Granularity

Abstract: The study is concerned with the fundamentals of granular computing. Granular computing, as the name itself stipulates, deals with representing information in the form of some aggregates (that embrace a number of individual entities) and their ensuing processing. We elaborate on the rationale behind granular computing. Next, a number of formal frameworks of information granulation are discussed including several alternatives such as fuzzy sets, interval analysis, rough sets, and probability. The notion of granularity itself is defined and quantified. A design agenda of granular computing is formulated and the key design problems are raised. A number of granular architectures are also discussed with an objective of delineating the fundamental algorithmic, and conceptual challenges. It is shown that the use of information granules of different size (granularity) lends itself to general pyramid architectures of information processing. The role of encoding and decoding mechanisms visible in this setting is also discussed in detail, along with some particular solutions. We raise an issue of interoperability of granular environments. The intent of the paper is to elaborate on the fundamentals and put the entire area in a certain perspective while not moving into specific algorithmic details.

Abstract: The microstructure of bulk samples of the copper-oxide high-temperature superconductors commonly is describable in terms of anisotropic grains of stoichiometric material separated by layers of nonstoichiometric interface material. The granularity strongly influences the electromagnetic properties, especially the transport critical-current density and the magnetization. In this paper, a simple theoretical model for the granularity is introduced and then used to discuss a number of electrodynamic properties (hysteretic magnetization versus magnetic field, zero-field-cooled and field-cooled magnetization versus temperature, ac susceptibility, and flux creep with logarithmic time dependence). Special attention is drawn to the importance of distinguishing between intragranular and intergranular effects.

Abstract: A methodology is described to systematically derive coarse-grained (CG) force fields for molecular liquids from the underlying atomistic-scale forces. The coarse graining of an interparticle force field is accomplished by the application of a force-matching method to the trajectories and forces obtained from the atomistic trajectory and force data for the CG sites of the targeted system. The CG sites can be associated with the centers of mass of atomic groups because of the simplicity in the evaluation of forces acting on these sites from the atomistic data. The resulting system is called a multiscale coarse-grained (MS-CG) representation. The MS-CG method for liquids is applied here to water and methanol. For both liquids one-site and two-site CG representations without an explicit treatment of the long-ranged electrostatics have been derived. In addition, for water a two-site model having the explicit long-ranged electrostatics has been developed. To improve the thermodynamic properties (e.g., pressure and density) for the MS-CG models, the constraint for the instantaneous virial was included into the force-match procedure. The performance of the resulting models was evaluated against the underlying atomistic simulations and experiment. In contrast with existing approaches for coarse graining of liquid systems, the MS-CG approach is general, relies only on the interatomic interactions in the reference atomistic system.