Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators

We study the existence and stability of phaselocked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical Hopf bifurcation. The coupling is limited to nearest neighbors and is linear. We analyze a model set of discrete dynamical equations using the method of plane waves. The resultant dispersion relation, which is valid for any arbitrary number of oscillators, displays important differences from similar relations obtained from continuum models. We discuss the general characteristics of the equilibrium states including their dependencies on various system parameters. We next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay. Time delay is found to expand the range of possible phaselocked patterns and to contribute favorably toward their stability. The amplitude death state is studied in the parameter space of time delay and coupling strength. It is shown that death island regions can exist for any number of oscillators N in the presence of finite time delay. A particularly interesting result is that the size of an island is independent of N when N is even but is a decreasing function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from TeX); minor additions; typos correcte

Specific heat of Ca0.32_{0.32}Na0.68_{0.68}Fe2_2As2_2 single crystals: unconventional s±_\pm multi-band superconductivity with intermediate repulsive interband coupling and sizable attractive intraband couplings

We report a low-temperature specific heat study of high-quality single crystals of the heavily hole doped superconductor Ca$_{0.32}$Na$_{0.68}$Fe$_2$As$_2$. This compound exhibits bulk superconductivity with a transition temperature $T_c \approx 34$\,K, which is evident from the magnetization, transport, and specific heat measurements. The zero field data manifests a significant electronic specific heat in the normal state with a Sommerfeld coefficient $\gamma \approx 53$ mJ/mol K$^{2}$. Using a multi-band Eliashberg analysis, we demonstrate that the dependence of the zero field specific heat in the superconducting state is well described by a three-band model with an unconventional s$_\pm$ pairing symmetry and gap magnitudes $\Delta_i$ of approximately 2.35, 7.48, and -7.50 meV. Our analysis indicates a non-negligible attractive intraband coupling,which contributes significantly to the relatively high value of $T_c$. The Fermi surface averaged repulsive and attractive coupling strengths are of comparable size and outside the strong coupling limit frequently adopted for describing high-$T_c$ iron pnictide superconductors. We further infer a total mass renormalization of the order of five, including the effects of correlations and electron-boson interactions.Comment: 8 Figures, Submitted to PR

Model of Low-pass Filtering of Local Field Potentials in Brain Tissue

Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances ($\approx$10~$\mu m$) from the recording electrode. Understanding this filtering is crucial to relate LFP signals with neuronal activity, but not much is known about the exact mechanisms underlying this low-pass filtering. In this paper, we investigate a possible biophysical mechanism for the low-pass filtering properties of LFPs. We investigate the propagation of electric fields and its frequency dependence close to the current source, i.e. at length scales in the order of average interneuronal distance. We take into account the presence of a high density of cellular membranes around current sources, such as glial cells. By considering them as passive cells, we show that under the influence of the electric source field, they respond by polarisation, i.e., creation of an induced field. Because of the finite velocity of ionic charge movement, this polarization will not be instantaneous. Consequently, the induced electric field will be frequency-dependent, and much reduced for high frequencies. Our model establishes that with respect to frequency attenuation properties, this situation is analogous to an equivalent RC-circuit, or better a system of coupled RC-circuits. We present a number of numerical simulations of induced electric field for biologically realistic values of parameters, and show this frequency filtering effect as well as the attenuation of extracellular potentials with distance. We suggest that induced electric fields in passive cells surrounding neurons is the physical origin of frequency filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig

Effect of short range order on electronic and magnetic properties of disordered Co based alloys

We here study electronic structure and magnetic properties of disordered CoPd and CoPt alloys using Augmented Space Recursion technique coupled with the tight-binding linearized muffin tin orbital (TB-LMTO) method. Effect of short range ordering present in disordered phase of alloys on electronic and magnetic properties has been discussed. We present results for magnetic moments, Curie temperatures and electronic band energies with varying degrees of short range order for different concentrations of Co and try to understand and compare the magnetic properties and ordering phenomena in these systems.Comment: 15 pages,17 postscript figures,uses own style file

Crystal Structure of the Sodium Cobaltate Deuterate Superconductor NaxCoO2o4xD2O (x=1/3)

Neutron and x-ray powder diffraction have been used to investigate the crystal structures of a sample of the newly-discovered superconducting sodium cobaltate deuterate compound with composition Na0.31(3)CoO2o1.25(2)D2O and its anhydrous parent compound Na0.61(1)CoO2. The deuterate superconducting compound is formed by coordinating four D2O molecules (two above and two below) to each Na ion in a way that gives Na-O distances nearly equal to those in the parent compound. One deuteron of the D2O molecule is hydrogen bonded to an oxygen atom in the CoO2 plane and the oxygen atom and the second deuteron of each D2O molecule lie approximately in a plane between the Na layer and the CoO2 layers. This coordination of Na by four D2O molecules leads to ordering of the Na ions and D2O molecules. The sample studied here, which has Tc=4.5 K, has a refined composition of Na0.31(3)CoO2o1.25(2)D2O, in agreement with the expected 1:4 ratio of Na to D2O. These results show that the optimal superconducting composition should be viewed as a specific hydrated compound, not a solid solution of Na and D2O (H2O) in NaxCoO2oyD2O. Studies of physical properties vs. Na or D2O composition should be viewed with caution until it is verified that the compound remains in the same phase over the composition range of the study.Comment: 22 pages, 8 figure

Thermodynamic Geometry Of Charged Rotating BTZ Black Holes

We study the thermodynamics and the thermodynamic geometries of charged rotating BTZ (CR-BTZ) black holes in (2+1)-gravity. We investigate the thermodynamics of these systems within the context of the Weinhold and Ruppeiner thermodynamic geometries and the recently developed formalism of geometrothermodynamics (GTD). Considering the behavior of the heat capacity and the Hawking temperature, we show that Weinhold and Ruppeiner geometries cannot describe completely the thermodynamics of these black holes and of their limiting case of vanishing electric charge. In contrast, the Legendre invariance imposed on the metric in GTD allows one to describe the CR-BTZ black holes and their limiting cases in a consistent and invariant manner

The Complex Wind Torus and Jets of PSR B1706-44

We report on Chandra ACIS imaging of the pulsar wind nebula (PWN) of the young Vela-like PSR B1706-44, which shows the now common pattern of an equatorial wind and polar jets. The structure is particularly rich, showing a relativistically boosted termination shock, jets with strong confinement, a surrounding radio/X-ray PWN and evidence for a quasi-static `bubble nebula'. The structures trace the pulsar spin geometry and illuminate its possible relation to SNR G343.1-2.3. We also obtain improved estimates of the pulsar flux and nebular spectrum, constraining the system age and energetics.Comment: To appear in the Astrophysical Journal. 15pp, 4 figures in 7 file