750 research outputs found
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
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
Stochastic Hysteresis and Resonance in a Kinetic Ising System
We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor,
kinetic Ising ferromagnet in an oscillating field, using Monte Carlo
simulations and analytical theory. Attention is focused on small systems and
weak field amplitudes at a temperature below . For these restricted
parameters, the magnetization switches through random nucleation of a single
droplet of spins aligned with the applied field. We analyze the stochastic
hysteresis observed in this parameter regime, using time-dependent nucleation
theory and the theory of variable-rate Markov processes. The theory enables us
to accurately predict the results of extensive Monte Carlo simulations, without
the use of any adjustable parameters. The stochastic response is qualitatively
different from what is observed, either in mean-field models or in simulations
of larger spatially extended systems. We consider the frequency dependence of
the probability density for the hysteresis-loop area and show that its average
slowly crosses over to a logarithmic decay with frequency and amplitude for
asymptotically low frequencies. Both the average loop area and the
residence-time distributions for the magnetization show evidence of stochastic
resonance. We also demonstrate a connection between the residence-time
distributions and the power spectral densities of the magnetization time
series. In addition to their significance for the interpretation of recent
experiments in condensed-matter physics, including studies of switching in
ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results
are relevant to the general theory of periodically driven arrays of coupled,
bistable systems with stochastic noise.Comment: 35 pages. Submitted to Phys. Rev. E Minor revisions to the text and
updated reference
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