On the Landau–Lifschitz Degrees of Freedom in 2-D Turbulence

We show that if the Kraichnan theory of fully developed turbulence holds, then the Landau–Lifschitz degrees of freedom is bounded (up to a logarithmic term) by G ^1/2, where G is the Grashof number.     

Statistical Estimates for the Navier–Stokes Equations and the Kraichnan Theory of 2-D Fully Developed Turbulence

A mathematical formulation of the Kraichnan theory for 2-D fully developed turbulence is given in terms of ensemble averages of solutions to the Navier–Stokes equations. A simple condition is given for the enstrophy cascade to hold for wavenumbers just beyond the highest wavenumber of the force up to a fixed fraction of the dissipation wavenumber, up to a logarithmic correction. This is followed by partial rigorous support for Kraichnan's eddy breakup mechanism. A rigorous estimate for the total energy is found to be consistent with Kraichnan's theory. Finally, it is shown that under our conditions for fully developed turbulence the fractal dimension of the attractor obeys a sharper upper bound than in the general case.     

Tunable complex photonic chiral lattices by reconfigurable optical phase engineering

We present a novel single-step fabrication approach, based on optical phase engineering, for tunable complex photonic chiral lattices of diverse geometries in a large area. By means of engineered reconfigurable phase patterns, we computationally simulate as well as experimentally investigate these complex structures. We show the generation of both periodic right- and left-handed chiral structures as well as photonic transversely quasi-crystallographic chiral structures. These complex chiral lattices are also demonstrated in a photorefractive material, and the lattice formation is analyzed by plane-wave-guided imaging as well as diffraction pattern imaging. Furthermore, complex photonic chiral structures with engineered tunable relative phase shifts between adjacent spiral units realizable in a single step are explored and analyzed.     

An applicatin of approximate inertial manifolds to a weakly damped nonlinear schrödinger equation

Nonlinear Galerkin methods (NGMs) based on pproximate inertial manifolds are applied to a weakly dissipative nonlinear Schrödinger equation. The purpose is to capture critical and chaotic behavior with as few modes as possible. Density functions are used on both the energy and instantaneous Lyapunov exponents to determine convergence of a chaotic attractor as the number of modes is increased. The computations presented here indicate a substantial reduction in the number of modes needed for the NGMs, compared to that needed for the traditional Galerkin method.     

Local structure in fluids of heteronuclear dumb-bells according to the RISM model

An integral equation formulated for molecular fluids by Chandler and Anderson for the rigid inter-site model has been solved for heteronuclear hard dumb-bells. Properties of the inter-site radial distribution and direct correlation functions are discussed. The static structure factor behaviour is also calculated.     

Triterpene Saponins from Four Species of the Polygalaceae Family

Twelve triterpene saponins were isolated by successive MPLC over silica gel from four species of Polygalaceae: From Polygala ruwenzoriensis, five new saponins 1 – 5 of which 1 – 4 as two pairs of (E)/(Z)‐isomers, together with the four known compounds tenuifoline, (E)‐ and (Z)‐senegasaponin b, (E)‐ and (Z)‐senegin II, and polygalasaponin XXVIII, from the genus Carpolobia, one new saponin 6 from C. alba and the known arilloside ( 11 ) from C. lutea, and another new triterpene glycoside 7 from Polygala arenaria. Their structures were established mainly by 600‐MHz 2D‐NMR techniques (¹H,¹H‐COSY, TOCSY, NOESY, HSQC, HMBC) as 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐α‐L ‐arabinopyranosyl‐(1 → 4)‐O‐β‐D ‐xylopyranosyl‐(1 → 4)‐O‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐4‐O‐[(E)‐4‐methoxycinnamoyl]‐β‐D ‐fucopyranosyl} ester ( 1 ) and its (Z)‐isomer 2 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐α‐L ‐arabinopyranosyl‐(1 → 4)‐O‐β‐D ‐xylopyranosyl‐(1 → 4)‐O‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐4‐O‐[(E)‐3,4‐dimethoxycinnamoyl]‐β‐D ‐fucopyranosyl} ester ( 3 ) and its (Z)‐isomer 4 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐[O‐β‐D ‐galactopyranosyl‐(1 → 4)‐O‐β‐D ‐xylopyranosyl‐(1 → 4)‐O‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐β‐D ‐fucopyranosyl] ester ( 5 ), 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐α‐L ‐arabinopyranosyl‐(1 → 3)‐O‐[β‐D ‐galactopyranosyl‐(1 → 4)]‐O‐β‐D ‐xylopyranosyl‐(1 → 4)‐O‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐O‐[β‐D ‐apiofuranosyl‐(1 → 3)]‐4‐O‐acetyl‐β‐D ‐fucopyranosyl} ester ( 6 ), and 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐β‐D ‐galactopyranosyl‐(1 → 4)‐O‐[β‐D ‐glucopyranosyl‐(1 → 3)]‐O‐β‐D ‐xylopyranosyl‐(1 → 4)‐O‐α‐L ‐rhamnopyranosyl‐(1 → 2)‐β‐D ‐fucopyranosyl} ester ( 7 ) (presenegenin = (2β,3β,4α)‐2,3,27‐trihydroxyolean‐12‐ene‐23,28‐dioic acid).     

Establishment of proficiency testing programs in the Philippines

Accreditation and Quality Assurance - In order to improve the competitiveness of Philippine food products in the global market, the Department of Science and Technology—Food and Nutrition...