Are polymer melts "ideal"?

It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain should exponentially decay with $s$. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, $P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise method for obtaining the statistical segment length \bstar in a computer experiment.Comment: 4 pages, 3 figure

Dynamic scaling and aging phenomena in short-range Ising spin glass: Cu0.5_{0.5}Co0.5_{0.5}Cl2_{2}-FeCl3_{3} graphite bi-intercalation compound

Static and dynamic behavior of short-range Ising-spin glass Cu$_{0.5}$Co$_{0.5}$Cl$_{2}$-FeCl$_{3}$ graphite bi-intercalation compounds (GBIC) has been studied with SQUID DC and AC magnetic susceptibility. The $T$ dependence of the zero-field relaxation time $\tau$ above a spin-freezing temperature $T_{g}$ (= 3.92 $\pm$ 0.11 K) is well described by critical slowing down. The absorption $\chi^{\prime\prime}$ below $T_{g}$ decreases with increasing angular frequency $\omega$, which is in contrast to the case of 3D Ising spin glass. The dynamic freezing temperature $T_{f}(H,\omega)$ at which d$M_{FC}(T,H)/$d$H=\chi^{\prime}(T,H=0,\omega)$, is determined as a function of frequency (0.01 Hz $\leq \omega/2\pi \leq$ 1 kHz) and magnetic field (0 $\leq H \leq$ 5 kOe). The dynamic scaling analysis of the relaxation time $\tau(T,H)$ defined as $\tau = 1/\omega$ at $T = T_{f}(H,\omega)$ suggests the absence of SG phase in the presence of $H$ (at least above 100 Oe). Dynamic scaling analysis of $\chi^{\prime \prime}(T, \omega)$ and $\tau(T,H)$ near $T_{g}$ leads to the critical exponents ($\beta$ = 0.36 $\pm$ 0.03, $\gamma$ = 3.5 $\pm$ 0.4, $\nu$ = 1.4 $\pm$ 0.2, $z$ = 6.6 $\pm$ 1.2, $\psi$ = 0.24 $\pm$ 0.02, and $\theta$ = 0.13 $\pm$ 0.02). The aging phenomenon is studied through the absorption $\chi^{\prime \prime}(\omega, t)$ below $T_{g}$. It obeys a $(\omega t)^{-b^{\prime \prime}}$ power-law decay with an exponent $b^{\prime \prime}\approx 0.15 - 0.2$. The rejuvenation effect is also observed under sufficiently large (temperature and magnetic-field) perturbations.Comment: 14 pages, 19 figures; to be published in Phys. Rev. B (September 1, 2003

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

Microscopic structure and dynamics of glass forming Zr2Co melts and the impact of different late transition metals on the melt properties

We studied the short-range order and the atomic dynamics of stable and undercooled binary Zr2Co alloy melts as well as their density and viscosity. The containerless processing technique of electrostatic levitation was used to achieve deep undercooling and to avoid contaminations. Static structure factors are determined by combining this technique with neutron and high energy X-ray diffraction. Co self-diffusion coefficients are measured by quasielastic neutron scattering. Our results reveal that the short-range order of the Zr2Co melts closely resembles that previously observed for Zr64Ni36. We consider this as the origin of the very similar melt dynamics of these two alloys at same temperatures. On the other hand, the difference in the structure and dynamics when compared with those of Zr2Cu and Zr2Pd shows clearly that not only the atomic sizes, but also electronic properties or chemical bonding have an important influence on the melt properties of Zr-based glass forming melts

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

A first-principles approach to electrical transport in atomic-scale nanostructures

We present a first-principles numerical implementation of Landauer formalism for electrical transport in nanostructures characterized down to the atomic level. The novelty and interest of our method lies essentially on two facts. First of all, it makes use of the versatile Gaussian98 code, which is widely used within the quantum chemistry community. Secondly, it incorporates the semi-infinite electrodes in a very generic and efficient way by means of Bethe lattices. We name this method the Gaussian Embedded Cluster Method (GECM). In order to make contact with other proposed implementations, we illustrate our technique by calculating the conductance in some well-studied systems such as metallic (Al and Au) nanocontacts and C-atom chains connected to metallic (Al and Au) electrodes. In the case of Al nanocontacts the conductance turns out to be quite dependent on the detailed atomic arrangement. On the contrary, the conductance in Au nanocontacts presents quite universal features. In the case of C chains, where the self-consistency guarantees the local charge transfer and the correct alignment of the molecular and electrode levels, we find that the conductance oscillates with the number of atoms in the chain regardless of the type of electrode. However, for short chains and Al electrodes the even-odd periodicity is reversed at equilibrium bond distances.Comment: 14 pages, two-column format, submitted to PR

Density functional method for nonequilibrium electron transport

We describe an ab initio method for calculating the electronic structure, electronic transport, and forces acting on the atoms, for atomic scale systems connected to semi-infinite electrodes and with an applied voltage bias. Our method is based on the density functional theory (DFT) as implemented in the well tested Siesta approach (which uses non-local norm-conserving pseudopotentials to describe the effect of the core electrons, and linear combination of finite-range numerical atomic orbitals to describe the valence states). We fully deal with the atomistic structure of the whole system, treating both the contact and the electrodes on the same footing. The effect of the finite bias (including selfconsistency and the solution of the electrostatic problem) is taken into account using nonequilibrium Green's functions. We relate the nonequilibrium Green's function expressions to the more transparent scheme involving the scattering states. As an illustration, the method is applied to three systems where we are able to compare our results to earlier ab initio DFT calculations or experiments, and we point out differences between this method and existing schemes. The systems considered are: (1) single atom carbon wires connected to aluminum electrodes with extended or finite cross section, (2) single atom gold wires, and finally (3) large carbon nanotube systems with point defects.Comment: 18 pages, 23 figure

Recoil Polarization for Delta Excitation in Pion Electroproduction

We measured angular distributions of recoil-polarization response functions for neutral pion electroproduction for W=1.23 GeV at Q^2=1.0 (GeV/c)^2, obtaining 14 separated response functions plus 2 Rosenbluth combinations; of these, 12 have been observed for the first time. Dynamical models do not describe quantities governed by imaginary parts of interference products well, indicating the need for adjusting magnitudes and phases for nonresonant amplitudes. We performed a nearly model-independent multipole analysis and obtained values for Re(S1+/M1+)=-(6.84+/-0.15)% and Re(E1+/M1+)=-(2.91+/-0.19)% that are distinctly different from those from the traditional Legendre analysis based upon M1+ dominance and sp truncation.Comment: 5 pages, 2 figures, for PR