155,041 research outputs found
Langevin Simulation of Thermally Activated Magnetization Reversal in Nanoscale Pillars
Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model
incorporating thermal fluctuations and dipole-dipole interactions (calculated
by the Fast Multipole Method) are presented for systems composed of nanoscale
iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated
under sinusoidally varying fields are obtained, while the coercive field is
estimated to be 1979 14 Oe using linear field sweeps at T=0 K. Thermal
effects are essential to the relaxation of magnetization trapped in a
metastable orientation, such as happens after a rapid reversal of an external
magnetic field less than the coercive value. The distribution of switching
times is compared to a simple analytic theory that describes reversal with
nucleation at the ends of the nanomagnets. Results are also presented for
arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a
separation of 300 nm, where the field from neighboring pillars is only 1
Oe, the interactions have a significant effect on the switching of the magnets.Comment: 19 pages RevTeX, including 12 figures, clarified discussion of
numerical technique
A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times
International audienc
Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions
Articles in Marketing and choice literatures have demonstrated the need for
incorporating person-level heterogeneity into behavioral models (e.g., logit
models for multiple binary outcomes as studied here). However, the logit
likelihood extended with a population distribution of heterogeneity doesn't
yield closed-form inferences, and therefore numerical integration techniques
are relied upon (e.g., MCMC methods).
We present here an alternative, closed-form Bayesian inferences for the logit
model, which we obtain by approximating the logit likelihood via a polynomial
expansion, and then positing a distribution of heterogeneity from a flexible
family that is now conjugate and integrable. For problems where the response
coefficients are independent, choosing the Gamma distribution leads to rapidly
convergent closed-form expansions; if there are correlations among the
coefficients one can still obtain rapidly convergent closed-form expansions by
positing a distribution of heterogeneity from a Multivariate Gamma
distribution. The solution then comes from the moment generating function of
the Multivariate Gamma distribution or in general from the multivariate
heterogeneity distribution assumed.
Closed-form Bayesian inferences, derivatives (useful for elasticity
calculations), population distribution parameter estimates (useful for
summarization) and starting values (useful for complicated algorithms) are
hence directly available. Two simulation studies demonstrate the efficacy of
our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative
Marketing and Economics vol 4 (2006), no. 2, 173--20
Statistical properties of inelastic Lorentz gas
The inelastic Lorentz gas in cooling states is studied. It is found that the
inelastic Lorentz gas is localized and that the mean square displacement of the
inelastic Lorentz gas obeys a power of a logarithmic function of time. It is
also found that the scaled position distribution of the inelastic Lorentz gas
has an exponential tail, while the distribution is close to the Gaussian near
the peak. Using a random walk model, we derive an analytical expression of the
mean square displacement as a function of time and the restitution coefficient,
which well agrees with the data of our simulation. The exponential tail of the
scaled position distribution function is also obtained by the method of
steepest descent.Comment: 31pages,9figures, to appear Journal of Physical Society of Japan
Vol.70 No.7 (2001
Statistical properties of inelastic Lorentz gas
The inelastic Lorentz gas in cooling states is studied. It is found that the
inelastic Lorentz gas is localized and that the mean square displacement of the
inelastic Lorentz gas obeys a power of a logarithmic function of time. It is
also found that the scaled position distribution of the inelastic Lorentz gas
has an exponential tail, while the distribution is close to the Gaussian near
the peak. Using a random walk model, we derive an analytical expression of the
mean square displacement as a function of time and the restitution coefficient,
which well agrees with the data of our simulation. The exponential tail of the
scaled position distribution function is also obtained by the method of
steepest descent.Comment: 31pages,9figures, to appear Journal of Physical Society of Japan
Vol.70 No.7 (2001
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