Difference between revisions of "Algorithms for Long Range Interactions"

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(Useful references)
(How to mimic bulky systems with long range interactions)
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The straight cut-off (sometimes including a shift) of the long-range interactions have been   
 
The straight cut-off (sometimes including a shift) of the long-range interactions have been   
observed to lead to many unphysical artifacts  in the simulations of bulky systems. Although  
+
observed to lead to many unphysical artifacts  in the simulations of bulky systems. Although
no perfect solution has been found, there exist some approaches to tackle with the problem:
+
no perfect solution has been found, there exist some approaches to tackle with the problem:
 
* Reaction Field Methods.
 
* Reaction Field Methods.
 
* Periodic Boundary Conditions (artificial periodicity): Lattice-Sum Methods
 
* Periodic Boundary Conditions (artificial periodicity): Lattice-Sum Methods
 
* Hybrids of the previous two approaches, eg. LSREF (Heinz2005).  
 
* Hybrids of the previous two approaches, eg. LSREF (Heinz2005).  
* MEMD – Maxwell Equations Molecular Dynamics (*2)
+
* MEMD – Maxwell Equations Molecular Dynamics (see ref.2)
  
 
==  Periodic Boundary Conditions  ==
 
==  Periodic Boundary Conditions  ==

Revision as of 00:23, 15 January 2008

Long Range interactions page is under construction

Long Range Interactions & the root of the problem

Formally a potential is defined to be short ranged if it decreases with distance  r quicker or similar than  \frac{1}{r^{d-1}} where  d is the dimensionality of the system. Electrostatic, gravitatory and dipolar interactions, present in many physical systems, are examples of long range interactions. When long range intgeractions are present in a system, the weight of the interactions comming from far particles is non negligible. This is due to the type of decay of the interaction with the distance: despite the particle-particle interaction decreases with the distance, the number of interactions increases in such way that the total contribution of the far particles may have a weight as large as the one due to the interaction of neighbouring particles.

The limited power of current computers makes impossible simulate macroscopic bulky systems. Small systems have a large surface vs volume ratio and therefore surface effects may govern the physics of the system. When long-range forces are present, the scenario to mimic bulky systems is even worse because we will neglect a substantial part of the long-range interaction.

Then, why we don't wait a little bit until computers become more powerful? Even if Moore´s law was able to hold on indefinitely, we would still need around two centuries to be able to tackle with systems of the size of about one cubic centimeter. Therefore, it is clear that we need to do some sort of approach in order to mimic bulky systems right now.

How to mimic bulky systems with long range interactions

The straight cut-off (sometimes including a shift) of the long-range interactions have been observed to lead to many unphysical artifacts in the simulations of bulky systems. Although no perfect solution has been found, there exist some approaches to tackle with the problem:

  • Reaction Field Methods.
  • Periodic Boundary Conditions (artificial periodicity): Lattice-Sum Methods
  • Hybrids of the previous two approaches, eg. LSREF (Heinz2005).
  • MEMD – Maxwell Equations Molecular Dynamics (see ref.2)

Periodic Boundary Conditions

Frequently, periodic boundary conditions are used in simulations in order to approach bulk systems within the limits of currently available computers.

...

Long Range interactions page is under construction

Links

Scientists

Collaborators

Publications


Useful references

[Heinz2005] Heinz et al , JCP 123, 034107, (2005)

[2] RottlerMaggs and DunwegPasichnyk,2004


Long Range interactions page is under construction