No abstract

The equation of state for hard spheres in a spherical cavity is calculated and compared with the results previously found when the containing boundary was a channel. It was found that the spherical surface provides a focusing effect on both the pressure and the compressibility factor. An examination of the results suggested that the density and compressibility factors could be expanded in a series of Maxwellian functions. It was found that a six-term series which was modified in the immediate vicinity of the wall was sufficient. This has an advantage over the usual Fourier series expansion in that less terms are required. In addition, an argument can be made that such a series has a foundation in the physics of the problem.

The paper considers the refraction of a plane shock wave at an interface between two streams of different Mach number. Particular attention is paid to the irregular wave systems. It is found that when the interface is slow-fast, that is when the speed of sound a0 in the first or incident wave medium is less than the speed of sound aB in the second or transmitted wave medium, then there are two irregular systems, one being a double Mach reflexion type and the other being a four-wave confluence type. There are also two irregular systems when the refraction is fast-slow; these are a single Mach reflexion type and an expansion wave type. This last system has a central expansion wave when the flow is steady and a continuous band expansion wave when the flow is self-similar. Only two of the irregular wave systems have been observed experimentally in the fully developed state. Possible degeneracies are discussed.

Infants (n = 24, mean age 13 months and n = 24, mean age 19 months) were tested on an extension of the method introduced by Tomasello and Haberl (2003) to examine the understanding of another person's interest in a novel object. Four objects were presented serially. For two objects, infants played with an experimenter. The infant played with one object alone, and the experimenter played with one object alone. Finally, all four objects were presented together, and the experimenter excitedly asked for one without indicating which. Results showed that younger infants tended to chose the object that they had not yet played with, whereas older infants were significantly more likely to choose the object that the experimenter had not yet played with. These results are discussed in the context of research on the development of understanding diversity of simple object-directed attitudes in the second year of life.

Dobutamine stress echocardiography is a common test to provoke myocardial ischemia in patients unable to undergo routine exercise stress testing. Heart rate elevation, achieved by staged increases in dobutamine doses, acts as a surrogate for exercise. The physicians monitor the ECG of the patient and echocardiographic images to evaluate for myocardial ischemia. However, the actual mechanical stress on the heart is not readily available to the physician. The motivation for the present preliminary study is to both investigate the feasibility of producing such information for clinicians as well as to investigate the variation between different patients as the heart rate varies. Echocardiograms were obtained from three patients undergoing dobutamine stress tests. Using standard equations of motion, the surface shear stress at the surface of the left ventricle was calculated. The average shear stress around the left ventricle is shown, as well as the peak stresses at selected locations as a function of time. It was found that generally the surface shear stress increased with heart rate around most of the left ventricle. While the time averaged shear stress may be important for diagnosis, the maximum shear stress is probably the limiting factor in terminating testing.