Non-uniform spin wave softening in 2D magnonic crystals as a tool for opening omnidirectional magnonic band gaps

By means of the plane wave method we study spin wave dynamics in two-dimensional bi-component magnonic crystals based on a squeezed hexagonal lattice and consist of a permalloy thin film with cobalt inclusions. We explore the dependence of a spin wave frequency on the external magnetic field, especially in weak fields where the mode softening takes place. For considered structures, the mode softening proves to be highly non-uniform on both the mode number and the wave vector. We found this effect to be responsible for the omnidirectional band gap opening. Moreover, we show that the enhancement of the demagnetizing field caused by the squeezing of the structure is of crucial importance for the non-uniform mode softening. This allows us to employ this mechanism to design magnonic gaps with different sensitivity for the tiny change of the external field. The effects we have found should be useful in designing and optimization of spin wave filters highly tunable by a small external magnetic field.Comment: Final versio

Using a finite horizon numerical optimisation method for a periodic optimal control problem

Computing a numerical solution to a periodic optimal control problem is difficult. A method of approximating a solution to a given (stochastic) optimal control problem using Markov chains was developed in [3]. This paper describes an attempt at applying this method to a periodic optimal control problem introduced in [2].Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

A report on using parallel MATLAB for solutions to stochastic optimal control problems

Parallel MATLAB is a recent MathWorks product enabling the use of parallel computing methods on multicore personal computers. SOCSol is the generic name of a suite of MATLAB routines that can be used to obtain optimal solutions to continuous-time stochastic optimal control problems. In this report, we compare the performance of a new version of SOCSol utilising parallel MATLAB with that of another version not using parallel computing methods.Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

InfSOCSol2 An updated MATLAB Package for Approximating the Solution to a Continuous-Time Infinite Horizon Stochastic Optimal Control Problem with Control and State Constraints

This paper is a successor of [AK08]. Both papers describe the same suite of MATLAB R° routines devised to provide an approximately optimal solution to an infinite horizon stochastic optimal control problem. The difference is that this paper explains how to allow for state and control constraints. The suite routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [Kra01c] and [Kra01b].Computational economics, Financial engineering, Approximating Markov decision chains

The competition of hydrogen-like and isotropic interactions on polymer collapse

We investigate a lattice model of polymers where the nearest-neighbour monomer-monomer interaction strengths differ according to whether the local configurations have so-called ``hydrogen-like'' formations or not. If the interaction strengths are all the same then the classical $\theta$-point collapse transition occurs on lowering the temperature, and the polymer enters the isotropic liquid-drop phase known as the collapsed globule. On the other hand, strongly favouring the hydrogen-like interactions give rise to an anisotropic folded (solid-like) phase on lowering the temperature. We use Monte Carlo simulations up to a length of 256 to map out the phase diagram in the plane of parameters and determine the order of the associated phase transitions. We discuss the connections to semi-flexible polymers and other polymer models. Importantly, we demonstrate that for a range of energy parameters two phase transitions occur on lowering the temperature, the second being a transition from the globule state to the crystal state. We argue from our data that this globule-to-crystal transition is continuous in two dimensions in accord with field-theory arguments concerning Hamiltonian walks, but is first order in three dimensions

Magnonic Crystal Theory of the Spin-Wave Frequency Gap in Low-Doped La1−xCaxMnO3La_{1-x}Ca_{x}MnO_{3} Manganites

A theory of three-dimensional (3D) hypothetical magnonic crystal (conceived as the magnetic counterpart of the well-known photonic crystal) is developed and applied to explain the existence of a spin-wave frequency gap recently revealed in low-doped manganites $La_{1-x}Ca_{x}MnO_{3}$ by neutron scattering. A successful confrontation with the experimental results allows us to formulate a working hypothesis that certain manganites could be regarded as 3D magnonic crystals existing in nature.Comment: 5 pages, 3 figures, submitted to PR

InfSOCSol2: an updated MATLAB package for approximating the solution to a continuous-time infinite horizon stochastic optimal control problem

This paper describes a suite of MATLAB routines devised to provide an approximately optimal solution to an infinite-horizon stochastic optimal control problem. The suite is an updated version of that described in [Kra01b]. Its routines implement a policy improvement algorithm to optimise a Markov decision chain approximating the original control problem, as described in [Kra01c].Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

Magnonic Band Structure, Complete Bandgap and Collective Spin Wave Excitation in Nanoscale Two--Dimensional Magnonic Crystals

We present the observation of a complete bandgap and collective spin wave excitation in two-dimensional magnonic crystals comprised of arrays of nanoscale antidots and nanodots, respectively. Considering that the frequencies dealt with here fall in the microwave band, these findings can be used for the development of suitable magnonic metamaterials and spin wave based signal processing. We also present the application of a numerical procedure, to compute the dispersion relations of spin waves for any high symmetry direction in the first Brillouin zone. The results obtained from this procedure has been reproduced and verified by the well established plane wave method for an antidot lattice, when magnetization dynamics at antidot boundaries is pinned. The micromagnetic simulation based method can also be used to obtain iso--frequency countours of spin waves. Iso--frequency contours are analougous of the Fermi surfaces and hence, they have the potential to radicalize our understanding of spin wave dynamics. The physical origin of bands, partial and full magnonic bandgaps has been explained by plotting the spatial distribution of spin wave energy spectral density. Although, unfettered by rigid assumptions and approximations, which afflict most analytical methods used in the study of spin wave dynamics, micromagnetic simulations tend to be computationally demanding. Thus, the observation of collective spin wave excitation in the case of nanodot arrays, which can obviate the need to perform simulations may also prove to be valuable

A parallel Matlab package for approximating the solution to a continuous-time stochastic optimal control problem

This article is a modified version of [AK06]. Both articles explain how a suite of MATLAB routines distributed under the generic name SOCSol can be used to obtain optimal solutions to continuous-time stochastic optimal control problems. The difference between the SOCSol suites described by the articles arises from the underlying computing platforms used. This article describes a beta version of SOCSol that utilises the MATLAB Parallel Computing Toolbox, while [AK06] describes a version of SOCSol that does not use parallel computing methods.Computational techniques; Economic software; Computational methods in stochastic optimal control; Computational economics; Approximating Markov decision chains

Substrate Adhesion of a Nongrafted Flexible Polymer in a Cavity

In a contact density chain-growth study we investigate the solubility-temperature pseudo-phase diagram of a lattice polymer in a cavity with an attractive surface. In addition to the main phases of adsorbed and desorbed conformations we find numerous subphases of collapsed and expanded structures.Comment: 20 pages, 6 figure