Bulk and surface magnetoinductive breathers in binary metamaterials

We study theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators. The two types of resonators differ in the size of their slits and this leads to different resonant frequencies. In the framework of the rotating-wave approximation (RWA) we construct several types of breather excitations for both the energy-conserved and the dissipative-driven systems by continuation of trivial breather solutions from the anticontinuous limit to finite couplings. Numerically-exact computations that integrate the full model equations confirm the quality of the RWA results. Moreover, it is demonstrated that discrete breathers can spontaneously appear in the dissipative-driven system as a results of a fundamental instability.Comment: 10 pages, 16 figure

Bayesian Optimisation for Safe Navigation under Localisation Uncertainty

In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.Comment: To appear in the proceedings of the 18th International Symposium on Robotics Research (ISRR 2017

Magnetoinductive breathers in magnetic metamaterials

The existence and stability of discrete breathers (DBs) in one-dimensional and two-dimensional magnetic metamaterials (MMs), which consist of periodic arrangem ents (arrays) of split-ring resonators (SRRs), is investigated numerically. We consider different configurations of the SRR arrays, which are related to the relative orientation of the SRRs in the MM, both in one and two spatial dimensions. In the latter case we also consider anisotropic MMs. Using standard numerical methods we construct several types of linearly stable breather excitations both in Hamiltonian and dissipative MMs (dissipative breathers). The study of stability in both cases is performed using standard Floquet analysi s. In both cases we found that the increase of dimensionality from one to two spatial dimensions does not destroy the DBs, which may also exist in the case of moderate anisotropy (in two dimensions). In dissipative MMs, the dynamics is governed by a power balance between the mainly Ohmic dissipation and driving by an alternating magnetic field. In that case it is demonstrated that DB excitation locally alters the magnetic response of MMs from paramagnetic to diamagnetic. Moreover, when the frequency of the applied field approaches the SRR resonance frequency, the magnetic response of the MM in the region of the DB excitation may even become negative (extreme diamagnetic).Comment: 12 pages 15 figure

Extreme events in discrete nonlinear lattices

We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.Comment: 5 pages, 4 figures; reference added, figure 2 correcte

Powerful H2_2 Line-cooling in Stephan's Quintet : I - Mapping the Significant Cooling Pathways in Group-wide Shocks

We present results from the mid-infrared spectral mapping of Stephan's Quintet using the Spitzer Space Telescope. A 1000 km/s collision has produced a group-wide shock and for the first time the large-scale distribution of warm molecular hydrogen emission is revealed, as well as its close association with known shock structures. In the main shock region alone we find 5.0 $\times10^{8}$ M$_{\odot}$ of warm H$_2$ spread over $\sim$ 480 kpc$^2$ and additionally report the discovery of a second major shock-excited H$_2$ feature. This brings the total H$_2$ line luminosity of the group in excess of 10$^42$ erg/s. In the main shock, the H$_2$ line luminosity exceeds, by a factor of three, the X-ray luminosity from the hot shocked gas, confirming that the H$_2$-cooling pathway dominates over the X-ray. [Si II]34.82$\mu$m emission, detected at a luminosity of 1/10th of that of the H$_2$, appears to trace the group-wide shock closely and in addition, we detect weak [FeII]25.99$\mu$m emission from the most X-ray luminous part of the shock. Comparison with shock models reveals that this emission is consistent with regions of fast shocks (100 < $V_{s}$ < 300 km/s) experiencing depletion of iron and silicon onto dust grains. Star formation in the shock (as traced via ionic lines, PAH and dust emission) appears in the intruder galaxy, but most strikingly at either end of the radio shock. The shock ridge itself shows little star formation, consistent with a model in which the tremendous H$_{2}$ power is driven by turbulent energy transfer from motions in a post-shocked layer. The significance of the molecular hydrogen lines over other measured sources of cooling in fast galaxy-scale shocks may have crucial implications for the cooling of gas in the assembly of the first galaxies.Comment: 23 pages, 15 figures, Accepted to Ap

Abrupt changes in alpha decay systematics as a manifestation of collective nuclear modes

An abrupt change in $\alpha$ decay systematics around the N=126 neutron shell closure is discussed. It is explained as a sudden hindrance of the clustering of the nucleons that eventually form the $\alpha$ particle. This is because the clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.Comment: 6 pages, 3 figures, submitted to Phys. Rev. C, a few new references adde

Re-evaluation of cosmic ray cutoff terminology

The study of cosmic ray access to locations inside the geomagnetic field has evolved in a manner that has led to some misunderstanding and misapplication of the terminology originally developed to describe particle access. This paper presents what is believed to be a useful set of definitions for cosmic ray cutoff terminology for use in theoretical and experimental cosmic ray studies

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education

Statistical mechanics of a nonlinear discrete system

Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of $T=\infty$, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.Comment: 4 pages, 3 figure