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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. the ee product ) that is higher or lower than the enantiomeric excess of the catalyst (ee catalyst , relative 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 ...
Example of a linear molecule. N atoms in a molecule have 3N degrees of freedom which constitute translations, rotations, and vibrations.For non-linear molecules, there are 3 degrees of freedom for translational (motion along the x, y, and z directions) and 3 degrees of freedom for rotational motion (rotations in R x, R y, and R z directions) for each atom.
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.
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.
A stirred BZ reaction mixture showing changes in color over time. The discovery of the phenomenon is credited to Boris Belousov.In 1951, while trying to find the non-organic analog to the Krebs cycle, he noted that in a mix of potassium bromate, cerium(IV) sulfate, malonic acid, and citric acid in dilute sulfuric acid, the ratio of concentration of the cerium(IV) and cerium(III) ions ...
Mean squared displacement for different types of anomalous diffusion Anomalous diffusion is a diffusion process with a non-linear relationship between the mean squared displacement (MSD), r 2 ( τ ) {\displaystyle \langle r^{2}(\tau )\rangle } , and time.
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 ...