Influence of higher-order harmonics on the saturation of the tearing mode

The nonlinear saturation of the tearing mode is revisited in slab geometry by taking into account higher-order harmonics in the outer solution. The general formalism for tackling this problem in the case of a vanishing current gradient at the resonant surface is derived. It is shown that, although the higher-order harmonics lead to corrections in the final saturation equation, they are of higher order in the perturbation parameter, which provides a formal proof that the standard one-harmonic approach is asymptotically correct.Comment: Accepted to Plasma Physics and Controlled Fusio

Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

Gravitational oscillations in multidimensional anisotropic model with cosmological constant and their contributions into the energy of vacuum

Were studied classical oscillations of background metric in the multidimensional anisotropic model of Kazner in the de-Sitter stage. Obtained dependence of fluctuations on dimension of space-time with infinite expansion. Stability of the model could be achieved when number of space-like dimensions equals or more then four. Were calculated contributions to the density of "vacuum energy", that are providing by proper oscillations of background metric and compared with contribution of cosmological arising of particles due to expansion. As it turned out, contribution of gravitational oscillation of metric into density of "vacuum energy" should play significant role in the de-Sitter stage

Characteristics of the wavelength of ripples on icicles

It is known that the wavelength of the ripples on icicles in nature is of centimeter-scale. Such study on morphological instability of ice-water interface during ice growth from flowing supercooled water film with one side being a free surface has recently been made [K. Ueno, Phys. Rev. E 68, 021603 (2003)]. This is a first theoretical study taking into account the influence of the shape of the water-air surface on the growth condition of infinitesimal disturbances of the ice-water interface. A simpler formula to determine the wavelength of the ripples than that in the previous paper is derived. It seems that the wavelength of ripples is insensitive to the water supply rates, diameters of the icicles and surrounding air temperatures. The details of dependence of the wavelengh of ripples on these parameters are investigated.Comment: 15 pages, 6 figure

Cosmic microwave background constraints on cosmological models with large-scale isotropy breaking

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole and/or quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding that the evidence in favor of the model is generally weak. We also compute approximate changes in estimated cosmological parameters in the broken-isotropy models. Only the overall normalization of the power spectrum is modified significantly.Comment: Accepted for publication in Phys. Rev.

A New Phase Time Formula for Opaque Barrier Tunneling

After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase time is in excellent agreement with the numerical simulations and shows that for wave packets whose upper limit of the momentum distribution is very close to the barrier height, the transit time is proportional to the barrier width.Comment: 9 pages, 2 figure

How to construct spin chains with perfect state transfer

It is shown how to systematically construct the $XX$ quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST). Sets of orthogonal polynomials (OPs) are in correspondence with such systems. The key observation is that for any admissible one-excitation energy spectrum, the weight function of the associated OPs is uniquely prescribed. This entails the complete characterization of these PST models with the mirror symmetry property arising as a corollary. A simple and efficient algorithm to obtain the corresponding Hamiltonians is presented. A new model connected to a special case of the symmetric $q$-Racah polynomials is offered. It is also explained how additional models with PST can be derived from a parent system by removing energy levels from the one-excitation spectrum of the latter. This is achieved through Christoffel transformations and is also completely constructive in regards to the Hamiltonians.Comment: 7 page

Prediction and explanation in the multiverse

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical? There is a widespread belief that this question is inherently vague, and that there are various possible choices for the types of reference objects which should be counted in. Here we argue that the ``ideal'' reference class (for the purpose of making predictions) can be defined unambiguously in a rather precise way, as the set of all observers with identical information content. When the observers in a given class perform an experiment, the class branches into subclasses who learn different information from the outcome of that experiment. The probabilities for the different outcomes are defined as the relative numbers of observers in each subclass. For practical purposes, wider reference classes can be used, where we trace over all information which is uncorrelated to the outcome of the experiment, or whose correlation with it is beyond our current understanding. We argue that, once we have gathered all practically available evidence, the optimal strategy for making predictions is to consider ourselves typical in any reference class we belong to, unless we have evidence to the contrary. In the latter case, the class must be correspondingly narrowed.Comment: Minor clarifications adde

Finding Evidence for Massive Neutrinos using 3D Weak Lensing

In this paper we investigate the potential of 3D cosmic shear to constrain massive neutrino parameters. We find that if the total mass is substantial (near the upper limits from LSS, but setting aside the Ly alpha limit for now), then 3D cosmic shear + Planck is very sensitive to neutrino mass and one may expect that a next generation photometric redshift survey could constrain the number of neutrinos N_nu and the sum of their masses m_nu to an accuracy of dN_nu ~ 0.08 and dm_nu ~ 0.03 eV respectively. If in fact the masses are close to zero, then the errors weaken to dN_nu ~ 0.10 and dm_nu~0.07 eV. In either case there is a factor 4 improvement over Planck alone. We use a Bayesian evidence method to predict joint expected evidence for N_nu and m_nu. We find that 3D cosmic shear combined with a Planck prior could provide `substantial' evidence for massive neutrinos and be able to distinguish `decisively' between many competing massive neutrino models. This technique should `decisively' distinguish between models in which there are no massive neutrinos and models in which there are massive neutrinos with |N_nu-3| > 0.35 and m_nu > 0.25 eV. We introduce the notion of marginalised and conditional evidence when considering evidence for individual parameter values within a multi-parameter model.Comment: 9 pages, 2 Figures, 2 Tables, submitted to Physical Review