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

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

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

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

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

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

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

Evolution of Universe to the present inert phase

We assume that current state of the Universe can be described by the Inert Doublet Model, containing two scalar doublets, one of which is responsible for EWSB and masses of particles and the second one having no couplings to fermions and being responsible for dark matter. We consider possible evolutions of the Universe to this state during cooling down of the Universe after inflation. We found that in the past Universe could pass through phase states having no DM candidate. In the evolution via such states in addition to a possible EWSB phase transition (2-nd order) the Universe sustained one 1-st order phase transition or two phase transitions of the 2-nd order.Comment: 19 pages, 3 figure