Advanced Simulation Methods SS 2015

Overview

Type

Lecture and Tutorials (2 SWS in total)

Lecturer

C. Holm, J. de Graaf, J. Smiatek, M. Fyta

Course language

English or German

Location

ICP, Allmandring 3; Room: tba.

Time

tba.

The course will consist of four modules supervised by C. Holm, J. de Graaf, J. Smiatek, and M. Fyta, that contain exercises, presentations, discussion meetings, and written reports, worked out in groups of up to four people.

A preliminary registration for this course is mandatory. Interested students write an Email to Jens Smiatek

Module 1: Christian Holm, Electrostatics and Lattice Boltzmann

Description

This module focuses on charged matter with electrostatic and hydrodynamic interactions. It should be taken in groups of three people. It consists of simulations, theory, a presentation and a short report on the simulation results. You only have to give one common presentation and hand in one report per group. It consists of three parts.

Contact

If you have any questions regarding the organisation or content of this module please do not hesitate to contact Florian Weik, Owen Hickey or Christian Holm. For questions regarding the practical part of the module and technical help contact Florian Weik or Owen Hickey.

Part 1: Electrostatics

Description

This part is about the theory of electrostatic algorithms for molecular dynamics simulations. It is concerned with state of the art algorithms beyond the Ewald sum, especially mesh Ewald methods. To this end the students should read the referenced literature and prepare a 20 minutes presentation. Hold the presentation with Christian Holm and discuss the content and open questions with him. The presentation should contain the students understanding of the P3M method as well as a discussion of its performance compared to other modern electrostatics methods.

Literature

• Markus Deserno, Christian Holm.
  How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines.
  The Journal of Chemical Physics 109:7678, 1998.
  [PDF] (307 KB) [DOI]
• Axel Arnold, Florian Fahrenberger, Christian Holm, Olaf Lenz, Matthias Bolten, Holger Dachsel, Rene Halver, Ivo Kabadshow, Franz Gähler, Frederik Heber, Julian Iseringhausen, Michael Hofmann, Michael Pippig, Daniel Potts, Godehard Sutmann.
  Comparison of scalable fast methods for long-range interactions.
  Physical Review E 88(6):063308, 2013.
  [PDF] (2.3 MB) [DOI]
• Axel Arnold, Christian Holm.
  Efficient methods to compute long range interactions for soft matter systems.
  In Advanced Computer Simulation Approaches for Soft Matter Sciences II, pages 59–109. Edited by C. Holm, K. Kremer. Part of Advances in Polymer Science.
  Springer, Berlin, 2005. ISBN: 9783540260912.
  [PDF] (1.1 MB) [DOI]

Part 2: Slit Pore

Description

This part is practical. It is concerned with the movement of ions in an charged slit pore. It is similar to the systems that are discussed in the Bachelors thesis of Georg Rempfer which is recommended reading. A slit pore consists of two infinite charge walls as shown in the figure to the right. In this exercise you should simulate such a system with ESPResSo. You are supposed to use a Lattice Boltzmann fluid coupled to explicit ions which are represented by charge Week-Chandler-Anderson spheres. In addition to the charge on the walls, the ions are also subject to an external electrical field parallel to the walls. Electrostatics should be handled by the P3M algorithm. A set of realistic parameters and an more in detail description of the system can be found in the thesis. You should measure the flow profile of the fluid and the density and velocity profiles of the ions. The case of the slit pore can be solved analytically either in the case of only counter ions (the so called salt free case) or in the high salt limit (Debye-Hueckel-Limit). Calculate the ion profiles in one or both of these cases and compare the results with the simulation.

Literature

Georg Rempfer, "Lattice-Boltzmann Simulations in Complex Geometries" (1.36 MB), 2010, Institute for Computational Physics, Stuttgart

• Kai Christian Grass.
  Towards realistic modelling of free solution electrophoresis: a case study on charged macromolecules.
  PhD thesis, Goethe-Universität Frankfurt am Main, 2008.
  [PDF] (5.3 MB)

Part 3: Electrophoresis of Polyelectrolytes

Description

In this part you simulate the movement of a charged polymer under the influence of an external electrical field and hydrodynamic interactions. Set up a system consisting of a charge polymer, ions with the opposite charge to make the system neutral and an Lattice Boltzmann fluid coupled the the ions and polymer. Apply an external field and measure the center of mass velocity of the polymer as a function of the length of the polymer for polymers of one to 20 monomers. Make sure the system is in equilibrium before you start the sampling. Compare your result to theory and experimental results (see literature).

Literature

• Kai Grass, Ute Böhme, Ulrich Scheler, Hervé Cottet, Christian Holm.
  Importance of Hydrodynamic Shielding for the Dynamic Behavior of Short Polyelectrolyte Chains.
  Physical Review Letters 100(9):096104, 2008.
  [PDF] (115 KB) [DOI]
• Kai Christian Grass.
  Towards realistic modelling of free solution electrophoresis: a case study on charged macromolecules.
  PhD thesis, Goethe-Universität Frankfurt am Main, 2008.
  [PDF] (5.3 MB)

Report

Please write together one report of 5 to 10 pages containing and discussing your simulation results from part 2 and 3.

Module 2: Joost de Graaf, Out-of-Equilibrium Systems and Active Matter

Description

This module focuses on out-of-equilibrium systems, specifically those comprised of active colloids. Here, we examine the unique properties of out-of-equilibrium systems and show how counter-intuitive results are obtained when compared to 'equivalent' equilibrium set-ups. We also consider simple active model systems, by which we can simulate the behavior of bacteria and catalytic self-propelled particles in microfluidic environments. The module consists of a theory, simulation, and oral and written presentation part. It is required to work in groups of 3.

Contact

If you have any questions regarding the organization or content of this module please do not hesitate to contact Joost de Graaf.

Part 1: Rectification Theory

Description

This part of the module explores the differences between equilibrium systems and out-of-equilibrium systems on the basis a simple experiments. Rectification is the property of active matter to move in a specific direction, based on the geometry of their environment. That is, in an out-of-equilibrium system, steady-state fluxes can exist. Careful tailoring of the environment can cause the accumulation of particles. The students should study the literature given below and present their findings. The presentation should at a minimum contain an explanation of the rectification problem in a simple geometry, and a discussion of how this model relates to experiments.

Literature

• N. Koumakis, C. Maggi, and R. Di Leonardo, "Directed transport of active particles over asymmetric energy barriers", Soft Matter 10, 5695 (2014)
• Berdakin, A.V. Silhanek, H.N. Moyano, V.I. Marconi, and C.A. Condat, "Quantifying the sorting efficiency of self-propelled run-and-tumble swimmers by geometric ratchets", Central Euro. J. Phys. 12, 1653 (2013)
• Berdakin, Y. Jeyaram, V.V. Moshchalkov, L. Venken, S. Dierckx, S.J. Vanderleydern, A.V. Silhanek, C.A. Condat, and V.I. Marconi, "Influence of swimming strategy on microorganism separation by asymmetric obstacles", Phys. Rev. E 87, 052702 (2013)
• N. Koumakis, A. Lepore, C. Maggi, and R. Di Leonardo, "Targeted delivery of colloids by swimming bacteria", Nature Commun. 4, 2588 (2013)

Part 2: Rectification in Practice

Description

This part is practical. Using the ENGINE feature of ESPResSo the students are expected to create a simulation which demonstrates the rectification of particles in a simple geometry.

Using the constraints, you are to create a circular channel with a saw-tooth like profile in the center and chambers at the end. Using both inert and active particles, the channel's rectifying properties can be studied. For this you 'seed' the geometry with a set of particles. The evolution of the density profile and stationary-state density profile can be used to determine channel's rectifying potential. The students should consider the effect of the geometry of the saw-tooth and the Peclet number of the particles. The particles and surfaces should interact via a WCA potential.

Literature

• Berdakin, Y. Jeyaram, V.V. Moshchalkov, L. Venken, S. Dierckx, S.J. Vanderleydern, A.V. Silhanek, C.A. Condat, and V.I. Marconi, "Influence of swimming strategy on microorganism separation by asymmetric obstacles", Phys. Rev. E 87, 052702 (2013)

Part 3: Hydrodynamics and Active Colloids

Description

In this part, which is also practical, the students are expected to couple the active particles to a hydrodynamic solver, namely the one in ESPResSo and study how active particle interact with a periodic structure. To do so, the students read the papers provided. In particular, they should examine the paper by Brown and Poon, and set up a similar hydrodynamic LB environment. For instance, a periodic box with a few pillars, or large bounce-back spheres arranged in a hexagonal crystal structure. Exploiting the periodicity of the box, it is straightforward to create a colloidal monolayer using only a few colloids. Bounce-back plates on the top and bottom close the sample in the z-direction. Inside this environment, a single pusher- or puller-type particle is to be studied. Its trajectories should be characterized and considered in the context of the theoretical papers that were published on the subject.

Literature

• Saverio E. Spagnolie, Gregorio R. Moreno-Flores, Denis Bartolo, and Eric Lauga, "Geometric capture and escape of a microswimmer colliding with an obstacle", Soft Matter 11, 3396 (2015)
• Aidan T. Brown, Ioana D. Vladescu, Angela Dawson, Teun Vissers, Jana Schwarz-Linek, Juho S. Lintuvuori, and Wilson C.K. Poon, "Swimming in a Crystal: Using Colloidal Crystals to Characterise Micro-swimmers", arXiv:1411.6847v2 (2015)
• Daisuke Takagi, Jeremie Palacci, Adam B. Braunschweig, Micheal J. Shelley, and Jun Zhang,"Hydrodynamic capture of microswimmers into sphere-bound orbits", Soft Matter 10, 1784 (2014)
• Dario Papavassiliou and Gareth P. Alexander, "Orbits of simmers around obstacles", arXiv:1407.1337v1 (2014)

Report

Please hand in one report per group of 5 to 10 pages containing and discussing your results from parts 2 and 3.