Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath

We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this {\em non-Gibbsian} state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather

Collisional transport across the magnetic field in drift-fluid models

Drift ordered fluid models are widely applied in studies of low-frequency turbulence in the edge and scrape-off layer regions of magnetically confined plasmas. Here, we show how collisional transport across the magnetic field is self-consistently incorporated into drift-fluid models without altering the drift-fluid energy integral. We demonstrate that the inclusion of collisional transport in drift-fluid models gives rise to diffusion of particle density, momentum and pressures in drift-fluid turbulence models and thereby obviate the customary use of artificial diffusion in turbulence simulations. We further derive a computationally efficient, two-dimensional model which can be time integrated for several turbulence de-correlation times using only limited computational resources. The model describes interchange turbulence in a two-dimensional plane perpendicular to the magnetic field located at the outboard midplane of a tokamak. The model domain has two regions modeling open and closed field lines. The model employs a computational expedient model for collisional transport. Numerical simulations show good agreement between the full and the simplified model for collisional transport

Khovanov homology is an unknot-detector

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.Comment: 124 pages, 13 figure

SLE-type growth processes and the Yang-Lee singularity

The recently introduced SLE growth processes are based on conformal maps from an open and simply-connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply-connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in the hierarchy. At grade two we find a direct correspondence to conformal field theory through the explicit construction of a level-four null vector in a highest-weight module of the Virasoro algebra. This conformal field theory has central charge c=-22/5 and is associated to the Yang-Lee singularity. Our construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version to be publishe

Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that the effective Peierls-Nabarro barrier potential is nonzero thereby indicating that this discrete model is quite likely nonintegrable

MRI and clinical resolution of a suspected intracranial toxoplasma granuloma with medical treatment in a domestic short hair cat

A two-year-old cat was presented with a left paradoxical vestibular syndrome. MRI of the brain revealed an extra-axial homogenously contrast enhancing mass in the region of the left caudal cerebellar peduncle. Toxoplasma serology was consistent with active infection and the lesion was suspected to be a toxoplasma granuloma. Following eight weeks of tapering oral prednisolone and 11 weeks of oral clindamycin treatment, repeat MRI revealed resolution of the lesion. Eighteen months after initial diagnosis, the cat remained neurologically normal. Differential diagnoses for a solitary, extra-axial, contrast enhancing mass lesion in the feline brain should include toxoplasma granuloma, which can undergo MRI and clinical resolution with medical treatment

Classroom dialogue and digital technologies: A scoping review

AbstractThis article presents a systematic scoping review of the literature focusing on interactions between classroom dialogue and digital technology. The first review of its type in this area, it both maps extant research and, through a process of thematic synthesis, investigates the role of technology in supporting classroom dialogue. In total, 72 studies (published 2000–2016) are analysed to establish the characteristics of existing evidence and to identify themes. The central intention is to enable researchers and others to access an extensive base of studies, thematically analysed, when developing insights and interpretations in a rapidly changing field of study. The discussion illustrates the interconnectedness of key themes, placing the studies in a methodological and theoretical context and examining challenges for the future.</jats:p

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