Magnetization Switching in Small Ferromagnetic Particles: Nucleation and Coherent Rotation

The mechanisms of thermally activated magnetization switching in small ferromagnetic particles driven by an external magnetic field are investigated. For low uniaxial anisotropy the spins rotate coherently while for sufficiently large uniaxial anisotropy they behave Ising-like, i.e. the switching then is due to nucleation. The crossover from coherent rotation to nucleation is studied for the classical three-dimensional Heisenberg model with uniaxial anisotropy by Monte Carlo simulations. From the temperature dependence of the metastable lifetime the energy barrier of a switching process can be determined. For the case of infinite anisotropy we compare numerical results from simulations of the Ising model with theoretical results for energy barriers for both, single-droplet and multi-droplet nucleation. The simulated barriers are in agreement with the theoretical predictions.Comment: 3 pages, Revtex, 4 Figures include

Exchange Bias driven by Dzyaloshinskii-Moriya interactions

The exchange bias effect in compensated IrMn3/Co(111) system is studied using multiscale modeling from "ab initio" to atomistic calculations. We evaluate numerically the out-of-plane hysteresis loops of the bi-layer for different thickness of the ferromagnetic layer. The results show the existence of a perpendicular exchange bias field and an enhancement of the coercivity of the system. In order to elucidate the possible origin of the exchange bias, we analyze the hysteresis loops of a selected bi-layer by tuning the different contributions to the exchange interactions across the interface. Our results indicate that the exchange bias is primarily induced by the Dzyaloshinskii-Moriya interactions, while the coercivity is increased mainly due to a spin-flop mechanism

Role of temperature-dependent spin model parameters in ultra-fast magnetization dynamics

In the spirit of multi-scale modelling magnetization dynamics at elevated temperature is often simulated in terms of a spin model where the model parameters are derived from first principles. While these parameters are mostly assumed temperature-independent and thermal properties arise from spin fluctuations only, other scenarios are also possible. Choosing bcc Fe as an example, we investigate the influence of different kinds of model assumptions on ultra-fast spin dynamics, where following a femtosecond laser pulse a sample is demagnetized due to a sudden rise of the electron temperature. While different model assumptions do not affect the simulational results qualitatively, their details do depend on the nature of the modelling.Comment: 8 pages, 6 figure

Heat and work distributions for mixed Gauss-Cauchy process

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $\alpha=2$ and $\alpha=1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system

A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete $d \times N$ matrix is finitely rank-$r$ completable if there are at most finitely many rank-$r$ matrices that agree with all its observed entries. Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability. The main contribution of this paper is a deterministic sampling condition for finite completability. We use this to also derive deterministic sampling conditions for unique completability that can be efficiently verified. We also show that under uniform random sampling schemes, these conditions are satisfied with high probability if $O(\max\{r,\log d\})$ entries per column are observed. These findings have several implications on LRMC regarding lower bounds, sample and computational complexity, the role of coherence, adaptive settings and the validation of any completion algorithm. We complement our theoretical results with experiments that support our findings and motivate future analysis of uncharted sampling regimes.Comment: This update corrects an error in version 2 of this paper, where we erroneously assumed that columns with more than r+1 observed entries would yield multiple independent constraint

Heat and mass transfer under an infant radiant warmer – Development of a numerical model

This is the post-print version of the final paper published in Medical Engineering & Physics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.The main objectives of this paper are to present a procedure of how to create and set up a model for the physical processes that take place within an infant radiant warmer and to validate that Computational Fluid Dynamics (CFD) can be used to resolve such problems. In this study, the results are obtained for a simplified model, both in terms of the geometry employed and the prescribed boundary conditions. The results were numerically verified in terms of the convergence history, monitor data and the physical correctness. This study shows that the physical situation is unsteady and the results tend to oscillate, almost periodically, around a mean value. The results presented in the paper are found to be in qualitative agreement with the experimental data. This gives us confidence that the techniques employed in this paper are appropriate and form the starting point for the inclusion of more realistic effects, e.g. real shape of the newborn and radiant lamp, heat generated inside the newborn, moisture transport, etc.European Union Marie Curie Fellowship programm

The Sample Complexity of Search over Multiple Populations

This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one population corresponding to distribution P1 with as few samples as possible. The main contribution is to quantify the number of samples needed to correctly find one such population. We consider two general approaches: non-adaptive sampling methods, which sample each population a predetermined number of times until a population following P1 is found, and adaptive sampling methods, which employ sequential sampling schemes for each population. We first derive a lower bound on the number of samples required by any sampling scheme. We then consider an adaptive procedure consisting of a series of sequential probability ratio tests, and show it comes within a constant factor of the lower bound. We give explicit expressions for this constant when samples of the populations follow Gaussian and Bernoulli distributions. An alternative adaptive scheme is discussed which does not require full knowledge of P1, and comes within a constant factor of the optimal scheme. For comparison, a lower bound on the sampling requirements of any non-adaptive scheme is presented.Comment: To appear, IEEE Transactions on Information Theor