The crystallization kinetics of polyamide-12

The crystallization kinetics of polyamide-12 has been investigated using a combination of differential scanning calorimetry (DSC) and hot-stage optical microscopy. The DSC data for isothermal crystallization were consistent with a simple two-parameter Avrami model for isothermal crystallization and optical measurements of the spherulite growth rates and nucleation density. On the basis of semiempirical expressions for these quantities, it is shown that with small adjustments the model can also account for DSC data for nonisothermal crystallization, provided that corrections are made for the dynamic heat balance between the sample and the DSC oven. Received: 9 March 2000 Accepted: 28 September 2000     

Enhanced electron–phonon coupling at metal surfaces

Recent advances in experimental techniques and theoretical capabilities associated with the study of surfaces show promise for producing in unprecedented detail a picture of electron–phonon coupling. These investigations on surfaces of relatively simple metals can be the platform for understanding functionality in complex materials associated with the coupling between charge and the lattice. In this article, we present an introduction to electron–phonon coupling, especially in systems with reduced dimensionality, and the recent experimental and theoretical achievements. Then, we try to anticipate the exciting future created by advances in surface physics.     

Toughness,binding number and restricted matching extension in a graph

A connected graph $G$ with at least $2m+2n+2$ vertices is said to satisfy the property $E(m,n)$ if $G$ contains a perfect matching and for any two sets of independent edges $M$ and $N$ with $\left|M\right|=m$ and $\left|N\right|=n$ with $M\cap N=?$, there is a perfect matching $F$ in $G$ such that $M?F$ and $N\cap F=?$. In particular, if $G$ is $E(m,0)$, we say that $G$ is $m$-extendable. One of the authors has proved that every $m$-tough graph of even order at least $2m+2$ is $m$-extendable (Plummer, 1988). Chen (1995) and Robertshaw and Woodall (2002) gave sufficient conditions on binding number for $m$-extendability. In this paper, we extend these results and give lower bounds on toughness and binding number which guarantee $E(m,n)$.     

Proximity thresholds for matching extension in the torus and Klein bottle

A graph $G$ is said to have the property $E_d(m,n)$ if, given any two disjoint matchings $M$ and $N$ such that the edges within $M$ are pair-wise distance at least $d$ from each other as are the edges in $N$, there is a perfect matching $F$ in $G$ such that $M?F$ and $F\cap N=0?$. This property has been previously studied for planar triangulations as well as projective planar triangulations. Here this study is extended to triangulations of the torus and Klein bottle.     

Jahn-Teller phonon anomaly and dynamic phase fluctuations in La0.7Ca0.3MnO3

Inelastic neutron scattering was used to study the temperature (T) dependence of the lattice excitations in La 0.7Ca 0.3MnO (3). An optical Jahn-Teller phonon exhibits continuous but anomalous damping with increasing temperature in the ferromagnetic-metallic phase and collapses above the Curie temperature T(C) (240 K). We attribute this anomaly to the growing dynamic phase segregation as T-->T(C), thus providing evidence of local fluctuations associated with the short-range polaron or charge/orbital ordering in the ferromagnetic-metallic state.     

Non-fermi-liquid behavior in quasi-one-dimensional Li0.9Mo6O17

We present temperature dependent scanning tunneling spectroscopy data of the quasi-one-dimensional conductor Li0.9Mo6O17. The differential tunneling current in our low-temperature spectra shows a power-law behavior around the Fermi energy, which is expected for a clean Luttinger liquid. The power-law exponent is found to be 0.6. Spectra for a temperature range of 5 to 55 K can be fitted fairly well with a model for tunneling into a Luttinger liquid at the appropriate temperature. A fit with a model based on a zero bias anomaly is significantly worse compared to the Luttinger liquid model. No signature of a phase transition at T = 24 K is observed in our temperature dependent data.     

Optimal design of efficient acoustic antenna arrays

Minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with many convex quadratic constraints and a nonconvex quadratic efficiency constraint. The variables of this problem are a scaling and phase shift applied to the output of each sensor. This problem is solved by applying Lagrangian relaxation to the convex quadratic constraints. Extensive computational experience shows that this approach can efficiently find near-optimal solutions of problems with up to 391 variables and 579 constraints. This work was supported by ONR Contracts N00014-83-C-0437 and N00014-82-C-824.