Effect of fluorine doping on phase formation and properties of Bi(Pb)-2223 ceramics

Superconducting ceramics of Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_yF_x (x = 0–0.6) are prepared in air by conventional solid state reaction and characterized. The study shows that the melting point of the samples decreases as fluorine content increases. As a consequence, the grain size increases with the doping level and for x = 0.6, the sample is completely deformed and presents a concave shape making impossible the measurements on it. The Vickers microhardness reaches its maximum for x = 0.2. The analysis of the X-ray diffraction results reveals that all the samples are composed of only Bi(Pb)-2212 and Bi(Pb)-2223 phases. The highest proportion of the high T_c phase (Bi(Pb)-2223) is also observed for x = 0.2 and is about 67.32%. The refinement of cell parameters is done by considering the structural modulation. The results show that the doping leads to a reduction of cell volume as well as the a axis component of modulation. From resistivity versus temperature measurements, it is shown that the doped phases exhibit higher onset critical transition temperatures than the undoped one. The residual resistivity increases with fluorine content suggesting that the doping introduces structural defects and disorder into the samples. The obtained critical current density at 77 K under zero magnetic field also increases with fluorine doping.     

Finite element modeling of contact conditions in multibody system dynamics

In this paper a new method is developed for the dynamic analysis of contact conditions in flexible multibody systems undergoing a rolling type of motion. The relative motion between the two contacting bodies is treated as a constraint condition describing their kinematic and geometric relations. Equations of motion of the system are presented in a matrix form making use of Kane's equations and finite element method. The method developed has been implemented in a general purpose program called DARS and applied to the simulation and analysis of a rotating wheel on a track. Both the bodies are assumed flexible and discretized using a three dimensional 8-noded isoparametric elements. The time variant constraint conditions are imposed on the nodal points located at the peripheral surfaces of the bodies under consideration. The simulation is carried out under two different boundary conditions describing the support of the track. The subsequent constraint forces associated with the generalized coordinates of the system are computed and plotted. The effects of friction are also discussed.     

Did Lewis Carroll own a copy of George Boole's Laws of thought? An argument from the sale catalogues

Private libraries of scientists offer valuable information on their character, work, and acquaintances. Charles L Dodgson (alias Lewis Carroll) constructed an impressive library of several thousand volumes. The sale catalogue of Carroll's library reveals that it contained at his death most of the major logic works that would be expected for a British mathematical logician of the time. However, there is dispute as to the presence of the most important logic book of all: George Boole's Laws of thought (1854). The absence of this work would make both an unfortunate and an intriguing gap. This paper explains the source of this dispute and introduces a new argument from the sale catalogues centred on the dissemination of the books after the sale of the library.     

Ab initio calculations of structural,electronic, optical and thermodynamic properties of alkaline earth tellurides BaxSr1−XTe

Structural, electronic and thermodynamic properties of SrTe and BaTe compounds and their ternary mixed crystals Ba_xSr_1−xTe in the rock-salt structure have been studied with density functional theory (DFT), whereas the optical properties have been obtained by using empirical methods such as the modified Moss relation. The exchange-correlation potential was calculated using the generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof (PBE) and the local density approximation (LDA) of Teter–Pade (TP). In the present work, we used the virtual-crystal approximation (VCA) to study the effect of composition (x). The calculated lattice parameters at equilibrium volume and the bulk modulus for x=0 and x=1 are in good agreement with the literature data. Furthermore, the Ba_xSr_1−xTe alloys are found to be an indirect band gap semiconductor. In addition, we have also predicted the heat capacities (C_V), the entropy(S), the internal energy (U) and the Helmholtz free energy (F) of the parent compounds SrTe and BaTe.     

Stability of a thermoelastic laminated system subject to a neutral delay

In this work, we consider a system of two identical beams of uniform thickness modeled as a Timoshenko system. The slip between the beams is taken into account, and the system is coupled with a heat equation. Moreover, the slip equation is subject to a distributed delay of neutral type. Delays are known to be of a destructive nature in general. Therefore, here, the delay will compete with a frictional damping and the dissipation produced by the heat equation. We provide sufficient conditions ensuring exponential and polynomial stability of the structure.     

Dynamic collision avoidance and constraint violation compensation

This paper uses concepts in multibody dynamics, together with a collision detection algorithm to study the dynamics of collision avoidance. Obstacle avoidance of a mechanical system in motion is expressed in terms of distances, relative velocities and relative accelerations between potentially colliding bodies. The generalized control forces (constraint forces) used to adjust the system dynamics are based on an n-timestep collision avoidance algorithm. Constraint violations resulting from sudden changes in motion direction are compensated for by feeding back the errors of position and velocity constraints to assure asymptotic stability. The procedures developed are illustrated through a maneuver in space of a robotic manipulator used for grasp and deployment.     

Control of a viscoelastic translational Euler–Bernoulli beam

In this paper, we study a cantilevered Euler–Bernoulli beam fixed to a base in a translational motion at one end and to a tip mass at its free end. The beam is subject to undesirable vibrations, and it is made of a viscoelastic material that permits a certain weak damping. By applying a control force at the base, we shall attenuate these vibrations in a fast manner. In fact, we establish the exponential stability of the system. Our method is based on the multiplier technique. Copyright © 2016 John Wiley & Sons, Ltd.     

Implementation of 3-D isoparametric finite elements on supercomputer for the formulation of recursive dynamical equations of multi-body systems

Kinematic formulation of the versatile three-dimensional isoparametric eight-noded brick element with six degrees of freedom at each node (three-translational and three-rotational), suitable for the discretization of flexible bodies with intricate geometric configurations, has been developed and implemented on the supercomputer IBM-3090 for the simulation of dynamical mechanical systems. The pipelining feature of the above vector-processor has been exploited for achieving a significant order of magnitude in computational efficiency. The concepts of indexed reference arrays have been utilised in the development of dynamical equations of motion, eliminating expensive Boolean matrix multiplication operations. The algorithm developed is an improvement and extension of [7], with the implementation of the brick element formulation. The recursive Kane's equations, modal analysis technique and strain energy principles are integrated into the procedure. The above technique is also applied to the constrained multi-body systems. An illustrative example of an spin-up maneuver of a space robot with three flexible links carrying a solar panel is presented. The prediction of dynamic behaviour of the system is carried out under a constrained environment and the effects of geometric stiffening and its subsequent restoring elastic forces are demonstrated.