Organisers

• Antonio Scala (SMC-ISC CNR-INFM Roma1)
• Cristiano De Michele (SOFT INFM-CNR and Dip. di Fisica - Univ. di Roma )

Supports

 SimBioMa

 CECAM

 COST - MolSimu

 COST - MolSimu

Description

It is currently possible in an efficient way to calculate the distance between two hard convex objects with a generic shape and to predict their collision [ED4HB]. The first application of such algorithms has been tested on the molecular dynamics of a systems of classical hard ellipsoids of revolution [DeMicheleHE06]. The same methods allows to simulate shaped step interactions[DeMichelSticky06]. The recent introduction of an algorithm for the rotation of objects with a generic inertia tensor completes such approach [vanZonCondMat]. Moreover,following the lines of [BD4HS], it seems to be possible to extend classical Molecular Dynamics simulation to the Brownian Dynamics simulation of interest in the field of colloids and suspensions.

A renewed interest for assemblies of hard shaped objects stems from the field of colloidal science; nevertheless,simulations of the dynamics of hard objects [Allen89,Allen93] needs to be revived and theoretical investigations on the dynamics of shaped objects reconsidered. Besides, we believe that there is a potential interest in several cross-disciplinary scientific and technological fields. Such belief stems from an analysis of the current investigations in several fields:

* theory of molecular liquids: while hard-spheres are widely
understood and form the reference system for many theories of
the dynamics and the statics, there no such understanding for
shaped objects [GrayGubbinsBook]

* granular fluids: simulations of shaped particles are
practically limited to hard needles

* geo-mechanics: soil rheology employs mostly models and
simulations where grains are spherical or, in the most
sophisticated cases, ellipsoidal [Ouadfel99,Ouadfel01].
The new rheology introduced by switching from spheres to
elongated objects should induce to take account of shape as a
must, not as an optional.

* powders: same situation than in geo-mechanics
[Ouadfel99,Antony04].

* fruit & vegetables: damages due to processing, transportation
and handling are studied via simulations of spheres that
represent potatoes, tomatoes, apples [LoodtsMSTh]. Damages are
predicted looking at the collision points on the spheres; from
our experience on ellipsoids, we believe that at least the
collision frequency and the magnitude of the impact is deeply
influenced even by a little elongation of the objects.
Moreover, experiments for the mechanical characterizations
require at least a description in terms of an ellipsoidal
object [Cherng05].

* colloids and nanoassembly: despite the possibility of
controlling the shape of the particles [vanDillen2004], hard
spheres remain the main reference system.

* lyotropic liquid crystals: several overlap criteria
[Allen93,Het99,Blaak99] allow the simulation of specific hard
objects and point out the importance of the shape on the
appearance of new liquid-crystal phases. No general method to
investigate and quantify such effect exists for at least convex
objects.

* coarse-grained proteins: from experimental data, at least
Human Serum Albumin can be modeled as an hard ellipsoid with
a repulsive stepwise potential [Sjoberg97].

* go-models [Go83] for folding: rigid sub-sequences of a protein
could be modelled by a single shaped unit speeding up the
simulations.

* computer science, computer graphics, game design, robotics,
virtual reality: distance calculations and collision prediction
are the core for the realization of virtual environments and
robotic manipulations; again, most algorithm are specific and
not shape-independent [Ju01,Eberly01].

In conclusion, we believe that it is timely to promote a cross-disciplinary meeting on the subject in order to create an enlarged community sharing the same interests on simulating hard bodies

Scientific Objectives

Recently, new event-driven methods have been introduced allowing efficient simulations of systems with non-spherical shapes [DeMicheleHE06], patchy interactions [DeMichelSticky06] and rigid or elastic constrains [CiccottiDIA, delaPenaCondMat]; a simple but important algorithm for such simulations is the exact time-propagator for free rotations [vanZonCondMat].

Also for the problem of the simulation of the Brownian dynamics of hard bodies [CiccottiSDE] it has been recently shown that event-driven algorithms improve the performances of the simulations of hard-spheres [BD4HS] and colloidal rods [Tao05].

Although these new methods address directly and represent a solution for the problems highlighted in the description section, they are not yet widespread and are still in an initial phase.

Moreover, the simulation of hard bodies with non-spherical shape and/or with constraints would be of interests to fields as different as the theory of molecular liquids, granular assemblies simulations [Ouadfel99, Ouadfel01, Antony04], liquid crystals [Allen93, Het99, Blaak99], colloids and nanoassembly, proteins and polymers, food processing and manipulation [LoodtsMSTh], but also computer graphics, game design, robotics, virtual reality [Eberly01, Ju01].

We therefore believe that it is timely to promote a meeting on the subject by the community interested on simulating the dynamics of hard bodies. Our aim is to stimulate the introduction and diffusion of the new methods, to discuss on their applications and possible improvements, and hopefully to develop new techniques and ideas. The long-time goal is the creation of free software libraries for the collision of hard shaped objects in order to allow easy implementation of event-driven simulations first by the scientific community and then by industrial subjects.

References

[RapaBook] D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge University Press, Kwiecie/n 2004.

[Miller04] S. Miller, S. Luding. Event-driven molecular dynamics in parallel. Journal of Computational Physics, 193:306-316, 2004.

[Paul06] G. Paul. A Complexity O(1) Priority Queue for Event Driven Molecular Dynamics Simulations. ArXiv Physics e-prints, physics/0606226 2006.

[Allen89] M.P. Allen, D. Frenkel, J. Talbot. Molecular dynamics simulation using hard particles. Comput. Phys. Rep., 9:301-353, 1989.

[Allen93] M. P. Allen, G.T. Evans, D. Frenkel, B. M. Mulder. Hard convex body fluids. Adv. Chem. Phys., 86:1-166, 1993.

[Dokholyan98] N. V. Dokholyan, S. V. Buldyrev, H. E. Stanley, E. I. Shakhnovich. Discrete molecular dynamics studies of the folding of a protein-like model. ArXiv Condensed Matter e-prints, cond-mat/9812291 1998.

[DeMicheleHE06] C. De Michele, A. Scala, R. Schilling, F. Sciortino. Molecular correlation functions for uniaxial ellipsoids in the isotropic state. J. Chem. Phys., 124:104509, 2006.

[DeMichelSticky06] C. De Michele, G. Gabrielli, P. Tartaglia, F. Sciortino. Dynamics in the presence of attractive patchy interactions. J. Phys. Chem. B, 110:8064, 2006.

[CiccottiDIA] G. Ciccotti, G. Kalibaeva. Simulation of a diatomic liquid using hard spheres model. Journal of Statistical Physics, 115:701-714, 2004.

[delaPenaCondMat] L.H. de la Pena, R. van Zon, J. Schofield, S.B. Opps. Discontinuous molecular dynamics for semi-flexible and rigid bodies. ArXiv Condensed Matter e-prints, cond-mat/0607527, 2006.

[vanZonCondMat] R. van Zon, J. Schofield. Numerical implementation of the exact dynamics of free rigid bodies. ArXiv Condensed Matter e-prints, cond-mat/0607529, 2006.

[CiccottiSDE] Ciccotti G., G. Kalibaeva. Deterministic and stochastic algorithms for mechanical systems under constraints. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 362:1583-1594, 2004.

[BD4HS] A. Scala, C. De Michele, Th. Voigtmann. Event-driven brownian dynamics for hard spheres. ArXiv Condensed Matter e-prints, 2006.

[Tao05] Y.-G. Tao, W. K. den Otter, W. J. Briels. Kayaking and Wagging of Rods in Shear Flow. Physical Review Letters, 95(23):237802, 2005.

[Ouadfel99] H. Ouadfel, L. Rothenburg. An algorithm for detecting inter-ellipsoid contacts. Computers and Geotechnics, 24:245-263, 1999.

[Ouadfel01] H. A Ouadfel, L. Rothenburg. `stress-force-fabric` relationship for assemblies of ellipsoids. Mechanics of Materials, 33:201-221, 2001.

[Antony04] S.J. Antony, R.O. Momoh, M.R. Kuhn. Micromechanical modelling of oval particulates subjected to bi-axial compression. Computational Materials Science, 29:494498, 2004.

[Het99] Mengtao Het, Paul Siders. Monte carlo calculation of orientationally anisotropic pair distributions and energy transfer in a model monolayer. J. Phys. Chem., 94:7280-7288, 1999.

[Blaak99] R. Blaak, D. Frenkel, B. M. Mulder. Do cylinders exhibit a cubatic phase? Journal of Chemical Physics, 100:11652-11659, 1999.

[LoodtsMSTh] J. Loodts. The discrete element method for the simulation of granular flows. Praca magisterska, Agricultural Engineering, Katholieke Universiteit Leuven, Belgium, 2001.

[Eberly01] D. H. Eberly. 3D Game Engine Design. Academic Press, 2001.

[Ju01] M. Ju, J. Liu, S. Shiang, Y. Chien, K. Hwang, W. Lee. A novel collision detection method based on enclosed ellipsoid. Proceedings of 2001 IEEE Conference on Robotics and Automation, pag.21-26, 2001.