Droplet shape of an anisotropic liquid

We investigate how a droplet of a complex liquid is modified by its internal nanoscale structure. As the liquid passes from an isotropic disordered state to an anisotropic layered morphology, the droplet shape switches from a smooth spherical cap to a terraced hyperbolic profile, which can be modeled as a stack of thin concentric circular disks with a repulsion between adjacent disk edges. Our ability to resolve the detailed shape of these defect-free droplets offers a unique opportunity to explore the underlying physics.     

Gauge-invariant inflaton in the minimal supersymmetric standard model

We argue that all the necessary ingredients for successful inflation are present in the flat directions of the Minimally Supersymmetric Standard Model. We show that out of many gauge-invariant combinations of squarks, sleptons, and Higgs bosons, there are two directions, LLe and udd, which are promising candidates for the inflaton. The model predicts more than 10(3) e-foldings, with an inflationary scale of H(inf) approximately O(1-10) GeV, provides a tilted spectrum with an amplitude of delta(H) approximately 10(-5) and a negligible tensor perturbation. The temperature of the thermalized plasma could be as low as T(rh) approximately O(1-10) TeV. Parts of the inflaton potential can be determined independently of cosmology by future particle physics experiments.     

Electronic properties of single-walled carbon nanotubes inside cyclic supermolecules

Possible ways for manipulating carbon nanotubes (CNTs) with cyclic supermolecules are studied using density functional theory. Electronic structure calculations with structure optimizations have been performed for the (4,4) and (8,0) single-walled carbon nanotubes (SWNTs) complexed with crown ethers as well as for the (4,0) SWNT with beta-cyclodextrin. A slight polarization of charge in both the nanotube and the supermolecule is observed upon rotaxane complexation, but the interaction is mainly repulsive, and the systems stay 2.8-3.5 A apart. The supermolecule does not affect the electronic band structure of the nanotube significantly within such a configuration. The situation differs noticeably for chemically cross-linked SWNTs and crown ethers, where a peak arises at the Fermi energy in the density of states. As a result, the band gap of semiconducting CNT(8,0) (0.5 eV) vanishes, and a new conduction channel opens for the metallic CNT(4,4).     

Quantum Instruments and Related Transformation Valued Functions

The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their ^*-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained.     

Ligand entrapment in twofold interpenetrating PtS matrixes by metallo-organic frameworks

Single-crystal X-ray crystallography was used to determine the structures of four metallo-organic frameworks (MOFs). A dendritic tetradentate ligand (tetrakis(isonicotinoxymethyl)methane, TINM) was used with first-row transition-metal elements copper, nickel, and cobalt to synthesize MOFs with a PtS interpenetration, due to both planar and tetrahedral junctions being present in the framework. Two different polymeric complexes, 1 and 2, were obtained from similar starting materials, TINM and Cu(NO(3))(2).3H(2)O, but different solvents. The use of dichloromethane in addition to methanol and water promoted the coordination of nitrate ions to the copper. With only methanol and water used as solvent, the copper atom was coordinated to water molecules instead. Compound 1 has pores going through the structure in two dimensions, along crystallographic axes a and c with diameters of the pores (the diameters correspond to the minimum distances between van der Waals surfaces of opposing walls defined by projection along channel axis) approximately 1.0 x 3.1 and 2.5 x 3.7 A, respectively. Compound 2 has channels along all crystallographic axes. The dimensions of the channels are 3.2 x 3.7, 3.7 x 5.0, and 2.8 x 4.1 A, respectively. The structures of 3 and 4 entrap a large guest ligand molecule in the framework. The guest ligand is uncoordinated, although the pattern that the entrapped guests form brings the two arms of any two guests within close range. The lack of 3-fold penetration is due to only two arms being close to each other and also the fact that there is no space for an additional set of metal centers.     

Two geometric character formulas for reductive Lie groups

In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation in terms of the same geometric data attached to . When specialized to the case of a compact Lie group, one of them reduces to Kirillov's character formula in the compact case, and the other, to an application of the Atiyah-Bott fixed point formula to the Borel-Weil realization of the representation .