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

Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.Comment: 15 pages, 4 figures, Phys. Rev. B., in pres

Alfalfa: Crop for the Future

Alfalfa use by dairy cattle has decreased in recent years because of excessive nonprotein nitrogen and low fiber digestibility. Ideal attributes for plant modification of alfalfa may include those that increase milk potential per acre and/or per ton, enhance digestible NDF, improve protein content and amino acid balance, improve agronomic traits for insect protection (safer forage supply), herbicide tolerance, virus resistance, drought tolerance, cold tolerance, improved mineral availability and enhanced yield. Progress in attaining these attributes will accelerate with the use of biotechnology. Livestock and hay enterprises will benefit from alfalfa that is less prone to contain mycotoxins or toxic weeds, or to induce bloat; have improved nutrient utilization for milk and meat production; and produce less animal wastes resulting in improved efficiency, profitability, and a better environment. Value-added traits of alfalfa are needed to provide farmers new high value profitable products. Processing alfalfa to obtain value added products includes three different fractionation methods: 1) wet fractionation; separation into juice fraction and a fiber fraction, 2) dry fractionation; separation into leaves and stems, and 3) fractionation by passage of the whole herbage through the digestive systems of ruminant animals, leaving a high fiber residue. Phytase from transgenic alfalfa has been tested in poultry and swine rations. Alfalfa hay can be fractionated to yield stems and leaf meal. Alfalfa leaf meal has been shown to be acceptable supplement to replace a portion of alfalfa hay and soybean meal in diets of lactating dairy cattle, replace protein supplement in beef cow diets, finishing steer diets and diets of growing turkeys. The fiber portion of alfalfa can produce lactic acid, ethanol or a bioadhesives for use in plywood

Vortices in the presence of a nonmagnetic atom impurity in 2D XY ferromagnets

Using a model of nonmagnetic impurity potential, we have examined the behavior of planar vortex solutions in the classical two-dimensional XY ferromagnets in the presence of a spin vacancy localized out of the vortex core. Our results show that a spinless atom impurity gives rise to an effective potential that repels the vortex structure.Comment: 6 pages, 2 figures, RevTex

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

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

Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR