Synchronization of coupled nonidentical dynamical systems

We analyze the stability of synchronized state for coupled nearly identical dynamical systems on networks by deriving an approximate Master Stability Function (MSF). Using this MSF we treat the problem of designing a network having the best synchronizability properties. We find that the edges which connect nodes with a larger relative parameter mismatch are preferred and the nodes having values at one extreme of the parameter mismatch are preferred as hubs.Comment: 11 pages, 4 figure

Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Quantifying the effects of spatial resolution and noise on galaxy metallicity gradients

Metallicity gradients are important diagnostics of galaxy evolution, because they record the history of events such as mergers, gas inflow and star-formation. However, the accuracy with which gradients can be measured is limited by spatial resolution and noise, and hence measurements need to be corrected for such effects. We use high resolution (~20 pc) simulation of a face-on Milky Way mass galaxy, coupled with photoionisation models, to produce a suite of synthetic high resolution integral field spectroscopy (IFS) datacubes. We then degrade the datacubes, with a range of realistic models for spatial resolution (2 to 16 beams per galaxy scale length) and noise, to investigate and quantify how well the input metallicity gradient can be recovered as a function of resolution and signal-to-noise ratio (SNR) with the intention to compare with modern IFS surveys like MaNGA and SAMI. Given appropriate propagation of uncertainties and pruning of low SNR pixels, we show that a resolution of 3-4 telescope beams per galaxy scale length is sufficient to recover the gradient to ~10-20% uncertainty. The uncertainty escalates to ~60% for lower resolution. Inclusion of the low SNR pixels causes the uncertainty in the inferred gradient to deteriorate. Our results can potentially inform future IFS surveys regarding the resolution and SNR required to achieve a desired accuracy in metallicity gradient measurements.Comment: 21 pages, 11 figures, 20 pages Supplementary Online Material provided with 10 additional figures, accepted for publication in MNRA

Sensitivity of the Cherenkov Telescope Array to spectral signatures of hadronic PeVatrons with application to Galactic Supernova Remnants

The local Cosmic Ray (CR) energy spectrum exhibits a spectral softening at energies around 3 PeV. Sources which are capable of accelerating hadrons to such energies are called hadronic PeVatrons. However, hadronic PeVatrons have not yet been firmly identified within the Galaxy. Several source classes, including Galactic Supernova Remnants (SNRs), have been proposed as PeVatron candidates. The potential to search for hadronic PeVatrons with the Cherenkov Telescope Array (CTA) is assessed. The focus is on the usage of very high energy γ-ray spectral signatures for the identification of PeVatrons. Assuming that SNRs can accelerate CRs up to knee energies, the number of Galactic SNRs which can be identified as PeVatrons with CTA is estimated within a model for the evolution of SNRs. Additionally, the potential of a follow-up observation strategy under moonlight conditions for PeVatron searches is investigated. Statistical methods for the identification of PeVatrons are introduced, and realistic Monte-Carlo simulations of the response of the CTA observatory to the emission spectra from hadronic PeVatrons are performed. Based on simulations of a simplified model for the evolution for SNRs, the detection of a γ-ray signal from in average 9 Galactic PeVatron SNRs is expected to result from the scan of the Galactic plane with CTA after 10 h of exposure. CTA is also shown to have excellent potential to confirm these sources as PeVatrons in deep observations with (100) hours of exposure per source

Specific Resistance of Pd/Ir Interfaces

From measurements of the current-perpendicular-to-plane (CPP) total specific resistance (AR = area times resistance) of sputtered Pd/Ir multilayers, we derive the interface specific resistance, 2AR(Pd/Ir) = 1.02 +/- 0.06 fOhmm^2, for this metal pair with closely similar lattice parameters. Assuming a single fcc crystal structure with the average lattice parameter, no-free-parameter calculations, including only spd orbitals, give for perfect interfaces, 2AR(Pd/Ir)(Perf) = 1.21 +/-0.1 fOhmm^2, and for interfaces composed of two monolayers of a random 50%-50% alloy, 2AR(Pd/Ir)(50/50) = 1.22 +/- 0.1 fOhmm^2. Within mutual uncertainties, these values fall just outside the range of the experimental value. Updating to add f-orbitals gives 2AR(Pd/Ir)(Perf) = 1.10 +/- 0.1 fOhmm^2 and 2AR(Pd/Ir)(50-50) = 1.13 +/- 0.1 fOhmm^2, values now compatible with the experimental one. We also update, with f-orbitals, calculations for other pairsComment: 3 pages, 1 figure, in press in Applied Physics Letter

Length and time scale divergences at the magnetization-reversal transition in the Ising model

The divergences of both the length and time scales, at the magnetization- reversal transition in Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument which explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and defined a pseudo-correlation length which has been observed to grow at the phase boundary of the transition.Comment: 9 pages Latex, 3 postscript figure