Generalized disks of contractivity for explicit and implicit Runge-Kutta methods

The A-contractivity of Runge-Kutta methods with respect to an inner product norm was investigated thoroughly by Butcher and Burrage (who used the term B-stability). Their theory is extended to contractivity in a region bounded by a circle through the origin. The largest possible circle is calculated for many known explicit Runge-Kutta methods. As a rule it is considerably smaller than the stability region, and in several cases it degenerates to a point. It is shown that an explicit Runge-Kutta method cannot be contractive in any circle of this class if it is more than fourth order accurate

New analysis method of the halo phenomenon in finite many-fermion systems. First applications to medium-mass atomic nuclei

A new analysis method to investigate halos in finite many-fermion systems is designed, as existing characterization methods are proven to be incomplete/inaccurate. A decomposition of the internal wave-function of the {$N$-body} system in terms of overlap functions allows a model-independent analysis of medium-range and asymptotic properties of the internal one-body density. The existence of a spatially decorrelated region in the density profile is related to the existence of three typical energy scales in the excitation spectrum of the {$(N-1)$-body} system. A series of model-independent measures, taking the internal density as the only input, are introduced. The new measures allow a quantification of the potential halo in terms of the average number of fermions participating to it and of its impact on the system extension. Those new "halo factors" are validated through simulations and applied to results obtained through energy density functional calculations of medium-mass nuclei. Performing spherical Hartree-Fock-Bogoliubov calculations with state-of-the-art Skyrme plus pairing functionals, a collective halo is predicted in drip-line Cr isotopes, whereas no such effect is seen in Sn isotopes.Comment: 27 Pages, 29 Figures. Accepted for publication in Phys. Rev. C back-to-back with second part (arXiv:0711.1275

Halo phenomenon in finite many-fermion systems. Atom-positron complexes and large-scale study of atomic nuclei

The analysis method proposed in Ref. \cite{rotival07a} is applied to characterize halo properties in finite many-fermion systems. First, the versatility of the method is highlighted by applying it to light and medium-mass nuclei as well as to atom-positron and ion-positronium complexes. Second, the dependence of nuclear halo properties on the characteristics of the energy density functional used in self-consistent Hartree-Fock-Bogoliubov calculations is studied. It is found that (a) the low-density behavior of the pairing functional and the regularization/renormalization scheme must be chosen coherently and with care to provide meaningful predictions, (b) the impact of pairing correlations on halo properties is significant and is the result of two competing effects, (c) the detailed characteristics of the pairing functional has however only little importance, (d) halo properties depend significantly on any ingredient of the energy density functional that influences the location of single-particle levels; i.e. the effective mass, the tensor terms and the saturation density of nuclear matter. The latter dependencies give insights to how experimental data on medium-mass drip-line nuclei can be used in the distant future to constrain some characteristics of the nuclear energy density functional. Last but not least, large scale predictions of halos among all spherical even-even nuclei are performed using specific sets of particle-hole and particle-particle energy functionals. It is shown that halos in the ground state of medium-mass nuclei will only be found at the very limit of neutron stability and for a limited number of elements.Comment: 24 Pages, 32 Figures. Accepted for publication in Phys. Rev. C back-to back with first part (nucl-th/0702050

Robustness to Algorithmic Singularities and Sensitivity in Computational Kinematics

A robust approach to computational kinematics intended to cope with algorithmic singularities is introduced in this article. The approach is based on the reduction of the original system of equations to a subsystem of bivariate equations, as opposed to the multivariate polynomial reduction leading to the characteristic univariate polynomial. The effectiveness of the approach is illustrated for the exact function-generation synthesis of planar, spherical, and spatial four-bar linkages. Some numerical examples are provided for the case of the spherical four-bar function generator with six precision points to show the benefits of the proposed method with respect to methods reported in the literature.The first author acknowledges the support of Universidad Politecnica de Valencia, research project PAID-00-09. The second author acknowledges the support of McGill University by means of a James McGill Professorship.Gracia Calandin, LI.; Angeles, J. (2011). Robustness to Algorithmic Singularities and Sensitivity in Computational Kinematics. Proceedings of the Institution of Mechanical Engineers part C - Journal of Mechanical Engineering Science. 225(4):987-999. doi:10.1243/09544062JMES2464S9879992254Raghavan, M., & Roth, B. (1993). Inverse Kinematics of the General 6R Manipulator and Related Linkages. Journal of Mechanical Design, 115(3), 502-508. doi:10.1115/1.2919218Lee, H. Y., Woernle, C., & Hiller, M. (1991). A Complete Solution for the Inverse Kinematic Problem of the General 6R Robot Manipulator. Journal of Mechanical Design, 113(4), 481-486. doi:10.1115/1.2912808Innocenti, C., & Parenti-Castelli, V. (1993). Echelon form solution of direct kinematics for the general fully-parallel spherical wrist. Mechanism and Machine Theory, 28(4), 553-561. doi:10.1016/0094-114x(93)90035-tGosselin, C. M., Sefrioui, J., & Richard, M. J. (1994). On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture. Journal of Mechanical Design, 116(2), 594-598. doi:10.1115/1.2919419Alizade, R. I., & Kilit, Ö. (2005). Analytical synthesis of function generating spherical four-bar mechanism for the five precision points. Mechanism and Machine Theory, 40(7), 863-878. doi:10.1016/j.mechmachtheory.2004.12.010Cervantes-Sánchez, J. J., Gracia, L., Rico-Martínez, J. M., Medellín-Castillo, H. I., & González-Galván, E. J. (2009). A novel and efficient kinematic synthesis approach of the spherical 4R function generator for five and six precision points. Mechanism and Machine Theory, 44(11), 2020-2037. doi:10.1016/j.mechmachtheory.2009.05.006Angeles, J. (2007). Fundamentals of Robotic Mechanical Systems. Mechanical Engineering Series. doi:10.1007/978-0-387-34580-2Bai, S., Hansen, M. R., & Angeles, J. (2009). A robust forward-displacement analysis of spherical parallel robots. Mechanism and Machine Theory, 44(12), 2204-2216. doi:10.1016/j.mechmachtheory.2009.07.005Sommese, A. J., & Wampler, C. W. (2005). The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. doi:10.1142/5763Forsythe, G. E. (1970). Pitfalls in Computation, or why a Math Book isn’t Enough. The American Mathematical Monthly, 77(9), 931. doi:10.2307/2318109Angeles, J., Hommel, G., & Kovács, P. (Eds.). (1993). Computational Kinematics. Solid Mechanics and Its Applications. doi:10.1007/978-94-015-8192-9Yang, A. T., & Freudenstein, F. (1964). Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms. Journal of Applied Mechanics, 31(2), 300-308. doi:10.1115/1.3629601Gupta, K. C., & Beloiu, A. S. (1998). Branch and circuit defect elimination in spherical four-bar linkages. Mechanism and Machine Theory, 33(5), 491-504. doi:10.1016/s0094-114x(97)00078-

Extensive collection of femtoliter pad secretion droplets in beetle Leptinotarsa decemlineata allows nanoliter microrheology

Pads of beetles are covered with long, deformable setae, each ending in a micrometric terminal plate coated with secretory fluid. It was recently shown that the layer of the pad secretion covering the terminal plates is responsible for the generation of strong attractive forces. However, less is known about the fluid itself because it is produced in extremely small quantity. We here present a first experimental investigation of the rheological properties of the pad secretion in the Colorado potato beetle {\it Leptinotarsa decemlineata}. Because the secretion is produced in an extremely small amount at the level of the terminal plate, we first develop a procedure based on capillary effects to collect the secretion. We then manage to incorporate micrometric beads, initially in the form of a dry powder, and record their thermal motion to determine the mechanical properties of the surrounding medium. We achieve such a quantitative measurement within the collected volume, much smaller than the $1 {\rm \mu}$l sample volume usually required for this technique. Surprisingly, the beetle secretion was found to behave as a purely viscous liquid, of high viscosity. This suggests that no specific complex fluid behaviour is needed during beetle locomotion. We build a scenario for the contact formation between the spatula at the setal tip and a substrate, during the insect walk. We show that the attachment dynamics of the insect pad computed from the high measured viscosity is in good agreement with observed insect pace. We finally discuss the consequences of the secretion viscosity on the insect adhesion

Granitoides peraluminosos con andalucita y cordierita magmáticas en la sierra de Velasco: implicancias para el orógeno famatiniano.

La combinación de estudios petrológicos, geoquímicos y de química mineral en el sector noreste de la sierra de Velasco, a la latitud de la localidad de Santa Vera Cruz, revelan la presencia de una unidad ígnea peraluminosa con andalucita (Si = 3,85, Al = 8,14 y Fe3+ = 0,04) y cordierita (K+Na = 0,33 y XFe = 0,40) magmáticas, la cual es denominada unidad Santa Cruz. La aluminosisad del magma (ISA = 1,30 - 1,42), evidenciada por la presencia de minerales aluminosos como cordierita, andalucita y muscovita y la geoquímica de roca total indican que esta unidad fue derivada de fusión parcial de una secuencia metasedimentaria (esencialmente pelítica) en la corteza superior, que se emplazó en un rango de presión - temperatura de 2 a 2,4 kbar y 670 a 720 ºC. Notablemente, las características geoquímicas de la unidad Santa Cruz sugieren una roca fuente diferente a la establecida para otras unidades peraluminosas del orógeno famatiniano. [ABSTRACT] Peraluminous granitoids with magmatic andalusite and cordierite in the Sierra de Velasco: Implications to the Famatinian Orogen. The combination of petrological, geochemical and mineral/chemical data for the NE sector of the Sierra de Velasco, at the latitud of the Santa Vera Cruz town, reveal the presence of peraluminous igneous unit with magmatic andalusite and cordierite, which has been named Santa Cruz unit. The aluminous of magma (ASI = 1.30 - 1.42), evident by the presence of aluminous minerals such as cordierite, andalusite and muscovite and the whole-rock geochemical, principally indicate that this unit was derived of the partial melting of a metasedimentary secuency (mainly pelitic) in the upper crustal, which was emplaced a pression - temperature range of 2 to 2.4 kb and 670 to 720 ºC. Remarkably, the geochemical characteristics of Santa Cruz unit suggest a different source rock than other peraluminous units founded in the Famatinian Orogen