Vortex motion in a finite-size easy-plane ferromagnet and application to a nanodot

We study the motion of a non-planar vortex in a circular easy-plane ferromagnet, which imitates a magnetic nanodot. Analysis was done using numerical simulations and a new collective variable theory which includes the coupling of Goldstone-like mode with the vortex center. Without magnetic field the vortex follows a spiral orbit which we calculate. When a rotating in-plane magnetic field is included, the vortex tends to a stable limit cycle which exists in a significant range of field amplitude B and frequency $\omega$ for a given system size L. For a fixed $\omega$, the radius R of the orbital motion is proportional to L while the orbital frequency $\Omega$ varies as 1/L and is significantly smaller than $\omega$. Since the limit cycle is caused by the interplay between the magnetization and the vortex motion, the internal mode is essential in the collective variable theory which then gives the correct estimate and dependency for the orbit radius $R\sim B L/\omega$. Using this simple theory we indicate how an ac magnetic field can be used to control vortices observed in real magnetic nanodots.Comment: 15 pages (RevTeX), 14 figures (eps

Fine and ultrafine particle number and size measurements from industrial combustion processes : primary emissions field data

This study is to our knowledge the first to present the results of on-line measurements of residual nanoparticle numbers downstream of the flue gas treatment systems of a wide variety of medium- and large-scale industrial installations. Where available, a semi-quantitative elemental composition of the sampled particles is carried out using a Scanning Electron Microscope coupled with an Energy Dispersive Spectrometer (SEM-EDS). The semi-quantitative elemental composition as a function of the particle size is presented. EU's Best Available Technology documents (BAT) show removal efficiencies of Electrostatic Precipitator (ESP) and bag filter dedusting systems exceeding 99% when expressed in terms of weight. Their efficiency decreases slightly for particles smaller than 1 mu m but when expressed in terms of weight, still exceeds 99% for bag filters and 96% for ESP. This study reveals that in terms of particle numbers, residual nanoparticles (NP) leaving the dedusting systems dominate by several orders of magnitude. In terms of weight, all installations respect their emission limit values and the contribution of NP to weight concentrations is negligible, despite their dominance in terms of numbers. Current World Health Organisation regulations are expressed in terms of PM2.5 wt concentrations and therefore do not reflect the presence or absence of a high number of NP. This study suggests that research is needed on possible additional guidelines related to NP given their possible toxicity and high potential to easily enter the blood stream when inhaled by humans

The decimation process in random k-SAT

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying assignments of F. This algorithm can be viewed as an attempt at implementing a certain thought experiment that we call the Decimation Process. In this paper we identify a variety of phase transitions in the decimation process and link these phase transitions to the performance of the algorithm

Switching between different vortex states in 2-dimensional easy-plane magnets due to an ac magnetic field

Using a discrete model of 2-dimensional easy-plane classical ferromagnets, we propose that a rotating magnetic field in the easy plane can switch a vortex from one polarization to the opposite one if the amplitude exceeds a threshold value, but the backward process does not occur. Such switches are indeed observed in computer simulations.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Nuclear spin dynamics influenced and detected by electron spin polarization in CdTe/CdMgTe quantum wells

Nuclear spin coherence and relaxation dynamics of all constituent isotopes of an n-doped CdTe/(Cd,Mg)Te quantum well structure are studied employing optically detected nuclear magnetic resonance. Using time-resolved pump-probe Faraday ellipticity, we generate and detect the coherent spin dynamics of the resident electrons. The photogenerated electron spin polarization is transferred into the nuclear spin system, which becomes polarized and acts back on the electron spins as the Overhauser field. Under the influence of resonant radio frequency pulses, we trace the coherent spin dynamics of the nuclear isotopes $^{111}$Cd, $^{113}$Cd, and $^{125}$Te. We measure nuclear Rabi oscillations, the inhomogeneous dephasing time $T_2^*$, the spin coherence time $T_2$, and the longitudinal relaxation time $T_1$. Furthermore, we investigate the influence of the laser excitation and the corresponding electron spin polarization on the nuclear spin relaxation time and find a weak extension of this time induced by interaction with the electron spins.Comment: 5 pages, 2 figure

On the ground states of the Bernasconi model

The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they exist, they are ground states. Using results from the mathematical theory of cyclic difference sets, we specify all values of N for which perfect sequences do exist and how to construct them. For other values of N, we investigate almost perfect sequences, i.e. sequences with two-valued off-peak correlations of minimum amount. Numerical and analytical results support the conjecture that almost perfect sequences do exist for all values of N, but that they are not always ground states. We present a construction for low-energy configurations that works if N is the product of two odd primes.Comment: 12 pages, LaTeX2e; extended content, added references; submitted to J.Phys.

Number partitioning as random energy model

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local random energy'' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.Comment: 8+2 pages, 9 figures, PDF onl

Optimal combinations of imperfect objects

We address the question of how to make best use of imperfect objects, such as defective analog and digital components. We show that perfect, or near-perfect, devices can be constructed by taking combinations of such defects. Any remaining objects can be recycled efficiently. In addition to its practical applications, our `defect combination problem' provides a novel generalization of classical optimization problems.Comment: 4 pages, 3 figures, minor change

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given