Axel Arnold

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<setdata> name=Arnold, Axel title=Dr. status=Postdoc phone=67609 room=201 email=arnolda image=Axel Arnold.png </setdata>

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As Axel Arnold is not a member of our working group anymore, the information on this page might be outdated.

Research interests


ESPResSo stands for Extensible Simulation Package for Resarch on Soft matter systems, and is a simulation package mainly for (charged) bead spring models of soft matter. Since the beginning in 2003, I am one of the core developers, and now work on its precessor, Espresso++.

Using GPUs for numerical calculations

In the last couple of years, the computational power of graphics cards has grown much faster than that of conventional CPUs, although at the same time the graphics cards have become true general purpose processors. Recent graphics processors reach speeds of up to a Teraflop on a single PCIe-board. With the introduction of easy-to-use programming languages for the GPU hardware, this computational power can be harnessed for many applications. Using NVidia's CUDA, Koos van Meel and I have demonstrated this for classical soft matter simulations. For details, see our MDGPU webpage.

Calculation of the electrostatic potential

Due to its long-ranged nature, the electrostatic interaction is very difficult to calculate in periodic systems. However, these systems are often used in computer simulation studies of bulk systems. Therefore, there has been and still is much interest in fast algorithms to calculate the Coulomb sum in periodic boundary conditions. For 3D periodic boundary conditions, many optimized algorithms exist, from the classical Ewald summation to particle-mesh methods, where the best method scale linearly in the number of particles.

My interest is in the calculation of this interaction in 3D systems, where only one or two coordinates are periodically replicated. For these systems, the classical Ewald method is slow to evaluate, and alternative approaches are necessary. I have developed the MMM1D/2D algorithms, and J. de Joannis and I found the electrostatic layer correction (ELC) method. This method consists of a correction term that is fast to calculate and allows to use any method for 3D-periodic boundary conditions for a quasi-2D system.

All these methods are implemented in ESPResSo, if you want to try them out.

(Charged) soft matter

Mostly using ESPResSo and the above-mentioned electrostatics methods, I investigated several systems of interest in soft matter physics. For example:

  • attraction of like-charged rods in the presence of multivalent counterions (here, MMM1D was used).
  • interactions of charged colloids (using MMM2D and ELC).
  • segregation of two overlapping flexible polymers in cylindrical confinement.
  • relaxation of a single flexible polymer in cylindrical confinement.


  • V. Ballenegger, A. Arnold and J. J. Cerdà.
    Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions. J. Chem. Phys. 131:094107 (2009).
  • T. Kalkbrenner, A. Arnold and S. Tans.
    Internal Dynamics of Supercoiled DNA Molecules. Biophysical Journal 96:4951-4955 (2009).
  • S. Tyagi, A. Arnold and C. Holm.
    Electrostatic layer correction with image charges: A linear scaling method to treat slab 2D+h systems with dielectric interfaces. J. Chem. Phys. 129:204102 (2008).
  • A. Arnold and C. Holm.
    Interactions of like-charged rods at low temperatures: Analytical theory vs. simulations. Euro. Phys. J. E, DOI:10.1140/epje/i2007-10347-4, 2008.
  • J. A. van Meel, A. Arnold, D. Frenkel, S. F. Portegies Zwart and R. G. Belleman.
    Harvesting graphics power for MD simulations. Molecular Simulation 34(3):259-266, 2008.
  • A. Arnold, B. Bozorgui, D. Frenkel, B.-Y. Ha and S. Jun.
    Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement. J. Chem. Phys. 127:164903, 2007.
  • S. Tyagi, A. Arnold and C. Holm.
    ICMMM2D: An accurate method to include planar dielectric interfaces via image charge summation. J. Chem. Phys. 127:154723, 2007.
  • A. Arnold and S. Jun.
    Time scale of entropic segregation of flexible polymers in confinement: Implications for chromosome segregation in filamentous bacteria. Phys. Rev. E 76:031901, 2007.
  • S. Jun, A. Arnold and B.-Y. Ha.
    Confined space and effective interactions of multiple self-avoiding chains. Phys. Rev. Lett. 98:128303, 2007.
  • H. Limbach, A. Arnold, B. A. Mann and C. Holm.
    ESPResSo - An Extensible Simulation Package for Research on Soft Matter Systems. Comp. Phys. Comm. 174:704-727, 2006.
  • A. Arnold and C. Holm.
    Simulating Charged Systems with ESPResSo. In Lecture Notes in Physics, 703, Springer, 2006.
  • A. Arnold and C. Holm.
    Efficient methods to compute long range interactions for soft matter systems. In C. Holm and K. Kremer, Advanced Computer Simulation Approaches for Soft Matter Sciences II, 59-109, Springer, 2005.
  • A. Arnold and C. Holm.
    MMM1D: A method for calculating electrostatic interactions in one-dimensional periodic geometries. J. Chem. Phys. 123(14):144103, 2005.
  • A. Arnold.
    Computer simulations of charged systems in partially periodic geometries. Disseration, J. Gutenberg-Universität, Mainz, Germany, 2004.
  • A. Naji, A. Arnold, C. Holm and R. R. Netz.
    Attraction and unbinding of like--charged rods. Europhys. Lett. 67:130-136, 2004.
  • M. Deserno, A. Arnold and C. Holm.
    Attraction and ionic correlations between charged stiff polyelectrolytes. Macromolecules 36(1):249-259, 2003.
  • A. Arnold and C. Holm.
    MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries. Comp. Phys. Comm. 148(3):327-348, 2002.
  • J. de Joannis, A. Arnold and C. Holm.
    Electrostatics in Periodic Slab Geometries II. J. Chem. Phys. 117:2503-2512, 2002.
  • A. Arnold, J. de Joannis and C. Holm.
    Electrostatics in Periodic Slab Geometries I. J. Chem. Phys. 117:2496-2502, 2002.
  • A. Arnold and C. Holm.
    A novel method for calculating electrostatic interactions in 2D periodic slab geometries. Chem. Phys. Lett. 354(3):324-330, 2002.
  • A. Arnold.
    Berechnung der elektrostatischen Wechselwirkung in 2d+h periodischen Systemen. Diploma thesis, J. Gutenberg-Universität, Mainz, Germany, 2001.

Curriculum vitae

Scientific education

since Jan. 2010 Post-doctoral researcher at the ICP, University of Stuttgart, Germany
Jan. 2008 - Dec. 2009 Post-doctoral researcher at the Fraunhofer institute SCAI, St. Augustin, Germany
Nov. 2005 - Dec. 2007 Post-doctoral researcher at the FOM-institute AMOLF, Amsterdam, The Netherlands
Dec. 2004 - Oct. 2005 Post-doctoral researcher at the Max-Planck-Institute for Polymer Research and the Frankfurt Institute for Advanced Studies (FIAS)
Dec. 2004 Doctor rer. nat. awarded at the Johannes Gutenberg-University of Mainz. Thesis:

Computer simulations of charged systems in partially periodic geometries

since 2003 One of the core developers of ESPResSo
Oct. 2001- Dec. 2004 Doctorate studies at the Max-Planck-Institute for Polymer Research in Mainz, Germany
Oct. 2001 Diploma in Mathematics at the Johannes Gutenberg- University of Mainz. Thesis:

Berechnung der elektrostatischen Wechselwirkung in 2d+h periodischen Systemen

Oct. 1996 - Oct.2001 Studies of Mathematics at the Johannes Gutenberg-University of Mainz
1998 - 2002 Participating in the RoboCup, a worldwide competition on multi-agent systems, as member of the Mainz Rolling Brains

Other skills

  • Languages:
    German and English (fluent), Dutch, Russian (beginner)
  • Computing languages: C, C++, Tcl/Tk, Python, MPI, CUDA, shell scripting
    System administration: Unix (Linux, Tru64, AIX, Irix, Solaris), MacOS/Darwin, Windows