Fundamental problems arise concerning multi-component diffusion because electrolyte solutions must be electrically neutral and as a result of D w differences, the flux of one ion must be linked to the flux of other ions to maintain this electro-neutrality.
A more fundamental problem arises when institutions are too weak to provide eventual remedies for such flaws -- a role often played by elected legislatures and, in America, the courts.
If we switch instead to a phonemic analysis of words, as being more fundamental, similar problems arise.
The fundamental numerical problem arising from topological scission has been solved.
It is well known that the p-Laplacian equation can describe a fundamental mechanics problem arising from turbulent flow in a porous medium; see [1].
The single-hop network assumption, albeit simplifying, is interesting and highly non-trivial since it captures the fundamental problems that arise due to interference, when multiple nodes attempt simultaneous channel access.
Upon completing this review, we shall conclusively demonstrate that the atomistic simulation tools themselves are not sufficient for many of the interesting and fundamental problems that arise in computational mechanics, and that these deficiencies lead to the thrust of multiple-scale methods.
No amount of standardized testing in the world, no teacher-quality-improvement program, no aggressive program of shutting down neighborhood schools can truly fix the fundamental problems that arise when impoverished children are hungry, homeless, sick and untreated, neglected, afraid, abused, often left to fend for themselves by single parents who are, often, barely out of childhood themselves.
In addition to the problems arising from the relaxed conditions, there are more fundamental exceptions to the above rationale.
