On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

Geometrically qualified ESPI vibration analysis of an engine

This paper presents an application in the automotive industry where a combination of electronic speckle-pattern interferometry and laser doppler velocimetry were used at a critical stage in the design process of an internal combustion engine. Combined deformation and surface relief measurements were used to study the phase and amplitude of deformation of a vibrating engine. The relief data was combined with the interferometer geometry and used to geometrically correct the deformation data, in an effort to improve accuracy. The measurements allowed rapid identification and quantification of design weaknesses, particularly those causing undesirable resonances. This led to a significant reduction in the design time and lowering of costs, when compared with existing design optimisation methods.     

Machine assignment in a nonlinear multi-product flowline

A group of machines for processing a set of jobs in a manufacturing system is often located in a serial line. An efficient strategy for locating these machines such that the total travel distance or the cost of transporting the jobs is minimized is desired. In this research, the assumption of a linear line with equally spaced machine location is relaxed. This research addressed problems of locating unique machines. It is found that the machine distances possess unique properties in this type of a problem. Utilizing these properties, heuristic strategies are proposed to obtain efficient solution where optimal methods are expected to be computationally prohibitive. A lower bound for the optimum solution is also proposed. Results are encouraging.     

Imaging mitochondrial organization in living primate oocytes and embryos using multiphoton microscopy.

We employed multiphoton laser scanning microscopy (MPLSM) to image changes in mitochondrial distribution in living rhesus monkey embryos. This method of imaging does not impair development; thus, the same specimen can be visualized multiple times at various developmental stages. Not only does this increase the amount of information that can be gathered on a single specimen but it permits the correlation of early events with subsequent development in the same specimen. Here we demonstrate the utility of MPLSM for determining changes in mitochondrial organization at various developmental stages and show that rhesus zygotes possess a distinct accumulation of mitochondria between the pronuclei prior to syngamy. We present evidence that suggests that this pronuclear accumulation may be positively correlated with development to the blastocyst stage-in the same embryo-thereby illustrating how MPLSM can be used to correlate cellular dynamics of primate oocytes and early embryos with their developmental potential. Understanding the relationship between mitochondrial distribution and the subsequent development of mammalian embryos, particularly primates, will increase our ability to improve embryo culture technologies, including those used for human assisted reproduction.     

HfO2/AlGaN/GaN structures with HfO2 deposited at ultra low pressure using an e‐beam

We show that HfO₂/AlGaN/GaN structures with HfO₂ layer deposited using an e‐beam in ultra high vacuum are suitable for field effect transistors. The dielectric constant of the HfO₂ was found ε_HfO > 23–24, which is close to the highest re‐ ported values for this material. The leakage current did not exceed 10^–4 A/cm² at the threshold voltage. The comparison of the losses in the samples with and without HfO₂ indicates low concentration of the interface traps. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparative study of the behaviour of 1H-indazoles and 1-(p-aminophenyl)indazoles under electron impact

The electron impact mass spectrometric fragmentation pathways for several 1H-indazoles and 1-(p-amino-phenyl)indazoles were investigated. An interesting relationship between the substitution pattern in the framework of the indazole derivatives and the fragmentation patterns was observed.     

Contractive multifunctions, fixed point inclusions and iterated multifunction systems

We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such operators T possess fixed points satisfying the relation x∈Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x₀∈X to a point x∈XT, the set of all fixed points of a multifunction operator T. We also prove a continuity result for fixed point sets XT as well as a “generalized collage theorem” for contractive multifunctions. These results can then be used to solve inverse problems involving contractive multifunctions. Two applications of contractive multifunctions are introduced: (i) integral inclusions and (ii) iterated multifunction systems.     

On the isomorphism problem in the class of extensions of a free group by an infinite cyclic group

In the automorphism group of a rank 3 free group we find two nonconjugate automorphisms whose mapping tori are isomorphic groups.     

Metric fluctuations,entropy, and the Wheeler-deWitt equation

Quantization using quantum potentials is described in terms of momentum fluctuations, and it is related to Fisher information and entropy. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 32–44, July, 2007.