On the determination and evolution of fabric in representative elementary volumes for a sand specimen in triaxial compression

The soil response in triaxial compression tests, that are commonly treated as element tests, is known to be inhomogeneous. Several studies have revealed the localisation of deformation throughout the whole specimen by digital image correlation techniques on X-ray tomographies. The fabric of a soil specimen has so far only been studied on complete specimens as a bulk measurement or in chosen subsets. In this contribution, we present a study on the spatial and temporal distribution of the fabric throughout one Hostun sand sample in triaxial compression. Therefore, we calibrated the minimum representative element size first for three chosen fabric variables considering three different criteria. By distributing the elements in a regular grid over the specimen, we are able to clearly identify the onset of the localisation in terms of void ratio, coordination number and contact fabric anisotropy. Spatially and temporally the contact fabric variables precede the void ratio changes as they are much more sensitive to small changes

General Relativistic Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star. II. Solution of the Induction Equations

We have solved numerically the general relativistic induction equations in the interior background spacetime of a slowly rotating magnetized neutron star. The analytic form of these equations was discussed in a recent paper (Rezzolla et al 2001a), where corrections due both to the spacetime curvature and to the dragging of reference frames were shown to be present. Through a number of calculations we have investigated the evolution of the magnetic field with different rates of stellar rotation, different inclination angles between the magnetic moment and the rotation axis, as well as different values of the electrical conductivity. All of these calculations have been performed for a constant temperature relativistic polytropic star and make use of a consistent solution of the initial value problem which avoids the use of artificial analytic functions. Our results show that there exist general relativistic effects introduced by the rotation of the spacetime which tend to decrease the decay rate of the magnetic field. The rotation-induced corrections are however generally hidden by the high electrical conductivity of the neutron star matter and when realistic values for the electrical conductivity are considered, these corrections become negligible even for the fastest known pulsar.Comment: 13 pages, 5 figures. Accepted for publication by MNRAS. Replaces previous version without unnecessary mn.st

Spot-like Structures of Neutron Star Surface Magnetic Fields

There is growing evidence, based on both X-ray and radio observations of isolated neutron stars, that besides the large--scale (dipolar) magnetic field, which determines the pulsar spin--down behaviour, small--scale poloidal field components are present, which have surface strengths one to two orders of magnitude larger than the dipolar component. We argue in this paper that the Hall--effect can be an efficient process in producing such small--scale field structures just above the neutron star surface. It is shown that due to a Hall--drift induced instability, poloidal magnetic field structures can be generated from strong subsurface toroidal fields, which are the result of either a dynamo or a thermoelectric instability acting at early times of a neutron star's life. The geometrical structure of these small--scale surface anomalies of the magnetic field resembles that of some types of ``star--spots''. The magnetic field strength and the length--scales are comparable with values that can be derived from various observations.Comment: 4 pages, 2 figures, accepted by Astronomy & Astrophysics Letters; language improved, 2nd para of Sect. 3 change

The effect of the neutron star crust on the evolution of a core magnetic field

We consider the expulsion of the magnetic field from the super-conducting core of a neutron star and its subsequent decay in the crust. Particular attention is paid to a strong feedback of the distortion of magnetic field lines in the crust on the expulsion of the flux from the core. This causes a considerable delay of the core flux expulsion if the initial field strength is larger than 10^{11} G. It is shown that the hypothesis on the magnetic field expulsion induced by the neutron star spin-down is adequate only for a relatively weak initial magnetic field $B \approx 10^{11}$ G. The expulsion time-scale depends not only on the conductivity of the crust, but also on the initial magnetic field strength itself. Our model of the field evolution naturally explains the existence of the residual magnetic field of neutron stars. Its strength is correlated with the impurity concentration in neutron star crusts and anti-correlated with the initial field strengths.Comment: 15 pages, 6 figures, accepted to MNRA

The Occurrence of the Hall--Instability in Crusts of Isolated Neutron Stars

In former papers we showed that during the decay of a neutron star's magnetic field under the influence of the Hall--drift, an unstable rise of small--scale field structures at the expense of the large--scale background field may happen. This linear stability analysis was based on the assumption of a uniform density throughout the neutron star crust, whereas in reality the density and all transport coefficients vary by many orders of magnitude. Here, we extend the investigation of the Hall--drift induced instability by considering realistic profiles of density and chemical composition, as well as background fields with more justified radial profiles. Two neutron star models are considered differing primarily in the assumption on the core matter equation of state. For their cooling history and radial profiles of density and composition we use known results to infer the conductivity profiles. These were fed into linear calculations of a dipolar field decay starting from various initial configurations. At different stages of the decay, snapshots of the magnetic fields at the equator were taken to yield background field profiles for the stability analysis. The main result is that the Hall instability may really occur in neutron star crusts. Characteristic growth times are in the order of \lesssim 10^4 ... 10^6 yrs depending on cooling age and background field strength. The influence of the equation of state and of the initial field configuration is discussed.Comment: 16 pages, 16 figures, PS, submitted to A&A. Justification/discussion slightly changed/extended in replying to the referee. Changes on p. 3, 11, 13, framed by XXX mark

Realistic Exact Solution for the Exterior Field of a Rotating Neutron Star

A new six-parametric, axisymmetric and asymptotically flat exact solution of Einstein-Maxwell field equations having reflection symmetry is presented. It has arbitrary physical parameters of mass, angular momentum, mass--quadrupole moment, current octupole moment, electric charge and magnetic dipole, so it can represent the exterior field of a rotating, deformed, magnetized and charged object; some properties of the closed-form analytic solution such as its multipolar structure, electromagnetic fields and singularities are also presented. In the vacuum case, this analytic solution is matched to some numerical interior solutions representing neutron stars, calculated by Berti & Stergioulas (Mon. Not. Roy. Astron. Soc. 350, 1416 (2004)), imposing that the multipole moments be the same. As an independent test of accuracy of the solution to describe exterior fields of neutron stars, we present an extensive comparison of the radii of innermost stable circular orbits (ISCOs) obtained from Berti & Stergioulas numerical solutions, Kerr solution (Phys. Rev. Lett. 11, 237 (1963)), Hartle & Thorne solution (Ap. J. 153, 807, (1968)), an analytic series expansion derived by Shibata & Sasaki (Phys. Rev. D. 58 104011 (1998)) and, our exact solution. We found that radii of ISCOs from our solution fits better than others with realistic numerical interior solutions.Comment: 13 pages, 13 figures, LaTeX documen

Acousto-optical multiple interference switches

The authors introduce an alternative approach for acousto-optical light control based on the interference of light propagating through several waveguides, each subjected to a periodic refractive index modulation induced by a surface acoustic wave. The feasibility of the concept is demonstrated by the realization of an optical switch for arbitrary time intervals with an on/off contrast ratio of 20