Static and dynamic properties of Single-Chain Magnets with sharp and broad domain walls

We discuss time-quantified Monte-Carlo simulations on classical spin chains with uniaxial anisotropy in relation to static calculations. Depending on the thickness of domain walls, controlled by the relative strength of the exchange and magnetic anisotropy energy, we found two distinct regimes in which both the static and dynamic behavior are different. For broad domain walls, the interplay between localized excitations and spin waves turns out to be crucial at finite temperature. As a consequence, a different protocol should be followed in the experimental characterization of slow-relaxing spin chains with broad domain walls with respect to the usual Ising limit.Comment: 18 pages, 13 figures, to be published in Phys. Rev.

Apparent Sizes and Spectral Line Profiles for Spherical and Disk Masers: Solutions to the Full Equations

Calculations are performed for the spectral line profiles and images of astrophysical maser radiation that emerges from isolated spheres and thin disks viewed edge-on. In contrast to previous investigations where various approximations are made, the full equations are solved here for the frequency-dependent radiative transport that includes the thermal motion of the molecules. The spectral line profiles for spheres and disks are found to rebroaden to the full thermal Doppler breadth with increasing saturation in essentially the same way as is well known to occur for a linear maser. The variation with frequency in the apparent angular sizes of masing spheres and thin disks is found to be negligible at frequencies within the spectral line where the flux is significant. Calculations also are performed for spherical and disk masers that are not isolated, but for which the seed radiation for the masers is incident from one side as would occur when a strong continuum source is on the far side of the masers. Again, the spectral line profiles are found to rebroaden to the full thermal breadths with increasing saturation and there are no significant variations in the apparent angular sizes with frequency. However, the full rebroadening does occur at somewhat higher saturation and the variation of the apparent angular sizes as a function of the degree of saturation is quite different from that of the isolated masers. Spheres and disks have served as idealized geometries with which to examine possible deviations from the linear approximation for astrophysical masers.Comment: accepted for Astrophysical Journa

Equation of the field lines of an axisymmetric multipole with a source surface

Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surface magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree ℓ and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace’s equation for the magnetostatic potential

Langevin equation with scale-dependent noise

A new wavelet based technique for the perturbative solution of the Langevin equation is proposed. It is shown that for the random force acting in a limited band of scales the proposed method directly leads to a finite result with no renormalization required. The one-loop contribution to the Kardar-Parisi-Zhang equation Green function for the interface growth is calculated as an example.Comment: LaTeX, 5 page

The views of older women towards mammographic screening: a qualitative and quantitative study

Purpose: Mammographic screening has improved breast cancer survival in the screened age group. This improved survival has not been seen in older women (>70 years) where screening uptake is low. This study explores the views, knowledge and attitudes of older women towards screening. Methods: Women (>70) were interviewed about breast screening. Interview findings informed the development of a questionnaire which was sent to 1000 women (>70) to quantify their views regarding screening. Results: Twenty-six women were interviewed and a questionnaire designed. The questionnaire response rate was 48.3% (479/992). Over half (52.9%, 241/456) of respondents were unaware they could request mammography by voluntary self-referral and were unaware of how to arrange this. Most (81.5% 383/470) had not attended breast screening since turning 70. Most (75.6%, 343/454) felt screening was beneficial and would attend if invited. Most, (90.1%, 412/457) felt screening should be offered to all women regardless of age or health. Conclusions: There is a lack of knowledge about screening in older women. The majority felt that invitation to screening should be extended to the older age group regardless of age or health. The current under-utilised system of voluntary self referral is not supported by older women

Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Peclet numbers.Comment: 4 pages, 1 figure; to appear in Phys. Rev. Let

Defect generation and deconfinement on corrugated topographies

We investigate topography-driven generation of defects in liquid crystals films coating frozen surfaces of spatially varying Gaussian curvature whose topology does not automatically require defects in the ground state. We study in particular disclination-unbinding transitions with increasing aspect ratio for a surface shaped as a Gaussian bump with an hexatic phase draped over it. The instability of a smooth ground state texture to the generation of a single defect is also discussed. Free boundary conditions for a single bump are considered as well as periodic arrays of bumps. Finally, we argue that defects on a bump encircled by an aligning wall undergo sharp deconfinement transitions as the aspect ratio of the surface is lowered.Comment: 24 page

Multiscale theory of turbulence in wavelet representation

We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of its wavelet components, we achieve the cancellation of loop divergences in the stochastic perturbation expansion. An extra contribution to the energy transfer from large to smaller scales is considered. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures based on the wavelet decomposition are constructed.Comment: LaTeX, 27 pages, 3 eps figure

Notes about Passive Scalar in Large-Scale Velocity Field

We consider advection of a passive scalar theta(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model the whole PDF's (probability distribution functions) for the single-point statistics of theta and for the passive scalar difference theta(r_1)-theta(r_2) (for separations r_1-r_2 lying in the convective interval) are found.Comment: 19 pages, RevTe

Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling

This paper is the first in a series of three papers that aim at understanding the scaling behaviour of hydrodynamic turbulence. We present in this paper a perturbative theory for the structure functions and the response functions of the hydrodynamic velocity field in real space and time. Starting from the Navier-Stokes equations (at high Reynolds number Re) we show that the standard perturbative expansions that suffer from infra-red divergences can be exactly resummed using the Belinicher-L'vov transformation. After this exact (partial) resummation it is proven that the resulting perturbation theory is free of divergences, both in large and in small spatial separations. The hydrodynamic response and the correlations have contributions that arise from mediated interactions which take place at some space- time coordinates. It is shown that the main contribution arises when these coordinates lie within a shell of a "ball of locality" that is defined and discussed. We argue that the real space-time formalism developed here offers a clear and intuitive understanding of every diagram in the theory, and of every element in the diagrams. One major consequence of this theory is that none of the familiar perturbative mechanisms may ruin the classical Kolmogorov (K41) scaling solution for the structure functions. Accordingly, corrections to the K41 solutions should be sought in nonperturbative effects. These effects are the subjects of papers II and III in this series, that will propose a mechanism for anomalous scaling in turbulence, which in particular allows multiscaling of the structure functions.Comment: PRE in press, 18 pages + 6 figures, REVTeX. The Eps files of figures will be FTPed by request to [email protected]