Freezing of Helium-4: Comparison of Different Density Functional Approaches

Solidification of superfluid helium-4 has been addressed within the framework of density functional theory. Early studies used a variational approach, approximating the density distribution in the solid phase by a sum of Gaussians on each lattice site. Recently, we performed an unconstrained minimization of the functional describing the helium system as reported by Ancilotto et al. (Phys. Rev. B, 72, 214522, 2005). At sufficiently high density, we find stable solid like solutions, which exhibit an anisotropic density profile around each lattice site. We compare these results to the previous variational approach, and attempt to improve the family of trial functions by adding a variational parameter to account for anisotropy.     

SOFTWARE AND PERFORMANCE MEASURES FOR EVALUATING MULTI-AGENT FRAMEWORKS

ABSTRACT

Nowadays, multi-agent frameworks allow to implement very complex systems by means of agent technology. However, this complexity makes it more difficult to evaluate software and runtime characteristics of multiagent systems (MAS). Our aim is to define and study some quantitative measures to measure MAS aspects like development time, reusability, scalability, etc. These measures could be used by engineers to guide the selection among several MAS frameworks. Our study has been carried out in several MAS frameworks like JADE, JATLite, SkeletonAgent, and ZEUS, which have been used to build a MAS application for news retrieval.     

An optimal expansion of Volterra models using independent Kautz bases for each kernel dimension

A new solution for the problem of selecting poles of the two-parameter Kautz functions in Volterra models is proposed. In general, a large number of parameters are required to represent the Volterra kernels, although this difficulty can be overcome by describing each kernel using a basis of orthonormal functions, such as the Kautz basis. This representation has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a non-linear static mapping represented by the Volterra series. The resulting Wiener/Volterra model can be truncated into fewer terms if the Kautz functions are properly designed. The underlying problem is how to select the arbitrary complex poles that fully parametrize these functions. This problem has been approached in previous research by minimizing an upper bound for the error resulting from the truncation of the kernel expansion. The present paper goes even further in that each multidimensional kernel is decomposed into a set of independent Kautz bases, each of which is parametrized by an individual pair of conjugate Kautz poles intended to represent the dominant dynamic of the kernel along a particular dimension. An analytical solution for one of the Kautz parameters, valid for Volterra models of any order, is derived. A simulated example is presented to illustrate these theoretical results. The same approach is then used to model a real non-linear magnetic levitation system with oscillatory behaviour.