Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure

Broad-scale patterns of body size in squamate reptiles of Europe and North America

Aim To document geographical interspecific patterns of body size of European and North American squamate reptile assemblages and explore the relationship between body size patterns and environmental gradients. Location North America and western Europe. Methods We processed distribution maps for native species of squamate reptiles to document interspecific spatial variation of body size at a grain size of 110 x 110 km. We also examined seven environmental variables linked to four hypotheses possibly influencing body size gradients. We used simple and multiple regression, evaluated using information theory, to identify the set of models best supported by the data. Results Europe is characterized by clear latitudinal trends in body size, whereas geographical variation in body size in North America is complex. There is a consistent association of mean body size with measures of ambient energy in both regions, although lizards increase in size northwards whereas snakes show the opposite pattern. Our best models accounted for almost 60% of the variation in body size of lizards and snakes within Europe, but the proportions of variance explained in North America were less than 20%. Main conclusions Although body size influences the energy balance of thermoregulating ectotherms, inconsistent biogeographical patterns and contrasting associations with energy in lizards and snakes suggest that no single mechanism can explain variation of reptile body size in the northern temperate zone

Advanced sensing and control techniques to facilitate semi-autonomous decommissioning. 1998 annual progress report

'This research is intended to advance the technology of semi-autonomous teleoperated robotics as applied to Decontamination and Decommissioning (D and D) tasks. Specifically, research leading to a prototype dual-manipulator mobile work cell is underway. This cell is supported and enhanced by computer vision, virtual reality and advanced robotics technology. This report summarizes work after approximately 1.5 years of a 3-year project. The autonomous, non-contact creation of a virtual environment from an existing, real environment (virtualization) is an integral part of the workcell functionality. This requires that the virtual world be geometrically correct. To this end, the authors have encountered severe sensitivity in quadric estimation. As a result, alternative procedures for geometric rendering, iterative correction approaches, new calibration methods and associated hardware, and calibration quality examination software have been developed. Following geometric rendering, the authors have focused on improving the color and texture recognition components of the system. In particular, the authors have moved beyond first-order illumination modeling to include higher order diffuse effects. This allows us to combine the surface geometric information, obtained from the laser projection and surface recognition components of the system, with a stereo camera image. Low-level controllers for Puma 560 robotic arms were designed and implemented using QNX. The resulting QNX/PC based low-level robot control system is called QRobot. A high-level trajectory generator and application programming interface (API) as well as a new, flexible robot control API was required. Force/torque sensors and interface hardware have been identified and ordered. A simple 3-D OpenGL-based graphical Puma 560 robot simulator was developed and interfaced with ARCL and RCCL to assist in the development of robot motion programs.

Age and petrology of the Usun Apau and Linau Balui volcanics: Windows to central Borneo’s interior

The Usun Apau plateau lies in a remote area of Sarawak along the Tinjar Line, which defines the onshore part of a suture between the Luconia and Dangerous Grounds blocks. Reconnaissance studies in late 1950s established that the plateau is composed of a bimodal suite of young volcanic rocks, but no further work exists to constrain the age and petrogenesis of the Usun Apau volcanics. We present and discuss new data from a suite of volcanic rocks recently collected from the Usun Apau region. These data include 40Ar–39Ar age dates of mineral separates, major and trace element geochemistry, and Sr, Nd, Pb isotope geochemistry. The Usun Apau plateau is constructed largely of dacite and andesite erupted between 3.9 and 4.1 Ma. Minor basaltic dikes and flows (ca. 2.1 Ma) represent a distinctly younger episode of volcanism that is similar in age and character to the Linau Balui basalts about 100 km SE of the plateau. Although the trace element and isotopic suites from both areas indicate the parental melts were generated from a garnet-bearing, LILE-enriched, non-HIMU OIB-like mantle source, depletion in the HREEs and a negative Nb anomaly impart some characteristics of an island arc-type source contribution. The Usun Apau and Linau Balui volcanics are too young to be directly linked to subduction beneath Borneo; indicating a source region possibly modified by an older episode of subduction. Sr, Nd, Pb inter-isotope correlations plot within the same arrays as Pliocene basalts from the Southern Sulu Arc (500 km NE) which suggests much of northern and central Borneo is underlain by similar lithosphere. Assimilation–fractional crystallization modeling indicates that differentiation of the Usun Apau dacite magmas included assimilation of continental crust with very low 143Nd/144Nd. Modeling different basement compositions as contaminants yielded non-unique results. Triassic Malay granite and different Archean granites represent plausible types of assimilants; whereas crust of Dangerous Grounds and Kontum Plateau do not