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In many cases, however, the singular structure of the solution is known, and its form may be exploited by the spectral element method.
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Calculations at large values of the aspect ratio take advantage of the singular asymptotic structure of the problem, whereby only the "inner" behavior at the ends of the flow channel is treated with a fine mesh in the longitudinal coordinate; a smoothly expanded mesh is sufficient for resolving the "outer" behavior in between.
Nonetheless, it is not entirely clear why we shouldn't be happy with a variety of types of singular structure, and with the permissive attitude that none should be considered the "right" definition of singularities.
The construction method used in its execution (cantilevered erection in a congested urban area), so as the characteristics of the bolted steel structure and the way it is anchored to the concrete core walls, employing post-tensioning systems and stud shear connectors, transform this building into a singular structure in the field of construction.
The final outcome is the design of a singular structure optimized for the NEXT experiment with a probability of failure against any standard earthquake of only 0.125%.
Even without an accepted, strict definition of singularity for relativistic spacetimes, the question can be posed of what it may mean to ascribe "existence" to singular structure under any of the available open possibilities.
As we have seen, there is no commonly accepted, strict definition of singularity, no physically reasonable definition of missing point, and no necessary connection of singular structure, at least as characterized by the presence of incomplete paths, to the presence of curvature pathology.
While path incompleteness seems to capture an important aspect of the intuitive picture of singular structure, it completely ignores another seemingly integral aspect of it: curvature pathology.
Many eminent physicists believe that general relativity's prediction of singular structure signals a serious deficiency in the theory; singularities are an indication that the description offered by general relativity is breaking down.
None of them integrate the health system into a more manageable, singular structure, and none of them attempt to lower costs through a radical expansion of government bargaining power.
Because of the way the issue of singular structure in relativistic spacetimes ramifies into almost every major open question in relativistic physics today, both physical and philosophical, it provides a peculiarly rich and attractive focus for these sorts of questions.
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