, or a Rayleigh speed does not exist andthe unilateral constraints cannot be satisfied for any subsonicsliding speed. Received 15 March 2000. Revised 22 November 2000.     

Rapid sliding motion of a rigid frictionless indentor with a flat base over a thermoelastic half-space

The three-dimensional, rapid sliding indentation of a deformable half-space by a rigid indentor of a flat elliptical base is treated in this paper. The response of the material that fills the half-space is assumed to be governed by coupled thermoelasticity. The indentor translates without friction on the half-space surface at a constant sub-Rayleigh speed and the problem is treated as a steady-state one. An exact solution is obtained that is based on a Green’s function approach, integral equations, and Galin’s theorem. A closed-form expression for the distributed contact pressure under the elliptical base of the indentor is derived. Representative numerical results are given illustrating the effects of the indentor velocity, indentor geometry, and parameters of the thermoelastic solid on the contact displacement. Since there is an analogy between the steady-state theories of thermoelasticity and poroelasticity, the present results carry over to the latter case directly.