As far as I understood, molecular simulation works in two types of scales:

  1. temporal scale - how much time is required to simulate the model.
  2. spatial scale - how much memory-space is required to simulate the model.

The more accurate the model is, the more time and memory it takes. I believe this is called the scale mismatch problem. Connectedly, Bridging of scale would refer to adopting techniques to simulate a more accurate model in less time and use less space in the memory.

Are my definitions of the bolded terms correct?

If YES, can you supply me with a reference that I can use to support my definitions? I haven't found a reference that explicitly states these definitions.


  1. Scale-mismatch => GoogleScholar search
  2. Bridging of scale => Computational Multiscale Modeling of Fluids and Solids - Theory and Applications, Page-253
  • 1
    $\begingroup$ Can you point to an example paper(s) where these terms were these terms were used? This would help to show that these are standard terms with a consistent definition that maybe we can infer from context even if it isn't explicitly stated. $\endgroup$
    – Tyberius
    Commented Jul 18, 2022 at 13:01

2 Answers 2


Multi-scale modelling refers to the modelling of a physical problems which involves the description of different time or space-scales. Think for example to the modelling of nonequilibrium dynamics of electrons and ions initiated by ultra-short laser pulses in condensed-matter.

At first a lase pulse of few femto-seconds (fs) may excite electrons in a nonequilibrium configuration. There will be a coherent electron dynamics on the time scale of few hundreds of fs. Coherences will eventually de-phase leading to non-coherent and non-thermal electron population dynamics. Electrons will reach a quasi-equilibrium statistical distribution at very high temperature and, on an even longer time-scale cool down. Due to the interaction with the lattice, also the phonons will evolve, in general on a longer time-scale compared to the electrons. There could be coherent phonons at first and later non-termal phonon distributions, phonon heating and cooling. On even longer time scales both electron diffusion may take place, as well as structural distortion of the material. See here for more info: Nature Materials

While a fully quantum mechanical approach could describe all these phenomena, the approach would be non feasible for all the phenomena (and also not needed). The fully quantum description would be useful to capture the initial coherent dynamics, Boltzmann rate equations to capture the non thermal occupations, effective temperature models to describe the cooling processes, etc ...

However each of the above mentioned approaches works on a specific aspect and on a different time scale. This means that there is a time (and space) scale mismatch. Putting together different kind of simulations is what I would call a "many scales" approach, i.e. you kind of partition the physical process in sub-problems. What a real "multi scales" approach would do instead, is to somehow interface the different approaches and enable one method to continue from the output of the previous. A "multi scales" approach would enable "scale bridging" physical problems with a "scale mismatch".

  • $\begingroup$ @user366312 Davide does not need to write a single letter more for you. I suggest that you ask what scale-bridging is in a new question. $\endgroup$ Commented Jul 25, 2022 at 13:53
  • $\begingroup$ I added a very short sentence at the end of the reply. $\endgroup$ Commented Jul 26, 2022 at 8:29
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    $\begingroup$ @user366312 ok but please don't tell users what they "need" to do :) $\endgroup$ Commented Jul 26, 2022 at 11:57

Scale-mismatch, more appropriately, Scale-gap, is the difference between the scale at which chemical or physical laws are available and the scales at which we want to study a phenomenon.

This gap can be present either on the temporal scale or spatial scale.

enter image description here

Image source: https://www.mdpi.com/1422-0067/19/11/3401/htm

For instance, in the above image, protein-folding takes place at the "seconds" time scale. However, the chemical or physical laws governing protein-folding occur at the femtosecond or picoseconds scale.

Therefore, this is an example of a temporal scale gap.


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