Bennett relation

The pinch effect can be presented as an example of magneto-hydrodynamic effects in plasma. The effect consists of the self-compression of plasma in its own magnetic field. Consider the pinch effect in a long cylindrical discharge plasma with an electric current along the axis of the cylinder (Fig. 3-20), which is the so-called Z-pinch (Allis, 1960). The equilibrium of the Z-pinch is determined by the Bennett relation (1934) ... 

Two successive compressions of the Plasma column are no more than oscillations near the equilibrium state which is given by the Bennett relation... 

The ratio of the average ion Larmor radius to pinch radius for a Z-pinch satisfying the Bennett relation (Eq.(14)) is 8.08 x 10 ... 

Related to Bennett s logical depth (see above), the thermodynamic depth, T) S) of a system S in state S measures how much information must be processed in order for S to evolve to S. 

Environmental Fate. The environmental fate of americium has been extensively studied in relation to its introduction into the Irish Sea from the BNFL nuclear fuel reprocessing plant at Sellafield, United Kingdom (Belot et al. 1982 Bennett 1976 Bunzl et al. 1994, 1995 Malcolm et al. 1990 McCartney et al. 1994 McKay et al. 1994a Murray et al. 1978, 1979 Pattenden and McKay 1994 Walker et al. 1986). 

The equation gives the chamber diameter required to separate the so-called d5o particle diameter, as a function of the slurry flow rate and the liquid and solid physical properties. The 6 5o particle diameter is the diameter of the particle, 50 per cent of which will appear in the overflow, and 50 per cent in the underflow. The separating efficiency for other particles is related to the d diameter by Figure 10.22, which is based on a formula by Bennett (1936). 

Bennett, D. C., Huszar, D., Laipis, P. J Jaenisch, R., and Jackson, I. J. (1990). Phenotypic rescue of mutant brown melanocytes by a retrovirus carrying a wild-type tyrosinase-related protein gene. Development 110 471-475. 

Doughty, S., Sloan, J., Bennett-Wood, V., Robertson, M., Robins-Brown, R. M., and Hartland, E. L. (2002). Identification of a novel fibrial gene cluster related to long polar fimbriae in locus of enterocyte effacement-negative strains of enterohemorrhagic Escherichia coli. Infect. Immun. 70, 6761-6769. 

There exist a number of correlations for the dispersion parameters a-y and CT as a function of downwind distance x and atmospheric stability. These correlations have been reviewed extensively and repeatedly, and the reader is referred to Gifford (1976), Weber (1976), American Meteorological Society Workshop (1977), Doran et al. (1978), Irwin (1979), and Sedefian and Bennett (1980) for comprehensive summaries of the available formulas. In particular, these references provide one with the relations necessary to select <7y and cr for a specific application. We do not endeavor to survey these relations here. 

Nicholl, D.J., Bennett, P., Hiller, L., et al. (1999) A study of five candidate genes in Parkinson s disease and related neurodegenerative disorders. European Study Group on Atypical Parkinsonism. Neurology, 53, 1415-1421. 

Smith, J.V. and Bennett, J.M. (1981) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates the infinite set of ABC-6 nets the Archimedean and. sigma.-related nets. Am. Mineral., 66 (7-8), 777-788. 

Hunter RL, Bennett B (1984) The adjuvant activity of nonionic block polymer surfactants. II. Antibody formation and inflammation related to the structure of the triblock and octablock copolymer. J Immunol 133 3167-3175... 

Three major reviews exist which give detailed coverage of the literature available up to about 1955. In particular, the review by Gresham et al. (G7) may be consulted for empirical correlations limited to specific flow patterns, and the papers by Isbin et al. (II) and by Bennett (B9) are particularly valuable for aspects of two-phase flow related to steam-water systems. Bennett has also given useful tabulations of available correlations (up to 1957) for the estimation of two-phase pressure drops. 

We wish to acknowledge the assistance of Mrs. Constance Bennett who has assumed and admirably dispatched many of the responsibilities related to the preparation of this volume. 

For a review of these and related reactions, see Abramovitch Barton Find Tetrahedron 1988, 44. 3039-3071. l, Barton Blazejewski Charpiot Find Motherwell Papoula Stanforth J. Chem. Soc.. Perkin Tram. 1 1985, 2667 O Donnell Bennett Jacobsen Ma Tetrahedron Lett. 1989, 30. 3913. 

Nerve injury, followed by pain related behaviour, is induced by loose ligation of the ischiatic nerve of one hind paw of the rat. 3-4 weeks after ligation, neuropathic pain-like behaviour is seen as increased sensitivity towards heat and pressure stimuli (hyperalgesia). Also pain reactions toward non-noxious tactile (mechanical allodynia) or cold stimuli (cold allodynia) can be observed. Mechanical allodynia is tested with von Frey hairs and cold allodynia by putting the animals on metal plate cooled to 4 °C. The number of paw liftings is counted (Bennett and Xie, Pain 1988, 33, 87-107). 

A periodically forced system may be considered as an open-loop control system. The intermediate and high amplitude forced responses can be used in model discrimination procedures (Bennett, 1981 Cutlip etal., 1983). Alternate choices of the forcing variable and observations of the relations and lags between various oscillating components of the response will yield information regarding intermediate steps in a reaction mechanism. Even some unstable phase plane components of the unforced system will become apparent through their role in observable effects (such as the codimension two bifurcations described above where they collide and annihilate stable, observable responses). 

Bennett JM, Kaminski MS, Leonard JP, Vase JM, et al. 2005. Assessment of treatment-related myelodysplastic syndromes and acute myeloid leukemia in patients with non-Hodgkin lymphoma treated with tositumomab and Iodine I 131 tositumomab. Blood. 1052 4576-4582. 

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