Hi,
I am trying to generate a wave pulse in nano wire (using LAMMPs). The wave pulse is a product of Sin(2*PI*q*dt) and Cos(2*PI*q*dt) function. Where q is the frequency and dt is the time.
The wave pulse is applied as a time dependent force at the middle of the nano wire to generate a wave along the length.
I have recorded the displacement profile with time at two locations along the length, I have noticed that the shape and magnitude of the displacement profile generated by the wave changes from one location to another for the complete time period.
In principle, the shape and magnitude of the displacement generated by the wave pulse should remain the same at all points with time, unless there is a damping, which causes dispersion.
Can any one comment, why there is a dispersion noticed in the displacement profile (the amplitude is reducing with time from one location to another and also the shape is distorting)?
Is there a damping in LAMMPs or My simulation is in correct.
Your help and comments are highly appreciated,
Best,
Dispersion and Losses are always coupled; Karmers-Kronig relationship! There is loss occurring in the material as the wave is propagating which is giving rise to dispersion. Losses are dependent on frequency, amplitude (nonlinearity) of the wave and material properties and size of its constituent. Nano wires are not lossless medium!
Thank you Vikash,
I am using Cu nano wire, frequency is of order 10 THz and amplitude is 2. I was wondering if LAMMPS considers damping, but nowhere it is mentioned in the LAMMPS manual regarding damping option.
can you suggest, how can I make the damping zero in my simulation, so that the wave does not change its shape and amplitude. I mean I want to reproduce the same wave after certain time at different location...
I know about wave propagation and dispersion, but have none idea about LAMMPs. Any decent simulation package must have damping incorporated in it, otherwise why it would be? If it lets you select the material; then may be the material parameters are taken into account automatically?
If you want to force zero dispersion; then you may have to multiply by suitable frequency dependent coefficient. See equation 4.1 to 4.3 in this link: http://arxiv.org/pdf/1508.00638.pdf
It is likely that you are observing your nanowire act as a wave guide, and therefore are observing dispersive wave propagation. From a wave propagation perspective, dispersion is a result of wave propagation in bounded media, not material damping. The boundary conditions (i.e., nanowire diameter, material the nanowire is in contact with, tractions (or tractionless) applied to boundaries, etc.) control how the guided mode sets up.
For isotropic plates, there are the Rayleigh-Lamb equations; there also exist rod modes, etc. A good place to start is to look at the ratio of the smallest dimension in your part (i.e., diameter of the nanowire) to the wavelength of the ultrasonic wave. A quick calculation assuming (f = 1 THz) and a bulk ultrasonic velocity of copper between 2000 m/s to 5000 m/s suggests the ultrasonic wavelengths are on the order of 2-5 nm. This would seem to be on the order of magnitude of a nanowire, and strongly suggest that your ultrasonic waves are propagating as guided rod wave modes.
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