A self-organizing network in the weak-coupling limit

We prove the existence of spatially localized ground states of the diffusive Haken model. This model describes a self-organizing network whose elements are arranged on a d-dimensional lattice with short-range diffusive coupling. The network evolves according to a competitive gradient dynamics in which the effects of diffusion are counteracted by a localizing potential that incorporates an additional global coupling term. In the absence of diffusive coupling, the ground states of the system are strictly localized, i.e. only one lattice site is excited. For sufficiently small non-zero diffusive coupling , it is shown analytically that localized ground states persist in the network with the excitations exponentially decaying in space. Numerical results establish that localization occurs for arbitrary values of in one dimension but vanishes beyond a critical coupling _c(d), when d> 1. The one-dimensional localized states are interpreted in terms of instanton solutions of a continuum version of the model.     

Synthesis and properties of polyethersulphone–polydimethyisiloxane block copolymers

High molecular weight alternating block copolymers of polyethesulphone (PES) and polydimethylsiloxane (PDMS) were prepared by the condensation of dimethylamino-terminated PDMS oligomers and hydroxy-terminated PES oligomers in 1,2-dichlorobenzene. Microphase separation of the block copolymers at exceptionally short block lengths was observed by differential scanning calorimetry (DSC) and transmission electron microscopy (TEM). The Si? O? C intersegment linkage in these materials appeared to display poor hydrolytic stability which is contrary to results obtained for other block copolymers.     

Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators

A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.     

The vertex-cover polynomial of a graph

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τ^r in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f⁻¹(x)f⁻¹(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ).     

Dynamic NMR study of the flexibility of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts

Dynamic NMR investigations of a number of 2-amino-3-aroyl-4,6-diaryl-pyrylium salts were carried out. The barrier to rotation of the partial C, N double bond was determined and proved to be in the range of 62 to 63 kJ/mol. Quantum chemical calculations of bond orders and electron densities of the different atoms in the molecules show the distinct double bond character of the exocyclic C, N bond. This is in agreement with the relatively high barrier to rotation. By quantum chemical ab initio 3-21G calculations, the dynamic behaviour of this kind of compounds was simulated; two pairs (image and mirror image) of ground state conformations, in coincidence with the experiment, were obtained. Received: 10 May 1996 / Revised: 1 July 1996 / Accepted: 4 July 1996     

The Kosterlitz-Thouless model in Perovskite superconductors

Il Nuovo Cimento D - The applicability of the Kosterlitz-Thouless theory to HTSC is examined. The model initially presented in its general lines for bidimensional systems is then applied to...     

Mechanisms of ion-beam-enhanced diffusion in amorphous silicon

We have investigated ion-beam-enhanced diffusion of Au in undoped and B doped amorphous Si. The diffusion coefficients depend linearly on ion flux and exibit an Arrhenius-like temperature dependence with an activation energy of 0.37 eV in the temperature range 200–350° C. Moreover the diffusivity is enhanced by a factor of 5 by B-doping at a concentration of 1×10²⁰ atoms/cm³. A similar enhancement is observed in thermal diffusion of Au which has an activation energy of 1.5 eV. On the basis of these results a model for the ion-beam-enhanced diffusion of Au is proposed where the high density of defects present in amorphous Si act as traps for the fast moving interstitial Au atoms. The effectiveness of this trapping process can be changed by the high concentration of mobile defects generated by the beam and also by a change in the charge state of the traps induced by the presence of B.