Molecular simulation
Liquids/fluids, simple and moderately complex
Nematic liquid crystals (Gay-Berne model)
Computational Physics
Robotics, inverse kinematic problem, CKSO-method

Dissertation project (finished):

Renato Lukac: "Simulationen von Gemischen von Flüssigkristallen"

Diploma projects:

Dorian Bridi: "NpT-Simulation von binären Flüssigen Kristallen"

Nikolaj Georgi: "Untersuchung der Entmischung mit Hilfe von Wavelets"

Director confinement: The "director" (i. e. the average axis orientation) in a computer sample of linear, axiosymmetric molecules is expected to be influenced by the artificial anisotropy of the simulation geometry. This influence will be even more pronounced if smectic layers have to "catch up" with themselves across the borders of the periodic cells. In other words, the dominant smectic wave vector has to coincide with one of the Fourier modes of the simulation supercrystal. Since these Fourier modes change upon compression, repeated breakup and reformation of smectic layers is necessary to approximately match the cell geometry. This is a spurious effect that severely hampers the simulations. To speed up the computation a method was devised to keep the director (and consequently the smectic vector) near a desired orientation, even while the cell is slowly shrunken to achieve a target density. The method consists in introducing a synthetic potential U=c*(d-d0)**2 coupling to the deviation of the director d from a given direction d0. It may be used in conjunction with MD or MC calculations. Details of the method, along with the results of performance tests, were presented at the European Conference on Liquid Crystals 99 (ECLC 99) in Hersonissos/Crete, April, 1999. They will be published in the Proceedings of that conference (see abstract below).

Liquid crystal films consisting of binary mixtures were studied by MC simulation. Strong orientational correlations were found for the longer molecules which tend to "anchor" at the cell walls. The results, including visualisations, were presented at ECLC 99 (see above) and will be included in the Proceedings of that conference (see abstract below).

Phase separation and wavelets: The separation of phases, be it upon condensation or demixing, is tantamount to a breaking of geometrical symmetry. In a computer simulation such symmetry breaking is difficult to quantify. Nikolaj Georgi has devised a method using wavelets to diagnose deviations from homogeneity, both on local and global scales.

Robotics: Software tools for the realistic simulation of robot arm dynamics, including the effects of gravity and inertia, were obtained and tested. In order to continue the previous studies, diploma and/or dissertation students interested in this field are currently searched for.

• Book:
  Vesely, Franz J.: Computational Physics - An Introduction.
  Plenum, New York-London 1994. Second, extended edition 2001, Kluwer Academic Publishers.
  
  
• Lecture Text:
  Vesely, Franz J.: Statistical Physics.
  Lecture manuscript; regularly revised (last revision 2005) / Skriptum zur Vorlesung "Statistische Physik" letzte Revision 2005.
  
  
• Refereed articles:
  • Vesely, Franz J.: "Lennard-Jones sticks: A new model for linear molecules".
    J. Chem. Phys. 125, (2006) 214106
    Abstract: We consider the anisotropic interaction between two line segments consisting of a homogeneous distribution of Lennard-Jones centers. The potential energy of such a pair cannot be expressed in closed form. However, we show that it may be approximated in a way that renders this intuitively appealing model competitive both for simulations and theory. JCP online
    
    
  • Vesely, Franz J.: "Smectic phases in hard particle mixtures: Koda's theory".
    Molecular Physics, Vol. 103, No. 5 (2005), 679.
    Abstract: Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this "smectic demixing" transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids, and sphero-ellipsoids.
    
    
  • Vesely, Franz J.: "Billiards in class, entropy after hours: Statistical physics for sophomores".
    Proceedings, Multimedia in Physics Teaching and Learning (MPTL9), Graz, September 9-11, 2004.
    
    
  • Vesely, Franz J.: "Explaining Gibbsean phase space to second year students".
    European Journal of Physics 26 (2005) 243.
    Abstract: A new approach to teaching introductory statistical physics is presented. We recommend making extensive use of the fact that even systems with a very few degrees of freedom may display chaotic behavior. This permits a didactic "bottom-up" approach, starting out with toy systems whose phase space may be depicted on a screen or blackboard, then proceeding to ever higher dimensions in Gibbsean phase space.
    
    
  • Vesely, Franz J., and Lukac, Renato: "How to simulate anchoring: confining the director".
    Mol. Cryst. Liqu. Cryst. 351 (2000) 667 (Proceedings of the 5th European Conference on Liquid Crystals 99, Hersonissos/Crete, April 25-30, 1999.)
    Abstract: We present a method to manipulate the average direction of linear model molecules. In contrast to a hard constraint, we use a soft confinement potential linked to the director orientation. The method is applied to a mixture of GayBerne molecules at high density, where smectic demixing occurs. Other possible applications, such as the simulation of "easy directions" in anchoring and the evaluation of elastic coefficients, are discussed. pdf file
    
    
  • Lukac, Renato, and Vesely, Franz J.: "Simulating Phase Transitions in Binary Liquid Crystal Films".
    Mol. Cryst. Liqu. Cryst. 351 (2000) 683 (Proceedings of the 5th European Conference on Liquid Crystals 99, Hersonissos/Crete, April 25-30, 1999.)
    Abstract: Liquid crystals (LC) are often subject to external orienting forces, arising either from applied fields or from surface anchoring. The molecular simulation of such systems is an important step towards the prediction of real LC behavior. Recently some progress has been made regarding the simulation of LC models, both in confined spaces (slabs, films) and under the influence of aligning torques. We present Monte Carlo (MC) simulations of Gay-Berne (ellipsoidal) model particles. The present article deals with a binary system of such molecules confined between two walls. Simulations were performed in 3 dimensions. The results are presented both as structure visualizations and in the form of various correlation functions.
    Keywords: LC film, Gay-Berne potential, binary equimolar mixture
    
    
  • Kastenmeier, Thomas, and Vesely, Franz J.: "Numerical robot kinematics based on stochastic and molecular simulation methods".
    Robotica 14(1996)329-337.
    Abstract: Multilink robot arms are geometrically similar to chain molecules. We investigate the performance of molecular simulation methods, combined with stochastic methods for optimization, when applied to problems of robotics. An efficient and flexible algorithm for solving the inverse kinematic problem for redundant robots in the presence of obstacles (and other constraints) is suggested. This "Constrained Kinematics / Stochastic Optimization" (CKSO) method is tested on various standard problems.
    
    

   

• Posters:
  • Thomas Kastenmeier, Franz J. Vesely: "Constrained Kinematics/Stochastic Optimization (An excursion into robotics)". Poster, Research Conference on Molecular Liquids, Blankenberge, 22.-27. September 1996 .
  • Thomas Kastenmeier, Franz J. Vesely: "A new algorithm for numerical robot kinematics". In I. J. Rudas (Ed.): Proceedings, 5th International Workshop on Robotics in the Alpe-Adria region, Budapest, June 10-13, 1996.
    Abstract: Exploiting the similarity between multilink robot arms and chain molecules, we apply methods of molecular simulation to problems of robotics. The "Constrained Kinematics / Stochastic Optimization" (CKSO) method performs well when applied to standard tasks.
  • Renato Lukac, Franz J. Vesely: "Demixing of binary liquid crystals: a simulation study". Poster, International Liquid State Conference, Kent State University, Ohio, June 1996.
  • Renato Lukac, Franz J. Vesely: "Influence of the elongation on molecular structure". Poster, European Molecular Liquids Group Conference, Balatonfüred, September 1996.
    Abstract: On the basis of our previous studies of liquid crystal mixtures with the Gay-Berne potential, we investigate the influence of the elongation parameter in the pure liquid. We report the results of compression from low to high density for the elongations 1.5, 2, 3, 4, 5, and 6. We find that short molecules do not have any orientational order even at high density, while with increasing elongation the ordering tendencies are much more pronounced. Therefore, the longest molecules are carefully observed at different temperatures, ranging from 0.5 to 2.0, by means of various correlation functions, the order parameter, and thermodynamic quantities.
  • Franz J. Vesely: Confined director dynamics in the simulation of nematics. (Internal paper; publication planned).
    Abstract: A method is proposed to hold the preferred direction of orientationally correlated molecules near some desired direction vector. In contrast to hard constraints, we use a soft confinement potential linked to the director orientation.

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  Patent (together with Thomas Kastenmeier):

  "Steuerungsverfahren für Roboter, unter Verwendung von geometrischen Zwangsbedingungen und Zufalls-Suchverfahren"

  [A method for robot control using geometrical constraints and stochastic search methods]

  In his diploma work, "Application of simulation methods in robotics" Thomas Kastenmeier developed a stochastic algorithm for robot control. It would be very interesting to investigate the performance of our technique in a real robot. To date the necessary facilities and engineering expertise are not available at this institute. However, an enterprising student could win himself laurels (and a diploma) with such a project. The needed knowhow could certainly be obtained by a cooperation with some other university department or company.

  Applet demonstrating the performance of the technique