Stochastic Rotation Dynamics (SRD) and Multi-Particle Collision Dynamics (MPC) are used with great success in soft matter physics to model mixtures of solvents, colloids, suspensions, etc. in fluids. I was wondering if there is any particular reason, or set of reasons why these same techniques could not be used in astrophysical settings such as in the process of star and planet formation, the dynamics of interstellar clouds, or even at the scale of galaxies wherein different types of stars, dark matter, planets, etc. become the "particles" in the simulation? Perhaps in the case of galaxy dynamics, the fact that it is a universally attractive gravitational force causing the "collisions" it wouldn't work, but what about the case of protoplanetary disks, where the collisions would seem to be almost the same as the case of soft matter physics.
Finally, are there pitfalls and downsides to the use of SRD? What should one be on the lookout for? Are there well known problems that need to be compensated for in order to get a realistic simulation?
Any information on SRD and its use in soft matter physics would be welcome as well as discussion on extending it to astrophysical applications.
SRD was introduced as an alternative solver for fluctuating hydrodynamics. It is based of artificial but efficient interactions between particles and acts like a solvent with both correct hydrodynamic interactions and consistent thermal fluctuations.
Its strength is also its downfall: it works great on scales where thermal fluctuations are essential or at least not harmful. As a rule of thumb, the Peclet number should be less than 10 or so. Thus, for soft matter applications such as polymers or small colloids with diameters of 1 micro and less, SRD is fine. But if you have a situation with Peclet numbers of 1000 or more, SRD is inefficient because one has to make the objects one embeds in the fluid/gas very large compared to the box size of SRD.
A SRD box typically contains 3 to 20 particles.
In other words, a lot of SRD particles need to collide with an embedded object to reduce the erratic Brownian motion of the embedded object. An example, SRD should not be used for, is pneumatic transport of centimeter-sized objects driven by pressured air. Here, the thermal fluctuations of the SRD-gas are counterproductive, they prevent the formation of plugs which are seen in experiments.
As far as I know, SRD has not been used in Astrophysics. I see a number of reasons.
First, as you said one needs long-range gravitational forces. The strength of SRD is based on very short-ranged interactions, which basically just cover the size of a lattice cell. Of cause, one could add gravity but then I don't see much difference to conventional Molecular Dynamics. Second, even in situations where gravity is not
that relevant, you still have the issue of the huge fluctuations I described above.
In situations with small or no fluctuations, I'd rather use another alternative solver like Lattice-Boltzmann, where fluctuations can be added per hand if needed (see papers by Mike Cates, Alexander Wagner, Tony Ladd).
Since you ask about pitfalls of SRD, here are a few more:
a) SRD has inertia and works well for Reynolds numbers (Re) around one, hence for turbulence (huge RE) or Stokes-flow (Re=0) it's not the best approach. If one wants to go to the Stokes-limit with SRD, one has to choose very small time steps. This makes the simulations very slow and leads to another issue : regular SRD does not conserve angular momentum in the collision step. For small time steps (=small mean free path)
this leads to an asymmetric stress tensor and causes other problems (see paper by Ingo Goetze and Gerhard Gompper in PRE). This problem can be remedied at the cost of making the code slower (by about a factor of 2 in 2D and a factor of 3-4 in 3D). Thus, for applications at very small Re, it's better to use Oseen tensor/Brownian dynamics approaches.
d) We (E. Tuzel, D. Kroll and me) once tested SRD for rarified flow (large Knudsen number), tried to match to a real gas and once again it turned out that SRD has barely any advantage compared to the traditional approach for this: Direct Simulation Monte Carlo, where binary collisions are used.
In summary, SRD is easy to program, is fun to play with, can be nicely treated analytically and is great for soft matter applications like star polymers in shear flow or sedimentation of small colloids. But for other applications, be cautious.
As I am a novice at this type of thing I hope you will forgive me for asking for a quick example. Suppose we looked at the Rings of Saturn, where the particles are water ice ranging from 1cm to 10m in size but are far enough apart that you could fix your box size to contain your range of from 3 to 20 particles on average. Of course, they are in an overall gravitational field from Saturn, but in a frame centered in the ring and rotating with it this overall field would seem to become irrelevant compared to more local interactions. The main forces in the ring would seem to be binary collisions,thermal fluctuations internal to the ring particle (from tidal forces, torque from the magnetic field, absorbing the radiation field), interactions with the magnetic field of Saturn, along with interactions caused by the gravitational tidal forces from all of the various moons, and local gravitational interactions between particles. There are also collisions with the interplanetary dust particles but I wouldn't expect they would be that important (?).
It seems (from a cursory glance at the literature) that most researchers are using mainly many particle 2-d and 3-d N body simulations as in http://arxiv.org/abs/1006.1643, http://arxiv.org/abs/1210.3358, and http://arxiv.org/abs/1006.1643 as well as calculations using Fokker-Planck equations (http://ntrs.nasa.gov/search.jsp?R=19740002673) and probably other calculations.
Do you think SRD would work in this situation? Probably your answer is no, but if one could modify it in some way to make it work would there be any advantage to using it even in that case? For example is it more efficient? Faster? Simpler? Easier to modify? or anything else that would entice one to even bother with it as opposed to just the usual N-body gravitational and collision simulations?
In the case your answer was "no" to Saturn's rings, are there any other conceivable astrophysical situations where you might guess SRD could be applicable? For example planetary nebulae where the medium is a mixture of gas and very small dust particles (http://arxiv.org/abs/astro-ph/9911006)? or what about planetary atmospheres? or very large scale situations such as galaxies where you could use a huge box size containing a few stars with a background gas of dark matter? or anything else?
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