Horizontal plane

Abstract: When a smooth jet of water falls vertically on to a horizontal plane, it spreads out radially in a thin layer bounded by a circular hydraulic jump, outside which the depth is much greater. The motion in the layer is studied here by means of boundary-layer theory, both for laminar and for turbulent flow, and relations are obtained for the radius of the hydraulic jump. These relations are compared with experimental results. The analogous problems of two-dimensional flow are also treated.

Abstract: A system (10) for externally locating a sensor in tissue, comprising an external probe including at least first and second electromagnetic output coils (12) with non-parallel longitudinal axes; and output coil (2) driver for alternately energizing the first and second output coils, for generating a time-varying magnetic field which penetrates the patient's skin (7); a sensor coil (30), having a longitudinal axis, for developing an induced electrical voltage in response to the time-varying magnetic field; a distance determinator, responsive to the induced voltage from the sensor coil (30), for determining from the induced voltage, the distance between the output coils (12) and the sensor coil (30), independently of the relative angle, in a horizontal plane, between the sensor coil (30) longitudinal axis, and the longitudinal axes of the output coils (12); and a direction determinator for determining and displaying the direction, in the horizontal plane, in which the sensor coil (30) longitudinal axis is pointing.

Abstract: 1. Complex and simple spike responses of Purkinje cells were recorded in the flocculus of anesthetized, paralyzed rabbits during rotating full-field visual stimuli produced by a three-axis planetarium projector. 2. On the basis of the spatial properties of their complex spike responses, floccular Purkinje cells could be placed into three distinct classes called Vertical Axis, Anterior (45 degrees) Axis and Posterior (135 degrees) Axis. The first two classes occurred in both monocular and binocular forms; the third class was encountered only in binocular form. For the binocular response forms, stimulation through one eye, called the dominant eye, elicited a stronger modulation of the complex spike firing rate than did stimulation of the other eye. The approximate orientation of that axis about which full-field rotation elicited the deepest modulation (the preferred axis) when presented to the dominant eye served as the class label. These classes are the same as those determined qualitatively for inferior olive neurons in the previous paper (47). The present study provides a quantitative description of their spatial tuning. 3. For Vertical Axis cells, the dominant eye was ipsilateral with respect to the flocculus recording site. The preferred axis was vertical and null (no-response) axes were in the horizontal plane. For the binocular response form of Vertical Axis cells (less than 10% of this class), the direction preferences for the two eyes were synergistic with respect to rotation about the vertical axis. 4. The dominant eye for the Anterior (45 degrees) Axis cells was contralateral, with the preferred axis oriented in the horizontal plane at approximately 45 degrees contralateral azimuth. The modulation depth showed a close to cosine relation with the angle between the preferred axis and the stimulus rotation axis. The average orientation (n = 10) for the dominant eye preferred axis, determined by the best-fit sinusoid, was 47 degrees contralateral azimuth. The preferred axis orientation for the ipsilateral (nondominant) eye in the binocular response forms was between 45 and 90 degrees azimuth in the horizontal plane. A null axis for each eye was at approximately 90 degrees to the preferred axis. 5. The Posterior (135 degrees) Axis cells were encountered only in binocular response forms. The dominant eye was ipsilateral, with the preferred axis oriented at approximately 135 degrees ipsilateral azimuth close to the horizontal plane. The modulation depth showed a close to cosine relation with the angle between the preferred axis and the stimulus rotation axis.(ABSTRACT TRUNCATED AT 400 WORDS)

Abstract: Methods of analysis of the response of soil deposits during earthquakes are presented. These methods include linear elastic analyses, a bilinear analysis, and an equivalent linear analysis. All these methods require that: (1) The surface of the layer, the interface between any two sublayers and the base of the layer be essentially horizontal, (2) the material properties of the layer be constant along any horizontal plane, and (3) the applied seismic excitation be also horizontal. The closed-form solutions are utilized to evaluate the accuracy and stability of the lumped-mass analysis and criteria for the accuracy and stability of the lumped-mass representation are proposed. A lumped-mass representation is also used for the analysis of soil layers having bilinear stress-strain characteristics. Finally, a procedure is outlined for obtaining equivalent linear parameters for soils with bilinear stress-strain characteristics. The results obtained by this procedure are shown to be in good agreement with those determined by the bilinear solution.