Hybrid materials based on vanadium pentoxide intercalation complexes

Neutral macrocyclic compounds (crown ethers and cryptands) and charged molecular species (alkylammonium iodides) were intercalated into vanadium oxide xerogel (V₂O₅ · nH₂O) to study their influence on the electrical behaviour of this inorganic 2D host lattice. Treatment with alkyl or arylammonium iodide solutions produced the intercalation of organic cations accompanied by the reduction of a fraction of V (V) to V (IV). Characterisation by different techniques allowed the postulation of the interlayer arrangement of the guest species. The study of electrical behaviour at different temperatures indicated that the properties of the hybrid materials can be mainly related to the nature of guest species, the degree of host lattice reduction, the interlayer water content, and the␣presence of metal ions deliberately introduced in the system. Received: 23 January 2001 Accepted: 5 April 2001     

The percolation staircase model and its manifestation in composite materials

We studied the tunneling percolation conductivity dependence on the site or bond occupation probability in the square lattice. The model predicts that in both, lattice and continuum systems in which there is a hierarchy of the local conductances, the dependence of the global conductivity on the site or volume occupation probability will yield a conductivity staircase. In particular we evaluate the implications of the staircase on the critical behavior of the conductivity. We then show experimental evidence for the predicted percolation-tunneling staircase in a Ag-Al₂O₃ granular metal system and in a carbon black-polymer composite. Following that, we propose that for carbon nanotube (CNT) polymer composites the data in the literature give ample support to a percolation-dispersion staircase behavior. The implication of the present findings on the percolation-hopping problem in composite materials is also discussed.     

Isotopic thermal diffusion factors of the noble gases

A new set of isotopic thermal diffusion factors for Ar, Kr and Xe is reported. The data have been obtained from thermal diffusion column measurements in a column previously calibrated with Ne gas, and complete the α_T data for the binary mixtures of noble gases given previously. The results lead to the conclusion that the thermal diffusion properties of the noble gases and their mixtures are well described by the law of corresponding states first proposed by Kestin, Ro and Wakeham. It is also concluded that the calibration technique used makes the thermal diffusion column a valuable instrument for the determination of the thermal diffusion factors of isotopic and non-isotopic dilute gas mixtures.     

Auditory stream segregation in monkey auditory cortex: effects of frequency separation, presentation rate, and tone duration

Auditory stream segregation refers to the organization of sequential sounds into "perceptual streams" reflecting individual environmental sound sources. In the present study, sequences of alternating high and low tones, "...ABAB...," similar to those used in psychoacoustic experiments on stream segregation, were presented to awake monkeys while neural activity was recorded in primary auditory cortex (A1). Tone frequency separation (AF), tone presentation rate (PR), and tone duration (TD) were systematically varied to examine whether neural responses correlate with effects of these variables on perceptual stream segregation. "A" tones were fixed at the best frequency of the recording site, while "B" tones were displaced in frequency from "A" tones by an amount = delta F. As PR increased, "B" tone responses decreased in amplitude to a greater extent than "A" tone responses, yielding neural response patterns dominated by "A" tone responses occurring at half the alternation rate. Increasing TD facilitated the differential attenuation of "B" tone responses. These findings parallel psychoacoustic data and suggest a physiological model of stream segregation whereby increasing delta F, PR, or TD enhances spatial differentiation of "A" tone and "B" tone responses along the tonotopic map in A1.     

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in and unstable in under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.     

Pattern Matching with Swaps

Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version T′ of T is a length n string derived from T by a series of local swaps (i.e., t′_ℓ ← t_ℓ + 1 and t′_ℓ + 1 ← t_ℓ), where each element can participate in no more than one swap. The pattern matching with swaps problem is that of finding all locations i for which there exists a swapped version T′ of T with an exact matching of P in location i of T′. It has been an open problem whether swapped matching can be done in less than O(nm) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(nm). We present an algorithm whose time complexity is O(nm^1/3 log m log σ) for a general alphabet Σ, where σ = min(m,Σ).     

Dynamic nuclear polarization assisted spin diffusion for the solid effect case

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole-dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core-bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and cross-relaxation rates. The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of (13)C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.