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These inputs and outputs are speci ed for each patch in a structured, possibly AMR, grid. Associated with each task is a C++ method that is used to perform the actual computation. A task graph representation by itself works well for coupling of multiple computational algorithms, but presents challenges for achieving scalability. A task graph that represents all communication in the problem would require time proportional to the number of computational elements to create. Creating this on a single processor, or on all processors would eventually result in a bottleneck. Uintah addresses this problem by introducing the concept of a tensor product task graph. Uintah components specify tasks for the algorithmic steps only, which are independent of problem size or number of processors. Each task in the task graph is then implicitly repeated on a portion of patches in the decomposed domain. The resulting graph, or tensor product task graph, is created collectively; each processor contains only the tasks that it owns and those that it communicates with. The graph exists only as a whole across all computational elements, resulting in a scalable representation of the graph. Communication requirements between tasks are also speci ed implicitly through a simple dependency algebra. Each execution of a task graph integrates a single timestep, or a single-nonlinear iteration, or some other coarse algorithm step. A portion of the MPM timestep graph is shown in Figure 10.3. Task graphs may be assembled recursively, with a typical Uintah simulation containing one for time integration and one for nonlinear integration. An AMR simulation may contain several more for implementing time subcycling and re nement/coarsening operators on the AMR grid.

A company may resort to underhanded means to learn what its competition is up to. Information is power, and in the field of corporate espionage, companies have frequently used underhanded techniques such as social engineering, the interception of sensitive documents, and surreptitious installation of spyware Trojans to gain a competitive advantage.

for a sinusoidal object vibration. Note that the speckle modulation term is not present with this technique. An example of fringes produced with EOH is shown in Figure 16.30. Figure 16.30(a) shows a rectangular plate undergoing static de ection and Figure 16.30(b) shows a timeaverage vibration mode of the same plate. EOH can also be used for shearography (shearing speckle interferometry) by utilizing a different optical system (Stetson, 1989).

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Figure 8.8 Obesity spreads through social contacts: distribution of obesity within a social network of over 2000 people in the Framingham Heart Study population. Each circle represents an individual. Blue and red borders respectively denote females and males, while a yellow ll indicates obesity (BMI 30 kg/m2; size proportional to BMI) and green a non-obese subject. Purple lines indicate non-genetic ties (friendship or marital) between individuals, and orange lines a familial tie. From (Christakis and Fowler, New England Journal of Medicine (2007), 370 9), with kind permission of the editor of the New England Journal of Medicine. An animation showing the spread of obesity through the social networks with time can be downloaded at www.nejm.org.

It can be seen that a drawback of this method is the necessity to solve (10.35) for xn+1 . This is generally a nonlinear problem requiring the techniques of 7. However, a strength of the implicit method is enhanced stability. This may be easily seen as follows. Apply (10.35) to the model problem (10.28), yielding xn+1 = xn + hxn+1 or xn+1 = Clearly xn = 1 1 h 1 xn . 1 h

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