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[1] [2] This deviation from linearity is described as the non-linear effect, NLE. [3] The linearity can be expressed mathematically , as shown in Equation 1. Stereoselection (i.e., ee product ) that is higher or lower than the enantiomeric excess of the catalyst (ee catalyst , with respect to the equation) is considered non-routine behavior.
The linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position , which varies with (time). An example of linear motion is an ...
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Some non-Newtonian fluids with shear-independent viscosity, however, still exhibit normal stress-differences or other non-Newtonian behavior. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian ...
Rectilinear motion along a line in a Euclidean space gives rise to a quasiperiodic motion if the space is turned into a torus (a compact space) by making every point equivalent to any other point situated in the same way with respect to the integer lattice (the points with integer coordinates), so long as the direction cosines of the rectilinear motion form irrational ratios.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Non-linear viscoelastic constitutive equations are needed to quantitatively account for phenomena in fluids like differences in normal stresses, shear thinning, and extensional thickening. [3] Necessarily, the history experienced by the material is needed to account for time-dependent behavior, and is typically included in models as a history ...
In chemistry and molecular physics, fluxional (or non-rigid) molecules are molecules that undergo dynamics such that some or all of their atoms interchange between symmetry-equivalent positions. [1] Because virtually all molecules are fluxional in some respects, e.g. bond rotations in most organic compounds , the term fluxional depends on the ...