Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results

We analyze the scaling laws for a set of two different species of long flexible polymer chains joined together at one of their extremities (copolymer stars) in space dimension D=2. We use a formerly constructed field-theoretic description and compare our perturbative results for the scaling exponents with recent conjectures for exact conformal scaling dimensions derived by a conformal invariance technique in the context of D=2 quantum gravity. A simple MC simulation brings about reasonable agreement with both approaches. We analyse the remarkable multifractal properties of the spectrum of scaling exponents.Comment: 5 page

Polycrystalline silicon study: Low-cost silicon refining technology prospects and semiconductor-grade polycrystalline silicon availability through 1988

Photovoltaic arrays that convert solar energy into electrical energy can become a cost effective bulk energy generation alternative, provided that an adequate supply of low cost materials is available. One of the key requirements for economic photovoltaic cells is reasonably priced silicon. At present, the photovoltaic industry is dependent upon polycrystalline silicon refined by the Siemens process primarily for integrated circuits, power devices, and discrete semiconductor devices. This dependency is expected to continue until the DOE sponsored low cost silicon refining technology developments have matured to the point where they are in commercial use. The photovoltaic industry can then develop its own source of supply. Silicon material availability and market pricing projections through 1988 are updated based on data collected early in 1984. The silicon refining industry plans to meet the increasing demands of the semiconductor device and photovoltaic product industries are overviewed. In addition, the DOE sponsored technology research for producing low cost polycrystalline silicon, probabilistic cost analysis for the two most promising production processes for achieving the DOE cost goals, and the impacts of the DOE photovoltaics program silicon refining research upon the commercial polycrystalline silicon refining industry are addressed

A role for the cleaved cytoplasmic domain of E-cadherin in the nucleus

Cell-cell contacts play a vital role in intracellular signaling, although the molecular mechanisms of these signaling pathways are not fully understood. E-cadherin, an important mediator of cell-cell adhesions, has been shown to be cleaved by γ-secretase. This cleavage releases a fragment of E-cadherin, E-cadherin C-terminal fragment 2 (E-cad/CTF2), into the cytosol. Here, we study the fate and function of this fragment. First, we show that coexpression of the cadherin-binding protein, p120 catenin (p120), enhances the nuclear translocation of E-cad/CTF2. By knocking down p120 with short interfering RNA, we also demonstrate that p120 is necessary for the nuclear localization of E-cad/CTF2. Furthermore, p120 enhances and is required for the specific binding of E-cad/CTF2 to DNA. Finally, we show that E-cad/CTF2 can regulate the p120-Kaiso-mediated signaling pathway in the nucleus. These data indicate a novel role for cleaved E-cadherin in the nucleus

Where two fractals meet: the scaling of a self-avoiding walk on a percolation cluster

The scaling properties of self-avoiding walks on a d-dimensional diluted lattice at the percolation threshold are analyzed by a field-theoretical renormalization group approach. To this end we reconsider the model of Y. Meir and A. B. Harris (Phys. Rev. Lett. 63:2819 (1989)) and argue that via renormalization its multifractal properties are directly accessible. While the former first order perturbation did not agree with the results of other methods, we find that the asymptotic behavior of a self-avoiding walk on the percolation cluster is governed by the exponent nu_p=1/2 + epsilon/42 + 110epsilon^2/21^3, epsilon=6-d. This analytic result gives an accurate numeric description of the available MC and exact enumeration data in a wide range of dimensions 2<=d<=6.Comment: 4 pages, 2 figure

Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral equation, a systematic way to determine the ensemble averaged eigenvalue spectrum for a general type of tree-like networks. Close to the percolation threshold we find characteristic scaling functions for the density of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for small lambda, where alpha_1 holds below and alpha_2 at the percolation threshold. In the range where the spectra are accessible from a numerical diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure

The potential of the ground state of NaRb

The X$^{1}\Sigma ^{+}$ state of NaRb was studied by Fourier transform spectroscopy. An accurate potential energy curve was derived from more than 8800 transitions in isotopomers $^{23}$Na$^{85}$Rb and $^{23}$Na$^{87}$Rb. This potential reproduces the experimental observations within their uncertainties of 0.003 \rcm to 0.007 \rcm. The outer classical turning point of the last observed energy level ($v''=76$, $J''=27$) lies at $\approx 12.4$ \AA, leading to a energy of 4.5 \rcm below the ground state asymptote.Comment: 8 pages, 6 figures and 2 table

Entropy-induced separation of star polymers in porous media

We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of $f$-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function $g(r) \sim r^{-a}$. Applying the field-theoretical renormalization group approach we show in a double expansion in $\epsilon=4-d$ and $\delta=4-a$ that there is a range of correlation strengths $\delta$ for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension $d=3$ and different values of the correlation parameter $a$ the corresponding scaling exponents $\gamma_f$ that govern entropic effects. We find that $\gamma_f-1$, the deviation of $\gamma_f$ from its mean field value is amplified by the disorder once we increase $\delta$ beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are: star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.Comment: 14 pages, 7 figure

Conversion of bright magneto-optical resonances into dark at fixed laser frequency for D2 excitation of atomic rubidium

Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2 line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser induced fluorescence (LIF) was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the Fg=2 --> Fe=3 transition of Rb-87 and near to the Fg=3 --> Fe=4 transition of Rb-85. The bright resonance became dark as the laser power density was increased above 0.6mW/cm2 or 0.8 mW/cm2, respectively. When the Fg=2 --> Fe=3 transition of Rb-87 was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.Comment: 9 pages, 7 figure