Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

Statistical mechanics of the Cluster-Ising model

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Neverthless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.Comment: To be published in Physical Review

Interplay between pairing and exchange in small metallic dots

We study the effects of the mesoscopic fluctuations on the competition between exchange and pairing interactions in ultrasmall metallic dots when the mean level spacing is comparable or larger than the BCS pairing energy. Due to mesoscopic fluctuations, the probability to have a non-zero spin ground state may be non-vanishing and shows universal features related to both level statistics and interaction. Sample to sample fluctuations of the renormalized pairing are enlightened.Comment: 10 pages, 5 figure

On the Rapid Collapse and Evolution of Molecular Clouds

Stars generally form faster than the ambipolar diffusion time, suggesting that several processes short circuit the delay and promote a rapid collapse. These processes are considered here, including turbulence compression in the outer parts of giant molecular cloud (GMC) cores and GMC envelopes, GMC core formation in an initially supercritical state, and compression-induced triggering in dispersing GMC envelopes. The classical issues related to star formation timescales are addressed: high molecular fractions, low efficiencies, long consumption times for CO and HCN, rapid GMC core disruption and the lack of a stable core, long absolute but short relative timescales with accelerated star formation, and the slow motions of protostars. We consider stimuli to collapse from changes in the density dependence of the ionization fraction, the cosmic ray ionization rate, and various dust properties at densities above ~10^5 cm^{-3}. We favor the standard model of subcritical GMC envelops and suggest they would be long lived if not for disruption by rapid star formation in GMC cores. The lifecycle of GMCs is illustrated by a spiral arm section in the Hubble Heritage image of M51, showing GMC formation, star formation, GMC disruption with lingering triggered star formation, and envelope dispersal. There is no delay between spiral arm dustlanes and star formation; the classical notion results from heavy extinction in the dust lane and triggered star formation during cloud dispersal. Differences in the IMF for the different modes of star formation are considered.Comment: 46 pages, 5 figures, scheduled for ApJ 668, October 20, 200

A Spitzer Survey of Novae in M31

We report the results of the first infrared survey of novae in the nearby spiral galaxy, M31. Both photometric and spectroscopic observations of a sample of 10 novae (M31N 2006-09c, 2006-10a, 2006-10b, 2006-11a, 2007-07f, 2007-08a, 2007-08d, 2007-10a, 2007-11d, and 2007-11e) were obtained with the Spitzer Space Telescope. Eight of the novae were observed with the IRAC (all but M31N 2007-11d and 2007-11e) and eight with the IRS (all but 2007-07f and 2007-08a), resulting in six in common between the two instruments. The observations, which were obtained between ~3 and ~7 months after discovery, revealed evidence for dust formation in two of the novae: M31N 2006-10a and (possibly) 2007-07f, and [Ne II] 12.8 micron line emission in a third (2007-11e). The Spitzer observations were supplemented with ground-based optical photometric and spectroscopic data that were used to determine the speed classes and spectroscopic types of the novae in our survey. After including data for dust-forming Galactic novae, we show that dust formation timescales are correlated with nova speed class in that dust typically forms earlier in faster novae. We conclude that our failure to detect the signature of dust formation in most of our M31 sample is likely a result of the relatively long delay between nova eruption and our Spitzer observations. Indeed, the two novae for which we found evidence of dust formation were the two "slowest" novae in our sample. Finally, as expected, we found that the majority of the novae in our sample belong to the Fe II spectroscopic class, with only one clear example of the He/N class (M31N 2006-10b). Typical of an He/N system, M31N 2006-10b was the fastest nova in our sample, not detected with the IRS, and just barely detected in three of the IRAC bands when it was observed ~4 months after eruption.Comment: 37 pages, 12 figures, accepted for publication in the Astrophysical Journa

Electrically Controlled Nano and Micro Actuation in Memristive Switching Devices with On-Chip Gas Encapsulation

Nanoactuators are a key component for developing nanomachinery. Here, an electrically driven device yielding actuation stresses exceeding 1 MPa withintegrated optical readout is demonstrated. 10 nm thick Al2O3 electrolyte films are sandwiched between graphene and Au electrodes. These allow reversible room-temperature solid-state redox reactions, producing Al metal and O2 gas in a memristive-type switching device. The resulting high-pressure oxygen micro-fuel reservoirs are encapsulated under the graphene, swelling to heights of up to 1 µm, which can be dynamically tracked by plasmonic rulers. Unlike standard memristors where the memristive redox reaction occurs in single or few conductive filaments, the mechanical deformation forces the creation of new filaments over the whole area of the inflated film. The resulting on–off resistance ratios reach 10^8 in some cycles. The synchronization of nanoactuation and memristive switching in these devices is compatible with large-scale fabrication and has potential for precise and electrically monitored actuation technology

Re-entrant spin susceptibility of a superconducting grain

We study the spin susceptibility chi of a small, isolated superconducting grain. Due to the interplay between parity effects and pairing correlations, the dependence of chi on temperature T is qualitatively different from the standard BCS result valid in the bulk limit. If the number of electrons on the grain is odd, chi shows a re-entrant behavior as a function of temperature. This behavior persists even in the case of ultrasmall grains where the mean level spacing is much larger than the BCS gap. If the number of electrons is even, chi(T) is exponentially small at low temperatures.Comment: 9 pages, 3 figures. To be published in PR

p-wave triggered superconductivity in single-layer graphene on an electron-doped oxide superconductor

Electron pairing in the vast majority of superconductors follows the Bardeen-Cooper-Schrieffer theory of superconductivity, which describes the condensation of electrons into pairs with antiparallel spins in a singlet state with an s-wave symmetry. Unconventional superconductivity was predicted in single-layer graphene (SLG), with the electrons pairing with a $\textit{p}$-wave or chiral d-wave symmetry, depending on the position of the Fermi energy with respect to the Dirac point. By placing SLG on an electron-doped (non-chiral) d-wave superconductor and performing local scanning tunnelling microscopy and spectroscopy, here we show evidence for a $\textit{p}$-wave triggered superconducting density of states in SLG. The realization of unconventional superconductivity in SLG offers an exciting new route for the development of p-wave superconductivity using two-dimensional materials with transition temperatures above 4.2 K.The work was funded by the following agencies: Royal Society (‘Superconducting Spintronics’), Leverhulme Trust (IN-2013-033), Schiff Foundation, the EPSRC (EP/N017242/1, EP/G037221/1, EP/K01711X/1, EP/K017144/1, EP/N010345/1, EP/M507799/1, EP/L016087/1), ERC Grant Hetero2D, EU Graphene Flagship, COST Action MP-1201, MSCA-IFEF-ST No. 656485-Spin3, Outstanding Academic Fellows programme at NTNU, Research Council of Norway (205591, 216700 and 24080)

p-wave triggered superconductivity in single-layer graphene on an electron-doped oxide superconductor

This is the final version. Available on open access from Nature Research via the DOI in this record.Data availability: The data set generated and analysed during this study are available for access at http://dx.doi.org/10.17863/CAM.6228Electron pairing in the vast majority of superconductors follows the Bardeen–Cooper–Schrieffer theory of superconductivity, which describes the condensation of electrons into pairs with antiparallel spins in a singlet state with an s-wave symmetry. Unconventional superconductivity was predicted in single-layer graphene (SLG), with the electrons pairing with a p-wave or chiral d-wave symmetry, depending on the position of the Fermi energy with respect to the Dirac point. By placing SLG on an electron-doped (non-chiral) d-wave superconductor and performing local scanning tunnelling microscopy and spectroscopy, here we show evidence for a p-wave triggered superconducting density of states in SLG. The realization of unconventional superconductivity in SLG offers an exciting new route for the development of p-wave superconductivity using two-dimensional materials with transition temperatures above 4.2 K.Royal SocietyLeverhulme TrustSchiff FoundationEngineering and Physical Sciences Research Council (EPSRC

p-wave triggered superconductivity in single-layer graphene on an electron-doped oxide superconductor

Electron pairing in the vast majority of superconductors follows the Bardeen–Cooper–Schrieffer theory of superconductivity, which describes the condensation of electrons into pairs with antiparallel spins in a singlet state with an s-wave symmetry. Unconventional superconductivity was predicted in single-layer graphene (SLG), with the electrons pairing with a p-wave or chiral d-wave symmetry, depending on the position of the Fermi energy with respect to the Dirac point. By placing SLG on an electron-doped (non-chiral) d-wave superconductor and performing local scanning tunnelling microscopy and spectroscopy, here we show evidence for a p-wave triggered superconducting density of states in SLG. The realization of unconventional superconductivity in SLG offers an exciting new route for the development of p-wave superconductivity using two-dimensional materials with transition temperatures above 4.2 K