452 research outputs found
Hysteresis loop areas in kinetic Ising models: Effects of the switching mechanism
Experiments on ferromagnetic thin films have measured the dependence of the
hysteresis loop area on the amplitude and frequency of the external field,
=, and approximate agreement with numerical simulations of
Ising models has been reported. Here we present numerical and theoretical
calculations of in the low-frequency regime for two values of ,
which bracket a temperature and system-size dependent crossover field. Our
previous Monte Carlo studies have shown that the hysteretic response of the
kinetic Ising model is qualitatively different for amplitudes above and below
this crossover field. Using droplet theory, we derive analytic expressions for
the low-frequency asymptotic behavior of the hysteresis loop area. In both
field regimes, the loop area exhibits an extremely slow approach to an
asymptotic, logarithmic frequency dependence of the form . Our results are relevant to the interpretation of data
from experiments and simulations, on the basis of which power-law exponents for
the hysteresis-loop area have been reported.Comment: 9 pages including 3 figures. Submitted as a manuscript for the 7th
Joint MMM-Intermag conference. To be published in the Journal of Applied
Physics and the IEEE Transactions on Magnetics. Contains 1 updated figure and
revised tex
Kinetic Ising model in an oscillating field: Finite-size scaling at the dynamic phase transition
We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor,
kinetic Ising ferromagnet in an oscillating field, using Monte Carlo
simulations. The period-averaged magnetization is the order parameter for a
proposed dynamic phase transition (DPT). To quantify the nature of this
transition, we present the first finite-size scaling study of the DPT for this
model. Evidence of a diverging correlation length is given, and we provide
estimates of the transition frequency and the critical indices ,
and .Comment: Accepted by Physical Review Letters. 9 page
Kinetic Ising System in an Oscillating External Field: Stochastic Resonance and Residence-Time Distributions
Experimental, analytical, and numerical results suggest that the mechanism by
which a uniaxial single-domain ferromagnet switches after sudden field reversal
depends on the field magnitude and the system size. Here we report new results
on how these distinct decay mechanisms influence hysteresis in a
two-dimensional nearest-neighbor kinetic Ising model. We present theoretical
predictions supported by numerical simulations for the frequency dependence of
the probability distributions for the hysteresis-loop area and the
period-averaged magnetization, and for the residence-time distributions. The
latter suggest evidence of stochastic resonance for small systems in moderately
weak oscillating fields.Comment: Includes updated results for Fig.2 and minor text revisions to the
abstract and text for clarit
The Sarbanes-Oxley Act and Fiduciary Duties
This article explores the implications of the Sarbanes-Oxley Act of 2002 for fiduciary duty analysis in corporate law. The article examines those provisions of the Act, and recent SEC, NYSE and NASDAQ rules, that most pointedly bear on corporate governance. The article develops in detail exactly how Sarbanes-Oxley and those rules may alter state fiduciary duty law. Sarbanes-Oxley makes unprecedented federal inroads into the area of corporate governance and, although the fact of federal incursion into corporate governance is important in its own right, the more intriguing issue concerns the eventual interplay between federal and state law. Specifically, on various subjects will federal law wholly supplant, or merely supplement, state law? After first describing those recent regulatory initiatives most likely to raise fiduciary duty issues, we describe the fiduciary duties of directors, giving special attention to the emerging obligation of good faith, and highlight the often-overlooked fiduciary status of corporate officers. We note critical differences between breach of fiduciary duty claims against corporate officers and such claims against directors.
We identify those few specific areas where Sarbanes-Oxley pre-empts inconsistent (and weaker) state fiduciary concepts, either in whole or in part. We also identify areas where the mandates of Sarbanes-Oxley, though lacking pre-emptive force, will be highly influential in state fiduciary duty analysis. We conclude, however, that state law will remain preeminent in the fiduciary duty area. This is because state law remains the lingua franca into which the mandates of Sarbanes-Oxley must inevitably be translated for fiduciary duty purposes. We therefore reject the view that Sarbanes-Oxley has somehow federalized the area of corporate fiduciary duty law. To be sure, federal law now plays a more significant role in corporate governance. The overall result of Sarbanes-Oxley in the corporate fiduciary duty area, however, is greater federal influence in a federalism arrangement in which fiduciary duties remain rooted in and dominated by state law
Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field
It has been well established that spatially extended, bistable systems that
are driven by an oscillating field exhibit a nonequilibrium dynamic phase
transition (DPT). The DPT occurs when the field frequency is on the order of
the inverse of an intrinsic lifetime associated with the transitions between
the two stable states in a static field of the same magnitude as the amplitude
of the oscillating field. The DPT is continuous and belongs to the same
universality class as the equilibrium phase transition of the Ising model in
zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et
al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed
that the DPT becomes discontinuous at temperatures below a tricritical point
[M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on
observations in dynamic Monte Carlo simulations of a multipeaked probability
density for the dynamic order parameter and negative values of the fourth-order
cumulant ratio. Both phenomena can be characteristic of discontinuous phase
transitions. Here we use classical nucleation theory for the decay of
metastable phases, together with data from large-scale dynamic Monte Carlo
simulations of a two-dimensional kinetic Ising ferromagnet, to show that these
observations in this case are merely finite-size effects. For sufficiently
small systems and low temperatures, the continuous DPT is replaced, not by a
discontinuous phase transition, but by a crossover to stochastic resonance. In
the infinite-system limit the stochastic-resonance regime vanishes, and the
continuous DPT should persist for all nonzero temperatures
Clinical and radiographic outcomes after posterior vertebral column resection for severe spinal deformity with five-year follow-up
Dynamic Magnetization-Reversal Transition in the Ising Model
We report the results of mean field and the Monte Carlo study of the dynamic
magnetization-reversal transition in the Ising model, brought about by the
application of an external field pulse applied in opposition to the existing
order before the application of the pulse. The transition occurs at a
temperature T below the static critical temperature T_c without any external
field. The transition occurs when the system, perturbed by the external field
pulse competing with the existing order, jumps from one minimum of free energy
to the other after the withdrawal of the pulse. The parameters controlling the
transition are the strength h_p and the duration Delta t of the pulse. In the
mean field case, approximate analytical expression is obtained for the phase
boundary which agrees well with that obtained numerically in the small Delta t
and large T limit. The order parameter of the transition has been identified
and is observed to vary continuously near the transition. The order parameter
exponent beta was estimated both for the mean field (beta =1) and the Monte
Carlo beta = 0.90 \pm 0.02 in two dimension) cases. The transition shows a
"critical slowing-down" type behaviour near the phase boundary with diverging
relaxation time. The divergence was found to be logarithmic in the mean field
case and exponential in the Monte Carlo case. The finite size scaling technique
was employed to estimate the correlation length exponent nu (= 1.5 \pm 0.3 in
two dimension) in the Monte Carlo case.Comment: 13 pages, latex, 8 figure
Nonequilibrium phase transition in the kinetic Ising model: Is transition point the maximum lossy point ?
The nonequilibrium dynamic phase transition, in the kinetic Ising model in
presence of an oscillating magnetic field, has been studied both by Monte Carlo
simulation (in two dimension) and by solving the meanfield dynamical equation
of motion for the average magnetization. The temperature variations of
hysteretic loss (loop area) and the dynamic correlation have been studied near
the transition point. The transition point has been identified as the
minimum-correlation point. The hysteretic loss becomes maximum above the
transition point. An analytical formulation has been developed to analyse the
simulation results. A general relationship among hysteresis loop area, dynamic
order parameter and dynamic correlation has also been developed.Comment: 8 pages Revtex and 4 Postscript figures; To appear in Phys. Rev.
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