The bane of Lagrangian hydrodynamics calculations is the premature breakdown of grid topology that results in severe degradation of accuracy and run termination often long before the assumption of a Lagrangian zonal mass has ceased to be valid.
It seems we'll have to do more to find our way into the 21st century history books than know stuff, because we are all starting with so much information that it has ceased to be a valid differentiator.
Many computer scientists have been warning for years that this time would come, that Moore's Law would cease to be valid because of increasing technical difficulties and the expense of overcoming them.
The Indian economy has been operating with 60% less currency since the November announcement by the prime minister, Narendra Modi, that the country's two most used cash bills would cease to be valid within hours.
"When does a formulation of thought cease to be valid," asks Francis, and answers: "When it loses sight of the human or even when it is afraid of the human or deluded about itself".
By using classical thermodynamics, the "top down" approach ceases to be valid when thermal energy kT becomes smaller than the energetic gap between two successive levels, δ.
After the passage of enough time or perhaps, after the passage of enough time during which no claim for rectification is made the right of rectification for a specific past rights-violation may cease to be valid.
This work demonstrates that below a threshold value, defined as transition length, these stress concentration factors cease to be valid and, notably, also demonstrates that below this threshold the magnitude of the stated factors may be significantly larger than existing values; a fact that may have important consequences for the accurate estimates of fatigue life.
If the Supreme Court rules that gay marriage is a constitutional right, then that instantly means that all the anti-gay-marriage "one man and one woman" laws would cease to be valid law.
