A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

Atom cooling using the dipole force of a single retroreflected laser beam

We present a mechanism for cooling atoms by a laser beam reflected from a single mirror. The cooling relies on the dipole force and thus in principle applies to arbitrary refractive particles including atoms, molecules, or dielectric spheres. Friction and equilibrium temperatures are derived by an analytic perturbative approach. Finally, semiclassical Monte-Carlo simulations are performed to validate the analytic results.

Class Responsibility Assignment (CRA) for Use Case Specification to Sequence Diagrams (UC2SD)

Identifying responsibility for classes in object oriented software design phase is a crucial task. This paper proposes an approach for producing high quality and robust behavioural diagrams (e.g. Sequence Diagrams) through Class Responsibility Assignment (CRA). GRASP or General Responsibility Assignment Software Pattern (or Principle) was used to direct the CRA process when deriving behavioural diagrams. A set of tools to support CRA was developed to provide designers and developers with a cognitive toolkit that can be used when analysing and designing object-oriented software. The tool developed is called Use Case Specification to Sequence Diagrams (UC2SD). UC2SD uses a new approach for developing Unified Modelling Language (UML) software designs from Natural Language, making use of a meta-domain oriented ontology, well established software design principles and established Natural Language Processing (NLP) tools. UC2SD generates a well-formed UML sequence diagrams as output.