Choosing appropriate length scale in condensed matter

[Sivasakthi]

Hi..
I was reading some papers on continuum dynamics and its application to various material dynamics. The determination of macroscopic behavior is being studied , considering phononic interactions. As a material consists of phonons of various wavelengths, it is necessary to account for various length/ dimensional structures internally like dealing with micro, meso and nano levels and analyzing what are the effects or errors or uncertainties produced by these length scales.
One thing I could not understand is, how is it possible to account all these various dimensional effects all together and obtain macroscopic analysis. Even if we do so, will that be right? Or is there any common method to implement these different variations in a single way?
Can anybody help me please?
Regards

 

[M Quack]

Hi..
I was reading some papers on continuum dynamics and its application to various material dynamics. The determination of macroscopic behavior is being studied , considering phononic interactions. As a material consists of phonons of various wavelengths, it is necessary to account for various length/ dimensional structures internally like dealing with micro, meso and nano levels and analyzing what are the effects or errors or uncertainties produced by these length scales.

The characteristic length scale of phonons are interatomic distances. The phonon dispersion is defined inside the Brillouin zone of reciprocal space.

Having said that, you get all kind of effects at larger length scales, e.g. phonon scattering at grain boundaries (length scale of ~micrometer), etc. So go get a realistic model of an engineering material you do have to take into account all length scales from interatomic to macroscopic.

One thing I could not understand is, how is it possible to account all these various dimensional effects all together and obtain macroscopic analysis. Even if we do so, will that be right? Or is there any common method to implement these different variations in a single way?
Can anybody help me please?
Regards

I do not know if this is possible at all. I have the impression that one tries to understand what is happening on one or two length scales, and then develop an effective continuum model that can be incorporated in the next one or two length scales up.

But then again I am not an expert. Maybe somebody else here can give a more qualified answer?

 

[Sivasakthi]

Even if we do have a method, how will that allocate all the scales? How can we know about the degree or a range to which a particular scale has importance?
I believe there should be some critical length scale for dealing with a situation like this..