Layer- and bulk roton excitations of 4He in porous media

We examine the energetics of bulk and layer-roton excitations of 4He in various porous medial such as aerogel, Geltech, or Vycor, in order to find out what conclusions can be drawn from experiments on the energetics about the physisorption mechanism. The energy of the layer-roton minimum depends sensitively on the substrate strength, thus providing a mechanism for a direct measurement of this quantity. On the other hand, bulk-like roton excitations are largely independent of the interaction between the medium and the helium atoms, but the dependence of their energy on the degree of filling reflects the internal structure of the matrix and can reveal features of 4He at negative pressures. While bulk-like rotons are very similar to their true bulk counterparts, the layer modes are not in close relation to two-dimensional rotons and should be regarded as a third, completely independent kind of excitation

Strict Deformation Quantization for a Particle in a Magnetic Field

Recently, we introduced a mathematical framework for the quantization of a particle in a variable magnetic field. It consists in a modified form of the Weyl pseudodifferential calculus and a C*-algebraic setting, these two points of view being isomorphic in a suitable sense. In the present paper we leave Planck's constant vary, showing that one gets a strict deformation quantization in the sense of Rieffel. In the limit h --> 0 one recovers a Poisson algebra induced by a symplectic form defined in terms of the magnetic field.Comment: 23 page

Excitations in confined helium

We design models for helium in matrices like aerogel, Vycor or Geltech from a manifestly microscopic point of view. For that purpose, we calculate the dynamic structure function of 4He on Si substrates and between two Si walls as a function of energy, momentum transfer, and the scattering angle. The angle--averaged results are in good agreement with the neutron scattering data; the remaining differences can be attributed to the simplified model used here for the complex pore structure of the materials. A focus of the present work is the detailed identification of coexisting layer modes and bulk--like excitations, and, in the case of thick films, ripplon excitations. Involving essentially two--dimensional motion of atoms, the layer modes are sensitive to the scattering angle.Comment: Phys. Rev. B (2003, in press

Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

Quantum sticking, scattering and transmission of 4He atoms from superfluid 4He surfaces

We develop a microscopic theory of the scattering, transmission, and sticking of 4He atoms impinging on a superfluid 4He slab at near normal incidence, and inelastic neutron scattering from the slab. The theory includes coupling between different modes and allows for inelastic processes. We find a number of essential aspects that must be observed in a physically meaningful and reliable theory of atom transmission and scattering; all are connected with multiparticle scattering, particularly the possibility of energy loss. These processes are (a) the coupling to low-lying (surface) excitations (ripplons/third sound) which is manifested in a finite imaginary part of the self energy, and (b) the reduction of the strength of the excitation in the maxon/roton region

Comprehensive analysis of gene expression patterns of hedgehog-related genes

BACKGROUND: The Caenorhabditis elegans genome encodes ten proteins that share sequence similarity with the Hedgehog signaling molecule through their C-terminal autoprocessing Hint/Hog domain. These proteins contain novel N-terminal domains, and C. elegans encodes dozens of additional proteins containing only these N-terminal domains. These gene families are called warthog, groundhog, ground-like and quahog, collectively called hedgehog (hh)-related genes. Previously, the expression pattern of seventeen genes was examined, which showed that they are primarily expressed in the ectoderm. RESULTS: With the completion of the C. elegans genome sequence in November 2002, we reexamined and identified 61 hh-related ORFs. Further, we identified 49 hh-related ORFs in C. briggsae. ORF analysis revealed that 30% of the genes still had errors in their predictions and we improved these predictions here. We performed a comprehensive expression analysis using GFP fusions of the putative intergenic regulatory sequence with one or two transgenic lines for most genes. The hh-related genes are expressed in one or a few of the following tissues: hypodermis, seam cells, excretory duct and pore cells, vulval epithelial cells, rectal epithelial cells, pharyngeal muscle or marginal cells, arcade cells, support cells of sensory organs, and neuronal cells. Using time-lapse recordings, we discovered that some hh-related genes are expressed in a cyclical fashion in phase with molting during larval development. We also generated several translational GFP fusions, but they did not show any subcellular localization. In addition, we also studied the expression patterns of two genes with similarity to Drosophila frizzled, T23D8.1 and F27E11.3A, and the ortholog of the Drosophila gene dally-like, gpn-1, which is a heparan sulfate proteoglycan. The two frizzled homologs are expressed in a few neurons in the head, and gpn-1 is expressed in the pharynx. Finally, we compare the efficacy of our GFP expression effort with EST, OST and SAGE data. CONCLUSION: No bona-fide Hh signaling pathway is present in C. elegans. Given that the hh-related gene products have a predicted signal peptide for secretion, it is possible that they constitute components of the extracellular matrix (ECM). They might be associated with the cuticle or be present in soluble form in the body cavity. They might interact with the Patched or the Patched-related proteins in a manner similar to the interaction of Hedgehog with its receptor Patched

On the Fredholm property of bisingular pseudodifferential operators

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added reference

Application of inelastic epithermal neutron scattering to the vibrational spectroscopy of adsorbed molecules: Butane physisorbed on graphite (0001) surfaces

doi:10.1063/1.448924Inelastic epithermal neutron scattering (IENS) has been used to investigate the intramolecular vibrations of butane [CH3(CH2)2CH3] physisorbed on the (0001) surfaces of a graphite powder. The purpose of these studies was to assess IENS as a vibrational spectroscopy for adsorbed species by using a relatively well‐characterized substrate (Carbopack B). The experiments were performed on the IN1 spectrometer located on a beam from the ''hot'' source at the Institut Laue‐Langevin reactor in Grenoble. Film coverages of 1.0 and 3.6 layers were investigated at a temperature of 78 K. The IENS spectra are rich in structure, containing eight vibrational bands in the energy‐transfer range from 280-3470 cm−1 (35-430 meV). The similarity in the spectra at the two coverages investigated indicates that in this energy‐transfer range the butane intramolecular modes are not strongly perturbed by physisorption on graphite. A detailed comparison is made between the monolayer IENS spectrum and those calculated from models of a free and adsorbed molecule. Both models employ a previously derived intramolecular force field in the normal mode calculation. A third calculation assumes the displacement eigenvectors of the free molecule but replaces the mode eigenfrequencies by their measured Raman and IR values. It reproduces the observed IENS spectra very well. The large number of vibrational bands observed and the close agreement with the calculated spectra suggest butane as a desirable adsorbate for similar experiments on catalytic substrates.This work was supported in part by National Science Foundation Grants DMR-1905958, INT- 8012228, and DMR-8304366 and by a grant of the Petroleum Research fund, administered by the American Chemical Society

Magnetic Structure in Fe/Sm-Co Exchange Spring Bilayers with Intermixed Interfaces

The depth profile of the intrinsic magnetic properties in an Fe/Sm-Co bilayer fabricated under nearly optimal spring-magnet conditions was determined by complementary studies of polarized neutron reflectometry and micromagnetic simulations. We found that at the Fe/Sm-Co interface the magnetic properties change gradually at the length scale of 8 nm. In this intermixed interfacial region, the saturation magnetization and magnetic anisotropy are lower and the exchange stiffness is higher than values estimated from the model based on a mixture of Fe and Sm-Co phases. Therefore, the intermixed interface yields superior exchange coupling between the Fe and Sm-Co layers, but at the cost of average magnetization.Comment: 16 pages, 6 figures and 1 tabl