In general the solutions to the Rayleigh and Pearson analysis ( linear theory ) assuming an infinite horizontal layer gives rise to degeneracy meaning that many patterns may be obtained by the system.
22.
For small values of " U ", say " U " < 5, a linear theory can be used, and at higher values nonlinear theories have to be used, like cnoidal wave theory.
23.
But some scientists, including many of the new BEIR review panel, contend the linear theory overstates the cancer risks and that, as a result, the radiation exposure levels may, in fact, be too stringent.
24.
However, for nonlinear waves, particles exhibit a Stokes drift for which a second-order expression can be derived from the results of Airy wave theory ( see the period, can be estimated using the results of linear theory:
25.
Steel, reversibility, it would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.
26.
In analysing the dynamics of wheelsets and complete rail vehicles, the contact forces can be treated as linearly dependent on the creep ( Kalker's linear theory, valid for small creepage ) or more advanced theories can be used from frictional contact mechanics.
27.
"' Euler Bernoulli beam theory "'( also known as "'engineer's beam theory "'or "'classical beam theory "') is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and beam that is subjected to lateral loads only.
28.
These include elaboration of nonlinear numerical methods of solving 3D cavitation problems, refinement of the known plane linear theories, development of asymptotic theories of axisymmetric and nearly axisymmetric flows, etc . As compared to the classical approaches, the new trend is characterized by expansion of the theory into the 3D flows.
29.
In the linear theory of elasticity "'Clapeyron's theorem "'states that the potential energy of deformation of a body, which is in equilibrium under a given load, is equal to half the work done by the external forces computed assuming these forces had remained constant from the initial state to the final state.
30.
Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident to some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map.
