Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

Frame-driven Extraction of Linked Data and Ontologies from Text

Ontology design and population -core aspects of semantic technologies- re- cently have become fields of great interest due to the increasing need of domain-specific knowledge bases that can boost the use of Semantic Web. For building such knowledge resources, the state of the art tools for ontology design require a lot of human work. Producing meaningful schemas and populating them with domain-specific data is in fact a very difficult and time-consuming task. Even more if the task consists in modelling knowledge at a web scale. The primary aim of this work is to investigate a novel and flexible method- ology for automatically learning ontology from textual data, lightening the human workload required for conceptualizing domain-specific knowledge and populating an extracted schema with real data, speeding up the whole ontology production process. Here computational linguistics plays a fundamental role, from automati- cally identifying facts from natural language and extracting frame of relations among recognized entities, to producing linked data with which extending existing knowledge bases or creating new ones. In the state of the art, automatic ontology learning systems are mainly based on plain-pipelined linguistics classifiers performing tasks such as Named Entity recognition, Entity resolution, Taxonomy and Relation extraction [11]. These approaches present some weaknesses, specially in capturing struc- tures through which the meaning of complex concepts is expressed [24]. Humans, in fact, tend to organize knowledge in well-defined patterns, which include participant entities and meaningful relations linking entities with each other. In literature, these structures have been called Semantic Frames by Fill- 6 Introduction more [20], or more recently as Knowledge Patterns [23]. Some NLP studies has recently shown the possibility of performing more accurate deep parsing with the ability of logically understanding the structure of discourse [7]. In this work, some of these technologies have been investigated and em- ployed to produce accurate ontology schemas. The long-term goal is to collect large amounts of semantically structured information from the web of crowds, through an automated process, in order to identify and investigate the cognitive patterns used by human to organize their knowledge.