Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flows

This paper presents new analytical results and the first numerical results for a recently proposed multiscale deconvolution model (MDM) recently proposed. The model involves a large‐eddy simulation closure that uses a novel deconvolution approach based on the introduction of two distinct filtering length scales. We establish connections between the MDM and two other models, and, on the basis of one of these connections, we establish an improved regularity estimate for MDM solutions. We also prove that the MDM preserves Taylor‐eddy solutions of the Navier–Stokes equations and therefore does not distort this particular vortex structure. Simulations of the MDM are performed to examine the accuracy of the MDM and the effect of the filtering length scales on energy spectra for three‐dimensional homogeneous and isotropic flows. Numerical evidence for all tests clearly indicates that the MDM gives very accurate coarse‐mesh solutions and that this multiscale approach to deconvolution is effective. Copyright © 2015 John Wiley & Sons, Ltd.     

Incompatible strains associated with defects in nematic elastomers

In a nematic elastomer the deformation of the polymer network chains is coupled to the orientational order of the mesogenic groups. Statistical arguments have derived the so-called neoclassical free energy that models this coupling. Here we show that the neoclassical model supplemented by the usual Frank energy predicts incompatible network strains associated with the formation of standard nematic textures. The incompatibility is measured by the Riemann curvature tensor, which we find to be nonzero for both radial hedgehog defects and escaped disclinations of strength +1 in circular cylinders. Analogous problems for conventional nonlinearly elastic solids do not possess solutions with such incompatibilities. Compatibility in nematic elastomers would require either more complicated nematic textures in elastomers than in conventional (polymeric and low molecular weight) liquid crystals or a free-energy density more complicated than the neoclassical expression.     

Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory

Meccanica - The principle of virtual power is used derive a microforce balance for a second-gradient phase-field theory. In conjunction with constitutive relations consistent with a free-energy...     

Continua described by a microstructural field

Using a balance law for microforces and an appropriate statement of the second law of thermodynamics, a framework is provided for continuum theories that involve a microstructural variable. Examples of specific physical theories that fall within that framework—spanning internal state-variable theories for plasticity and polymeric solutions, order-parameter based theories for phase transitions, and various theories for liquid crystals-are given.     

Gradient nanoscale polycrystalline elasticity: Intergrain interactions and triple-junction conditions

Using the principle of virtual power, we develop general balance equations, interface conditions, triple-junction conditions, and boundary conditions for second-grade nanocrystalline elastic materials undergoing infinitesimal deformations. We further develop thermodynamically consistent constitutive equations and provide a weak formulation of resulting boundary-value problems that automatically yields internal conditions such those that hold across interfaces and at triple junctions.     

Cloning, expression, and biochemical characterization of Streptomyces rubellomurinus genes required for biosynthesis of antimalarial compound FR900098

The antibiotics fosmidomycin and FR900098 are members of a unique class of phosphonic acid natural products that inhibit the nonmevalonate pathway for isoprenoid biosynthesis. Both are potent antibacterial and antimalarial compounds, but despite their efficacy, little is known regarding their biosynthesis. Here we report the identification of the Streptomyces rubellomurinus genes required for the biosynthesis of FR900098. Expression of these genes in Streptomyces lividans results in production of FR900098, demonstrating their role in synthesis of the antibiotic. Analysis of the putative gene products suggests that FR900098 is synthesized by metabolic reactions analogous to portions of the tricarboxylic acid cycle. These data greatly expand our knowledge of phosphonate biosynthesis and enable efforts to overproduce this highly useful therapeutic agent.