Rings with finite Gorenstein injective dimension

In this paper we prove that for any associative ring , and for any left -module with finite projective dimension, the Gorenstein injective dimension equals the usual injective dimension . In particular, if is finite, then also is finite, and thus is Gorenstein (provided that is commutative and Noetherian).

     

Real loci of symplectic reductions

Let be a compact, connected symplectic manifold with a Hamiltonian action of a compact -dimensional torus . Suppose that is equipped with an anti-symplectic involution compatible with the -action. The real locus of is the fixed point set of . Duistermaat introduced real loci, and extended several theorems of symplectic geometry to real loci. In this paper, we extend another classical result of symplectic geometry to real loci: the Kirwan surjectivity theorem. In addition, we compute the kernel of the real Kirwan map. These results are direct consequences of techniques introduced by Tolman and Weitsman. In some examples, these results allow us to show that a symplectic reduction has the same ordinary cohomology as its real locus , with degrees halved. This extends Duistermaat's original result on real loci to a case in which there is not a natural Hamiltonian torus action.

     

Design of a doubly-hydrophilic block copolypeptide that directs the formation of calcium carbonate microspheres

The crystallization of calcium carbonate into microspheres has been accomplished using the rationally-designed, doubly-hydrophilic block copolypeptide poly(Nepsilon-2[2-(2-methoxyethoxy)ethoxy]acetyl-L-lysine)(100)-b-poly(L-aspartate sodium salt)30 as a structure-directing agent.     

CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy

We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1:1:2 resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the CO2 molecule. We uncover quantum monodromy of CO2 as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states.     

Synthesis of ether-linked fluorocarbon surfactants and their aggregational properties in organic solvents

A series of single- and double-tailed hydrocarbon-fluorocarbon (HF) surfactants were prepared to evaluate the effect of molecular structure on aggregate formation in organic solvents. The molecules were designed with ether linkages to permit facile syntheses of both sets of molecules. Solvent foaming studies were used to rapidly assess the surface-active properties of the surfactants, while dynamic light scattering provided quantitative critical micelle concentrations (CMC) and hydrodynamic radius (R(h)) measurements of the aggregates in solution. The single-tailed surfactants did not produce any foaming action in a number of hydrocarbon solvents, nor was any micellar formation observed up to 100 mM concentrations. Double-tailed surfactants, on the other hand, gave low CMC values in dodecane but with R(h) values that indicated a tight micelle structure. Bilayer formation was expected but not observed for these molecules, which is believed to be due to their unusual structural geometry, imparted by the glycerol backbone. No thermotropic liquid crystalline (LC) behavior was observed for any of the single- or double-tailed molecules. These data contrast with the known behavior of perfluorinated alkanes and other fluorinated surfactants, suggesting that the ether linkage plays an important role in the self-organizing behavior of these molecules.     

Swelling of polyelectrolyte networks

Employing molecular dynamics simulations of a coarse-grained model, the equilibrium swelling behavior of a cross-linked polyelectrolyte gel has been investigated with a bead-spring defect-free network with diamond-like topology under good solvent conditions and close to the theta-point, the counterions were treated explicitly. To examine the validity range of simple scaling arguments we varied the amount of charges in the system, the length of the network chains, the strength of the electrostatic interactions for both solvent qualities over a wide range of parameters. We find that classical theories only apply in the limit of weak electrostatics and suggest corrections based on the microscopic interplay of the systems' components accessible in a simulation, which model successfully our measured data.     

Xenon NMR measurements of permeability and tortuosity in reservoir rocks

In this work we present measurements of permeability, effective porosity and tortuosity on a variety of rock samples using NMR/MRI of thermal and laser-polarized gas. Permeability and effective porosity are measured simultaneously using MRI to monitor the inflow of laser-polarized xenon into the rock core. Tortuosity is determined from measurements of the time-dependent diffusion coefficient using thermal xenon in sealed samples. The initial results from a limited number of rocks indicate inverse correlations between tortuosity and both effective porosity and permeability. Further studies to widen the number of types of rocks studied may eventually aid in explaining the poorly understood connection between permeability and tortuosity of rock cores.     

Boundary Effects on Exact Solutions of the Lagrangian-Averaged Navier–Stokes-α Equations

In order to clarify the behavior of solutions of the Lagrangian-averaged Navier–Stokes- (LANS-) equations in the presence of solid walls, we identify a variety of exact solutions of the full equations and their boundary layer approximations. The solutions demonstrate that boundary conditions suggested for the LANS- equations in the literature⁽¹⁾ for a bounded domain do not apply in a semi-infinite domain. The convergence to solutions of the Navier–Stokes equations as 0 is elucidated for infinite-energy solutions in a semi-infinite domain, and non-uniqueness of these solutions is discussed. We also study the boundary layer approximation of LANS- equations, denoted the Prandtl- equations, and report solutions for turbulent jets and wakes. Our version of the Prandtl- equations includes an extra term necessary to conserve linear momentum and corrects an earlier result of Cheskidov.⁽²⁾