THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge between the moments of jump of the random walk and interpreted as an energy function over the bridge connfiguration; the random walk acts as the random environment. This model provides a continuum version of a model with some relevance to protein conformation. The thermodynamic limit of the specific free energy is shown to exist and to be self-averaging, i.e. it is equal to a trivial --- explicitly computed --- random variable. An estimate of the asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip

The maximum modulus of a trigonometric trinomial

Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda

Anomalous codeposition of cobalt and ruthenium from chloride-sulfate baths

Codeposition of Ru and Co was studied at room temperature and at 50oC with various Ru3+ and Co2+ concentrations in the electrolyte. The codeposition of Co and Ru proved to be anomalous since no pure Ru could be obtained in the presence of Co2+ in the electrolyte, but a significant Co incorporation into the deposit was detected at potentials where the deposition of pure Co was not possible. The composition of the deposits varied monotonously with the change of the concentration ratio of Co2+ and Ru3+. The deposition of Ru was much hindered and the current efficiency was a few percent only when the molar fraction of Co in the deposit was low. Continuous deposits could be obtained only when the molar fraction of Co in the deposit was at least 40 at.%. The deposit morphology was related to the molar fraction of Co in the deposit. The X-ray diffractograms are in conformity with a hexagonal close-packed alloy and indicate the formation of nanocrystalline deposits. Two-pulse plating did not lead to a multilayer but to a Co-rich alloy. Magnetoresistance of the samples decreased with increasing Ru content

Finite time and asymptotic behaviour of the maximal excursion of a random walk

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods. Then we focus on the early time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$ exhibits a systematic overshooting of the long time exponent. Exact results are obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions, on a regular lattice and on the Sierpi\'nski gasket we find numerically that the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.Comment: 9 pages, 4 figures, accepted J. Phys.

Fundamentals of interface phenomena in advanced bulk nanoscale materials

The review is devoted to a study of interface phenomena influencing advanced properties of nanoscale materials processed by means of severe plastic deformation, high-energy ball milling and their combinations. Interface phenomena include processes of interface defect structure relaxation from a highly nonequilibrium state to an equilibrium condition, grain boundary phase transformations and enhanced grain boundary and triple junction diffusivity. On the basis of an experimental investigation, a theoretical description of the key interfacial phenomena controlling the functional properties of advanced bulk nanoscale materials has been conducted. An interface defect structure investigation has been performed by TEM, high-resolution x-ray diffraction, atomic simulation and modeling. The problem of a transition from highly non-equilibrium state to an equilibrium one, which seems to be responsible for low thermostability of nanoscale materials, was studied. Also enhanced grain boundary diffusivity is addressed. Structure recovery and dislocation emission from grain boundaries in nanocrystalline materials have been investigated by analytical methods and modeling

Making fluency research accessible to second language teachers: the impact of a training intervention

The study reported in this paper was aimed at investigating whether making the findings of second language fluency research accessible to language teachers has an impact on their self-reported understanding of the concept of oral fluency, confidence in promoting it, and classroom practice in short and medium term. The data come from 106 initial and 32 delayed questionnaires and nine interviews, eliciting both qualitative and quantitative data, from second language teachers in England after attending a one-day research-informed and practice-oriented training workshop. The results indicate a positive impact on teachers’ understanding of fluency, confidence in helping their learners, and self-reported practice in short term, with the positive impact being reported in medium term (e.g., two to six months after the intervention). The findings confirm previous research (e.g., Lennon, 1990) that adopting a narrow perspective to defining and conceptualizing fluency is linked with a more in-depth understanding of fluency and enhanced confidence and ability for using fluency-focused classroom activities

Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic