Witness (Delaunay) Graphs

Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations. We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We study in detail two concrete examples, both related to Delaunay graphs, and consider as well some problems on stabbing geometric objects and point set discrimination, that can be naturally described in terms of witness graphs.Comment: 27 pages. JCCGG 200

Witness Gabriel Graphs

We consider a generalization of the Gabriel graph, the witness Gabriel graph. Given a set of vertices P and a set of witnesses W in the plane, there is an edge ab between two points of P in the witness Gabriel graph GG-(P,W) if and only if the closed disk with diameter ab does not contain any witness point (besides possibly a and/or b). We study several properties of the witness Gabriel graph, both as a proximity graph and as a new tool in graph drawing.Comment: 23 pages. EuroCG 200

Piezoelectric Electromechanical Transducers for Underwater Sound, Part II

The book presents a broad-scope analysis of piezoelectric electromechanical transducers and the related aspects of practical transducer design for underwater applications. It uses an energy method for analyzing transducer problems that provides the physical insight important for the understanding of electromechanical devices. Application of the method is first illustrated with transducer examples that can be modeled as systems with a single degree of freedom, (such as spheres, short cylinders, bars and flexural disks and plates made of piezoelectric ceramics). Thereupon, transducers are modeled as devices with multiple degrees of freedom. In all these cases, results of modeling are presented in the form of equivalent electromechanical circuits convenient for the calculation of the transducers’ operational characteristics. Special focus is made on the effects of coupled vibrations in mechanical systems on transducer performance. The book also provides extensive coverage of acoustic radiation including acoustic interaction between the transducers. The book is inherently multidisciplinary. It provides essential background regarding the vibration of elastic passive and piezoelectric bodies, piezoelectricity, acoustic radiation, and transducer characterization. Scientists and engineers working in the field of electroacoustics and those involved in education in the field will find this material useful not only for underwater acoustics, but also for electromechanics, energy conversion and medical ultrasonics. Part II contains general information on vibration of mechanical systems, electromechanical conversion in the deformed piezoceramic bodies, and acoustic radiation that can be used independently for treatment transducers of different type

Piezoelectric Electromechanical

The book is the most comprehensive coverage of piezoelectric acoustic transducers and all the related aspects of practical transducer designing for underwater applications in the field. It uses a physics-based energy method for analyzing transducer problems. This gives great physical insight into the understanding of the electromechanical devices. The great benefit of the energy method is that the multidisciplinary subject of electro-mechano-acoustics can be presented in parts and the solutions to the problems (electrical, electro-piezo, mechanical, and radiation) are combined using equivalent electrical circuit network theory. The energy and equivalent electromechanical circuit method at first is illustrated with transducer examples that can be modeled as a single degree of freedom system (such as spheres, short cylinders and flexural beams and plates). Then transducers are modeled as multiple degrees of freedom devices and the results are presented using multi contour electromechanical circuits. Special focus is made on the effects of coupled vibrations on the transducer performance. The Book gives also extensive coverage of acoustic radiation including acoustic interaction between the transducers. It provides practical results that are directly useful for the transducers modeling. While there have been many studies of acoustic radiation of various shapes, non-previous presented the results in terms of such practical utility