iMechanica - MD - Comments

What MD program do you use?

Lianqing Zheng — Mon, 30 Jun 2008 10:20:49 -0400

What MD program do you use? If it's home-made, you need to do
some coding (of course, know the theory first). Langevin dynamics can
be found everywhere: any MD book, or simply google.

Also, if possible, try to thermostat the atoms in the outer layer .

Using Langevin thermostat..how can I..

prasad_nano — Mon, 30 Jun 2008 10:11:55 -0400

Prasad MVD

Langevin

Lianqing Zheng — Mon, 30 Jun 2008 09:40:52 -0400

Try Langevin dynamics. It's probably the best thermostat for small systems.

Questions for you

Adrian S. J. Koh — Sun, 29 Jun 2008 21:51:57 -0400

Hi Prasad,

I have performed MD simulations on NVT ensembles. I need to clarify the
following with you:

1. Exactly how many atoms did you thermostated?

2. How did you take care of the kinematics of the atoms at the interface
between the thermostated and un-thermostated atomic layers?

3. I think you are aware that, by partially thermostating your CNT, you are
handling an MD problem with mixed ensembles (NVT & NVE). Hybrid
ensembles frequently leads to incorrect physical properties inferred from the
atomic data. Did you account for the mixed ensemble in the statistical
mechanical sense?

4. I gather that you are trying to obtain a target temperature for the
entire CNT by thermostating two-thirds of the CNT. Correct me if I am wrong.
But if I read it correctly, may I ask, why are you doing this? It didn't seem
physically possible to thermostat a part of the problem and expect the entire
problem to approach the targeted temperature.

Thank you.

Adrian KSJ

many thanks

Dong Kong — Tue, 22 Jan 2008 23:53:28 -0500

Dear Prof. Chen and Prof. Eom,

Thanks a lot for your very useful comments.

Continuum description on protein molecules

Kilho Eom — Mon, 10 Sep 2007 03:32:13 -0400

As far as I know, there are very few works on continuum description on protein molecules. Very recently, as Prof. Chen commented, he and his collaborators have proposed the multi-scale model of protein, i.e. mechano-sensitive ion channel, based on combination of MD simulation and FE model (See here).

Except Prof. Chen's work, the continuum descriptions on single-molecule chain (e.g. DNA) have been proposed by Kratky and Porod, renowned as Worm-Like-Chain (WLC) model. WLC model has succeeded in depicting the nonlinear elastic behavior of single-stranded DNA based on pulling experiments by Bustamante group (See paper by Bustamante et al., Science, 265, p1599-1600, 1994). Such model has recently enabled Frey and coworkers to study the mechanical properties (bending properties) of microtubule based on real-time observation of microtubule tip connected to a bead with optical apparatus (for details, see here). Based on their experiments with comparison to WLC model, they showed that WLC model allows for depicting the bending behavior of microtubule as a function of contour length.

Such chain model have also allowed me and my advisors (Prof. Makarov and Prof. Rodin) to understand the mechanical properties of cross-linked single-molecule chain, which provides the insight into remarkable mechanical properties of some mechanical proteins such as titin Ig domain (See Refs: Ref at JPC and Ref at PRE).

More recently, the single-molecule experiments on spider silk fiber and spider silk protein by Hansma and coworkers have revealed that the mechanical behaviors of both spider silk fiber and spider silk protein are well delineated by scaling law, indicating that fiber consists of single-molecule chain in a hierarchical manner (See here). Such experimental results have resulted in the emergence of hierarchical model of spider silk fiber based on single-molecule chain (e.g., See here). Such hierarchical model based on single-molecule chain such as WLC has enabled the quantitative descriptions on the nonlinear elastic behavior of biological gels such as actin, collagen, neurofilament, etc. (for details, see here). In the issue of last week (Aug. 30, 2007) at PRL, the cover article is about the model of a fiber made of WLC chains with chirality (see here).

As shown above, the continuum-like model for a fiber made of single-molecules in a hierarchical manner has been one of hot issues in recent modeling researches in biomolecules. Such issue may be intriguing mechanicist, physicist, and chemists whose backgrounds are based on both theory and experiments.

We have some preliminary works in this area

Xi Chen — Fri, 07 Sep 2007 08:54:38 -0400

See http://www.imechanica.org/node/92 which is a top-down approach. More publications along such direction are forthcoming.

Vikas, The paper by M. Zhou

Arun K. Subramaniyan — Wed, 21 Feb 2007 01:04:40 -0500

Vikas,

The paper by M. Zhou looks at the virial stress from a linear momentum balance formulation. However, the question of the thermal stress for a system at thermal equilibrium is not addressed in that paper. It is in this regard that I said we are not aware of any analytical proof.

An interesting paper by Dommelen commenting on the above paper by M Zhou can be found here :

http://www.eng.fsu.edu/~dommelen/papers/virial/

Yes indeed and the proof has been published in the Royal Society

vikastomar — Tue, 20 Feb 2007 23:54:15 -0500

Please see the proof in the following reference:

M. Zhou, A New Look at the Atomic Level Virial Stress--On Continuum-Molecular System Equivalence, Proceedings of the Royal Society of London A; 459, 2347-2392, 2003

The above article can be downloaded from http://diva.me.gatech.edu.

Analytical proof

Arun K. Subramaniyan — Tue, 20 Feb 2007 16:10:34 -0500

Indeed at 0 Kelvin the virial stress reduces to just the potential part. However at elevated temperature, without the velocity term in the stress definition, we cannot match the stress state to a continuum cauchy stress definition. You can check by performing simple MD simulations as detailed above. We have not tried to prove this analytically yet.

Virial Stress

Arun K. Subramaniyan — Tue, 20 Feb 2007 15:58:48 -0500

Dr. Gray,

Thanks for pointing me to your papers. I was aware of these papers. In fact many of these papers got us interested in the debate on virial stress.

Before getting into the analytical aspects of this problem, we thought it best to see if a simple thermoelastic problem can shed some light on this issue. The outcome of this exercise is what I have posted here. Although there are many alternate measures of stress (without velocity) at the atomic level, I am not sure if they can produce the actual continuum stress in the three simple cases we used. It would be interesting to see if the alternate measures of atomic stress produce the same stress state as that produced by the total virial stress (which in this case is the same as the continuum cauchy stress).

Can we analytically approve it?

szhang1 — Tue, 20 Feb 2007 01:28:58 -0500

We have recently written a paper in IJNME, in which we proved that the Virial stress is the Cauchy-stress for crystal materials at 0 K. If kinetic part is taken into account, I wonder if we can mathematically approve that. Our paper is now on-line and titled as

A Bridging Domain and Strain Computation Method for Coupled Atomistic-Continuum Modeling of Solids.

written by Sulin Zhang, Roopam Khare, Qiang Lu, and Ted Belytschko

you should have a look at our papers on this subject

Gary L. Gray — Mon, 19 Feb 2007 13:20:06 -0500

See:

Pedro C. Andia, Francesco Costanzo, and Gary L. Gray (2006) "A Classical Mechanics Approach to the Determination of the Stress-Strain Response of Particle Systems," Modelling and Simulation in Materials Science and Engineering, 14, pp. 741–757.

Pedro C. Andia, Francesco Costanzo, and Gary L. Gray (2005) "A Lagrangian-Based Continuum Homogenization Approach Applicable to Molecular Dynamics Simulations," International Journal of Solids and Structures, 42(24-25), pp. 6409–6432.

Francesco Costanzo, Gary L. Gray, and Pedro C. Andia (2005) "On the Definitions of Effective Stress and Deformation Gradient for Use in MD: Hill's Macro-homogeneity and the Virial Theorem," International Journal of Engineering Science, 43(7), pp. 533–555.

Francesco Costanzo, Gary L. Gray, and Pedro C. Andia (2004) "On the Notion of Average Mechanical Properties in MD Simulation via Homogenization," Modelling and Simulation in Materials Science and Engineering, 12, pp. S333–S345.

In particular, the first reference has a nice discussion of the relation between the effective Cauchy stress and the virial stress.

All the best,
Gary

thanks for the pre-print

Pradeep Sharma — Mon, 19 Feb 2007 09:29:38 -0500

Arun, thanks for the pre-print. I will take a look at this.