Multi-particle collision dynamics - Revision history

Carl McBride: Slight tidy + some more inetrnal links.

2009-11-10T10:27:42Z

Slight tidy + some more inetrnal links.

← Older revision		Revision as of 12:27, 10 November 2009
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	~~{{Stub-general}}~~		'''Multi-particle collision dynamics''' (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids", Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science '''221''' p. 1 (2009)]</ref>, is a particle-based mesoscale [[Computer simulation techniques \|simulation technique]] for [[complex fluids]] <ref>[http://dx.doi.org/10.1063/1.478857 A. Malevanets and R. Kapral "Mesoscopic model for solvent dynamics", Journal of Chemical Physics '''110''' pp. 8605-8613 (1999)]</ref>. Coupling of embedded particles to the [[Coarse graining \|coarse-grained]] solvent is achieved through [[molecular dynamics]] <ref>[http://dx.doi.org/10.1063/1.481289 A. Malevanets and R. Kapral "Solute molecular dynamics in a mesoscale solvent", Journal of Chemical Physics '''112''' pp. 7260-7269 (2000)]</ref>.
	~~[[Category:Computer simulation techniques]]~~

	Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids", Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science '''221''' p. 1 (2009)]</ref>, is a particle-based mesoscale simulation technique for complex fluids <ref>[http://dx.doi.org/10.1063/1.478857 A. Malevanets and R. Kapral "Mesoscopic model for solvent dynamics", Journal of Chemical Physics '''110''' pp. 8605-8613 (1999)]</ref>. Coupling of embedded particles to the coarse-grained solvent is achieved through [[molecular dynamics]] <ref>[http://dx.doi.org/10.1063/1.481289 A. Malevanets and R. Kapral "Solute molecular dynamics in a mesoscale solvent", Journal of Chemical Physics '''112''' pp. 7260-7269 (2000)]</ref>.
	==Method of simulation==		==Method of simulation==
	The solvent is modelled as a set of <math>N</math> point particles of mass <math>m</math> with continuous coordinates <math>\vec{r}_{i}</math> and velocities <math>\vec{v}_{i}</math>. The simulation consists of streaming and collision steps.		The solvent is modelled as a set of <math>N</math> point particles of mass <math>m</math> with continuous coordinates <math>\vec{r}_{i}</math> and velocities <math>\vec{v}_{i}</math>. The simulation consists of streaming and collision steps.
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	During the streaming step, the coordinates of the particles are updated according to		During the streaming step, the coordinates of the particles are updated according to

	<math>\vec{r}_{i}(t+\delta t_{\mathrm{MPC}}) = \vec{r}_{i}(t) + \vec{v}_{i}(t) \delta t_{\mathrm{MPC}}</math>		:<math>\vec{r}_{i}(t+\delta t_{\mathrm{MPC}}) = \vec{r}_{i}(t) + \vec{v}_{i}(t) \delta t_{\mathrm{MPC}}</math>

	where <math>\delta t_{\mathrm{MPC}}</math> is a chosen simulation time step which is typically much larger than a molecular dynamics [[time step]].		where <math>\delta t_{\mathrm{MPC}}</math> is a chosen simulation [[time step]] which is typically much larger than a molecular dynamics time step.

	After the streaming step, interactions between the solvent particles are modelled in the collision step. The particles are sorted into collision cells with a lateral size <math>a</math>. Particle velocities within each cell are updated according to the collision rule		After the streaming step, interactions between the solvent particles are modelled in the collision step. The particles are sorted into collision cells with a lateral size <math>a</math>. Particle velocities within each cell are updated according to the collision rule
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	where <math>\vec{v}_{\mathrm{CMS}}</math> is the centre of mass velocity of the particles in the collision cell and <math>\hat{\mathbf{R}}</math> is a rotation matrix. In two dimensions, <math>\hat{\mathbf{R}}</math> performs a rotation by an angle <math>+\alpha</math> or <math>-\alpha</math> with probability <math>1/2</math>. In three dimensions, the rotation is performed by an angle <math>\alpha</math> around a random rotation axis. The same rotation is applied for all particles within a given collision cell, but the direction (axis) of rotation is statistically independent both between all cells and for a given cell in time.		where <math>\vec{v}_{\mathrm{CMS}}</math> is the centre of mass velocity of the particles in the collision cell and <math>\hat{\mathbf{R}}</math> is a rotation matrix. In two dimensions, <math>\hat{\mathbf{R}}</math> performs a rotation by an angle <math>+\alpha</math> or <math>-\alpha</math> with probability <math>1/2</math>. In three dimensions, the rotation is performed by an angle <math>\alpha</math> around a random rotation axis. The same rotation is applied for all particles within a given collision cell, but the direction (axis) of rotation is statistically independent both between all cells and for a given cell in time.

	If the structure of the collision grid defined by the positions of the collision cells is fixed, [[Galilean invariance]] is violated. If is restored with the introduction of a random shift of the collision grid <ref>[http://dx.doi.org/10.1103/PhysRevE.67.066705 T. Ihle and D. Kroll "Stochastic rotation dynamics. I. Formalism, Galilean invariance, and Green-Kubo relations", Physical Review E '''67''' 066705 (2003)]</ref>.		If the structure of the collision grid defined by the positions of the collision cells is fixed, [[Galilean invariance]] is violated. It is restored with the introduction of a random shift of the collision grid <ref>[http://dx.doi.org/10.1103/PhysRevE.67.066705 T. Ihle and D. Kroll "Stochastic rotation dynamics. I. Formalism, Galilean invariance, and Green-Kubo relations", Physical Review E '''67''' 066705 (2003)]</ref>.

	==References==		==References==
	<references/>		<references/>
			[[Category:Computer simulation techniques]]

Teegee at 10:57, 8 November 2009

2009-11-08T10:57:38Z

← Older revision		Revision as of 12:57, 8 November 2009
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	{{Stub-general}}		{{Stub-general}}
			[[Category:Computer simulation techniques]]

	Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids", Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science '''221''' p. 1 (2009)]</ref>, is a particle-based mesoscale simulation technique for complex fluids <ref>[http://dx.doi.org/10.1063/1.478857 A. Malevanets and R. Kapral "Mesoscopic model for solvent dynamics", Journal of Chemical Physics '''110''' pp. 8605-8613 (1999)]</ref>. Coupling of embedded particles to the coarse-grained solvent is achieved through [[molecular dynamics]] <ref>[http://dx.doi.org/10.1063/1.481289 A. Malevanets and R. Kapral "Solute molecular dynamics in a mesoscale solvent", Journal of Chemical Physics '''112''' pp. 7260-7269 (2000)]</ref>.		Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids", Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science '''221''' p. 1 (2009)]</ref>, is a particle-based mesoscale simulation technique for complex fluids <ref>[http://dx.doi.org/10.1063/1.478857 A. Malevanets and R. Kapral "Mesoscopic model for solvent dynamics", Journal of Chemical Physics '''110''' pp. 8605-8613 (1999)]</ref>. Coupling of embedded particles to the coarse-grained solvent is achieved through [[molecular dynamics]] <ref>[http://dx.doi.org/10.1063/1.481289 A. Malevanets and R. Kapral "Solute molecular dynamics in a mesoscale solvent", Journal of Chemical Physics '''112''' pp. 7260-7269 (2000)]</ref>.
	==Method of simulation==		==Method of simulation==

Teegee: User:Teegee/Multi-particle collision dynamics moved to Multi-particle collision dynamics

2009-11-08T10:52:44Z

User:Teegee/Multi-particle collision dynamics moved to Multi-particle collision dynamics

← Older revision	Revision as of 12:52, 8 November 2009
(No difference)

Teegee at 10:52, 8 November 2009

2009-11-08T10:52:03Z

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 Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids", Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science '''221''' p. 1 (2009)]</ref>, is a particle-based mesoscale simulation technique for complex fluids <ref>[http://dx.doi.org/10.1063/1.478857 A. Malevanets and R. Kapral "Mesoscopic model for solvent dynamics", Journal of Chemical Physics '''110''' pp. 8605-8613 (1999)]</ref>. Coupling of embedded particles to the coarse-grained solvent is achieved through [[molecular dynamics]] <ref>[http://dx.doi.org/10.1063/1.481289 A. Malevanets and R. Kapral "Solute molecular dynamics in a mesoscale solvent", Journal of Chemical Physics '''112''' pp. 7260-7269 (2000)]</ref>.
 ==References==
 <references/>

Teegee: New page: Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler...

2009-11-08T10:16:08Z

New page: Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler...

New page

Multi-particle collision dynamics (MPC), also known as stochastic rotation dynamics (SRD)<ref>[http://dx.doi.org/10.1007/978-3-540-87706-6_1 G. Gompper, T. Ihle, K. Kroll and R. G. Winkler "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids", Advanced Computer Simulation Approaches for Soft Matter Sciences III, Advances in Polymer Science '''221''' p. 1 (2009)]</ref>, is a particle-based mesoscale simulation technique for complex fluids <ref>[http://dx.doi.org/10.1063/1.478857 A. Malevanets and R. Kapral "Mesoscopic model for solvent dynamics", Journal of Chemical Physics '''110''' pp. 8605-8613 (1999)]</ref>. Coupling of embedded particles to the coarse-grained solvent is achieved through [[molecular dynamics]] <ref>[http://dx.doi.org/10.1063/1.481289 A. Malevanets and R. Kapral "Solute molecular dynamics in a mesoscale solvent", Journal of Chemical Physics '''112''' pp. 7260-7269 (2000)]</ref>.
==References==
<references/>