Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)

The critical and asymptotic behaviors of solutions of the sixth Painlev\'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.Comment: 30 pages, 1 figure; Nonlinearity 201

Numerical Differentiation of Approximated Functions with Limited Order-of-Accuracy Deterioration

We consider the problem of numerical differentiation of a function f from approximate or noisy values of f on a discrete set of points; such discrete approximate data may result from a numerical calculation (such as a finite element or finite difference solution of a partial differential equation), from experimental measurements, or, generally, from an estimate of some sort. In some such cases it is useful to guarantee that orders of accuracy are not degraded: assuming the approximating values of the function are known with an accuracy of order O(h^r), where h is the mesh size, an accuracy of O(h^r) is desired in the value of the derivatives of f. Differentiation of interpolating polynomials does not achieve this goal since, as shown in this text, n-fold differentiation of an interpolating polynomial of any degree ≥ (r − 1) obtained from function values containing errors of order O(h^r) generally gives rise to derivative errors of order O(h^(r−n)); other existing differentiation algorithms suffer from similar degradations in the order of accuracy. In this paper we present a new algorithm, the LDC method (low degree Chebyshev), which, using noisy function values of a function f on a (possibly irregular) grid, produces approximate values of derivatives f^((n)) (n = 1, 2 . . .) with limited loss in the order of accuracy. For example, for (possibly nonsmooth) O(h^r) errors in the values of an underlying infinitely differentiable function, the LDC loss in the order of accuracy is “vanishingly small”: derivatives of smooth functions are approximated by the LDC algorithm with an accuracy of order O(h^r) for all r' < r. The algorithm is very fast and simple; a variety of numerical results we present illustrate the theory and demonstrate the efficiency of the proposed methodology

Accurate evolutions of inspiralling and magnetized neutron-stars: equal-mass binaries

By performing new, long and numerically accurate general-relativistic simulations of magnetized, equal-mass neutron-star binaries, we investigate the role that realistic magnetic fields may have in the evolution of these systems. In particular, we study the evolution of the magnetic fields and show that they can influence the survival of the hypermassive-neutron star produced at the merger by accelerating its collapse to a black hole. We also provide evidence that even if purely poloidal initially, the magnetic fields produced in the tori surrounding the black hole have toroidal and poloidal components of equivalent strength. When estimating the possibility that magnetic fields could have an impact on the gravitational-wave signals emitted by these systems either during the inspiral or after the merger we conclude that for realistic magnetic-field strengths B<~1e12 G such effects could be detected, but only marginally, by detectors such as advanced LIGO or advanced Virgo. However, magnetically induced modifications could become detectable in the case of small-mass binaries and with the development of gravitational-wave detectors, such as the Einstein Telescope, with much higher sensitivities at frequencies larger than ~2 kHz.Comment: 18 pages, 10 figures. Added two new figures (figures 1 and 7). Small modifications to the text to match the version published on Phys. Rev.

Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind

The anisotropy of magnetophydrodynamic turbulence is investigated by using solar wind data from the Helios 2 spacecraft. We investigate the behaviour of the complete high-order moment tensors of magnetic field increments and we compare the usual longitudinal structure functions which have both isotropic and anisotropic contributions, to the fully anisotropic contribution. Scaling exponents have been extracted by an interpolation scaling function. Unlike the usual turbulence in fluid flows, small-scale magnetic fluctuations remain anisotropic. We discuss the radial dependence of both anisotropy and intermittency and their relationship.Comment: 7 pages, 2 figures, in press on Europhys. Let

Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields

We consider ferromagnetic long-range Ising models which display phase transitions. They are long-range one-dimensional Ising ferromagnets, in which the interaction is given by $J_{x,y} = J(|x-y|)\equiv \frac{1}{|x-y|^{2-\alpha}}$ with $\alpha \in [0, 1)$, in particular, $J(1)=1$. For this class of models one way in which one can prove the phase transition is via a kind of Peierls contour argument, using the adaptation of the Fr\"ohlich-Spencer contours for $\alpha \neq 0$, proposed by Cassandro, Ferrari, Merola and Presutti. As proved by Fr\"ohlich and Spencer for $\alpha=0$ and conjectured by Cassandro et al for the region they could treat, $\alpha \in (0,\alpha_{+})$ for $\alpha_+=\log(3)/\log(2)-1$, although in the literature dealing with contour methods for these models it is generally assumed that $J(1)\gg1$, we can show that this condition can be removed in the contour analysis. In addition, combining our theorem with a recent result of Littin and Picco we prove the persistence of the contour proof of the phase transition for any $\alpha \in [0,1)$. Moreover, we show that when we add a magnetic field decaying to zero, given by $h_x= h_*\cdot(1+|x|)^{-\gamma}$ and $\gamma >\max\{1-\alpha, 1-\alpha^* \}$ where $\alpha^*\approx 0.2714$, the transition still persists.Comment: 13 page

A systematic comparison of supervised classifiers

Pattern recognition techniques have been employed in a myriad of industrial, medical, commercial and academic applications. To tackle such a diversity of data, many techniques have been devised. However, despite the long tradition of pattern recognition research, there is no technique that yields the best classification in all scenarios. Therefore, the consideration of as many as possible techniques presents itself as an fundamental practice in applications aiming at high accuracy. Typical works comparing methods either emphasize the performance of a given algorithm in validation tests or systematically compare various algorithms, assuming that the practical use of these methods is done by experts. In many occasions, however, researchers have to deal with their practical classification tasks without an in-depth knowledge about the underlying mechanisms behind parameters. Actually, the adequate choice of classifiers and parameters alike in such practical circumstances constitutes a long-standing problem and is the subject of the current paper. We carried out a study on the performance of nine well-known classifiers implemented by the Weka framework and compared the dependence of the accuracy with their configuration parameter configurations. The analysis of performance with default parameters revealed that the k-nearest neighbors method exceeds by a large margin the other methods when high dimensional datasets are considered. When other configuration of parameters were allowed, we found that it is possible to improve the quality of SVM in more than 20% even if parameters are set randomly. Taken together, the investigation conducted in this paper suggests that, apart from the SVM implementation, Weka's default configuration of parameters provides an performance close the one achieved with the optimal configuration

The genus Bolbelasmus in the western and southern regions of the Mediterranean Basin (Coleoptera: Geotrupidae: Bolboceratinae)

The Bolbelasmus Boucomont, 1911 species of the western and southern regions of the Mediterranean Basin (Northern Africa, Iberian Peninsula and France) are revised. The following three new species are described: Bolbelasmus brancoi Hillert & Král sp. nov. and Bolbelasmus howdeni Hillert & Král sp. nov., both from Spain and Gibraltar, and Bolbelasmus nikolajevi Hillert, Arnone, Král & Massa sp. nov. from Egypt, Libya and Tunisia. Bolbelasmus vaulogeri (Abeille de Perrin, 1898) stat. restit. is removed from synonymy with B. bocchus (Erichson, 1841) and reinstated as a separate species. Bolbelasmus romanorum Arnone & Massa, 2010 is considered a junior subjective synonym of B. vaulogeri. Lectotypes for Bolboceras bocchus Erichson, 1841 and Bolboceras vaulogeri Abeille de Perrin, 1898 are designated. Relevant diagnostic characters (head, pronotum, elytron, external male genitalia) are illustrated. Identifi cation keys for both males and females, and an annotated list of the Western Palaearctic representatives of the genus Bolbelasmus are presented. Finally, fi rst records are given for B. gallicus (Mulsant, 1842) from Corsica and the Midi-Pyrénées region of France, B. keithi Miessen & Trichas, 2011 from the Greek island of Rhodes, and B. unicornis (Schrank von Paula, 1789) from the Tuscany province of Italy

On the Thermodynamic Limit in Random Resistors Networks

We study a random resistors network model on a euclidean geometry \bt{Z}^d. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics

Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions

We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere in the fluid context [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the Orszag-Tang solutions with pseudo-spectral computations are performed. We demonstrate for moderate Reynolds numbers that the algorithms using both static and refined grids reproduce the pseudo--spectral solutions quite well. We show that low-order truncation--even with a comparable number of global degrees of freedom--fails to correctly model some strong (sup--norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic

Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M. We also calculate the temperature scaling of the 2-ion anisotropy in L10 FePt, and recover the experimentally observed M^2.1 scaling. The method is newly applied to evaluate the temperature dependent effective anisotropy in the presence of the N'eel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures