In this paper we formulate a non-isothermal, non-Newtonian Hele-Shaw flow with nonlinear thermal conductivity from the injection molding. Then we study the existence of the resulting nonlinear system. Copyright (c) 2005 John Wiley & Sons, Ltd.

This paper deals with an inverse acoustics problem in the ocean. The problem we investigate is the location of a non-homogeneity caused by a sea-mount or some object lying on a slopping seabed. This problem is solved by constructing an acoustic Green's function for the wedge. This is done by using the method of images. The inversion procedure is motivated by our earlier work on the seamount problem for a shallow ocean of uniform depth [17].

The inverse problem is solved by least-squares matching of theoretical fields (for trial objects), employing an approximate field ansatz, to the scattered acoustic wavefield measured on a cylinder fully enclosing the object.

Underwater sonar acoustic surveying, such as deep ocean bathymetry has usually been carried out by having a single multibeam sonar equipped survey ship travel along a prescribed track, transmitting discrete fixed frequency sonar pulses and intercepting their backscattered echoes. Measuring the round-trip travel time of the signal returns from angular spacing across a narrow 90 to 120 degree wide swath centered about the ship's track, and incorporating the local sound velocity profile, leads to the determination of the depth of points angularly distributed across the swath. Interpolation between neighboring pairs of swaths produces a continuous contour map of the ocean floor. For contour mapping, very accurate relative positioning is a necessity. Until recently the use of two or more ships working together to map a common ocean floor region between them, using both forward and back scattered signals, was precluded, because sufficiently accurate relative positioning measurements were not attainable. With the advent of an operational satellite Global Positioning System (GPS), obtaining accurate relative positioning infermation should no longer be a problem for multiplatform mapping systems. In fact, using differential GPS techniques, produces relative positioning accuracy down to fractions of a meter for platform separations of tens or even hundreds of kilometers. Such a system is thus converted into virtually the equivalent of a single huge platform. Multi-platform surveying provides the facility for not only mapping wider swath regions on a single pass, but also for locating, tracking an imaging submerged objects