Franz Vesely | Research
Liquids/fluids, simple and moderately complex
Robotics, inverse kinematic problem, CKSO-method
Vesely, Franz J.:
Computational Physics - An Introduction.
Plenum, New York-London 1994. Second, extended edition 2001,
Kluwer Academic Publishers.
(together with Thomas Kastenmeier):
Vesely, Franz J.:
"Nematic-smectic transition of parallel hard spheroellipsoids".
J. Chem. Phys. 141, 064109 (2014)
Spheroellipsoids are truncated ellipsoids with spherical end caps. If gradients are assumed to change smoothly at the junction of body and cap, the truncation height z 0 determines the geometry uniquely. The resulting model particle has only two shape parameters, namely, the aspect ratio c/a of the basic ellipsoid and the cutoff z 0/a. These two parameters can be tuned to yield a continuous transformation between a pure ellipsoid and a spherocylinder. Since parallel hard spherocylinders display a nematic-smectic A phase transition, while ellipsoids do not, the influence of the particle shape on the possibility of a smectic phase may be investigated. A density functional analysis is used to detect the dividing line, in the (c/a, z 0/a) plane, between the presence and absence of the N-S transition. Since spheroellipsoids may be useful as generic model particles for anisotropic molecules, we provide a computationally efficient overlap criterion for a pair in a general, non-parallel configuration.
Vesely, Franz J.:
"Of pendulums, polymers, and robots: Computational mechanics with constraints".
Am. J. Phys. 81, 537 (2013)
The motion of point masses under the influence of a potential can be computed by simple methods. However, if the trajectories are restricted by mechanical constraints such as strings, rails, crankshafts, and molecular bonds, special numerical techniques must be invoked. The need for efficient computational strategies is particularly pressing for molecular simulations, where large systems of compound molecules are tracked. The best strategy is the use of Cartesian coordinates in combination with constraint forces in the Lagrange formulation. This approach has led to the extremely successful SHAKE and RATTLE algorithms. The same ideas may be profitably applied in very different fields such as robotics, mechanics, and geometry, and the study of chaos in simple systems.
De las Heras Daniel, Varga Szabolcs, and Vesely Franz J.:
"Mesophase formation in a system of top-shaped hard molecules: density functional theory and Monte Carlo simulation".
J. Chem. Phys. 134 (2011) 214902
We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.
Varga Sz. and Vesely F. J.:
"A new generic model potential for mesogenic systems: square-well line potential of variable range".
J. Chem. Phys. 131 (2009) 194506
A single-site pair potential is derived to approximate the linear n-site square well interaction. The resulting square well line (SWL) potential is analytical, fairly smooth, and reproduces the distance and orientation dependence of the multisite pair energy. It contains only three control parameters n, L, and s2, in addition to the units of length s1 and energy ε. The advantages of the new model over the traditional potentials such as Gay–Berne and Kihara are that n, L, and s2 are physically meaningful quantities and that no additional adjustable parameters are introduced. With the SWL potential even very long square well chain molecules may be treated in Monte Carlo(MC) simulations; moreover the model is well suited for perturbation theory. Using Onsager-like theories we test the effect of molecular elongation, temperature, and the range of the square well potential on the vapor-liquid and nematic-smectic A (NS) phase transitions. We find that the vapor-liquid binodal of the SWL fluid is in good agreement with MC results for square well dumbbells. For repulsive SWL particles, varying the interaction range s2 results in a similar effect on the NS transition as the change in the ionic strength in a real suspension of fd viruses.
Varga Sz., Velasco E., and Vesely F. J.:
"Stability of the columnar and smectic phases of length-bidisperse parallel hard cylinders".
Mol. Phys. 107, 23 (2009) 2481
The effect of length-bidispersity on the stability of nematic, smectic and columnar phases of rod-like particles is studied in the perfect alignment limit using Onsager's second virial theory. The rod-like particles are modelled as hard cylinders of equal diameters (D) but different lengths ( ). Three different smectic structures are observed: (i) the conventional smectic (S1) phase, where both components accommodate in the same layer; (ii) the microsegregated smectic (S2) phase, which can be considered as an alternation of fluid layers rich in short and long rods, respectively; and (iii) two layers of short rods accommodate inside one layer of long rods, which gives the third smectic (S3) structure. Due to the inefficient packing of the short and long rods into a layered structure along the symmetry axes of the rods, the smectic phase is destabilised with respect to nematic and columnar phases upon mixing the short and long components. With decreasing length ratio ( ) the smectic phase is destabilised with respect to the nematic phase at compositions rich in short rods and two forms of smectic phases, namely S1 and S2, take place in alternation. The alternation of the structure is the consequence of the minimisation of the number of overlapping layers of the short rods with one long rod. In mixtures rich in long rods, the short and long rods are in the same layer up to l = 0.39, while the short rods can accommodate into the interstitial region of long rods for l < 0.39 and the system forms a S2 phase. The S3 phase is observed in the range 0.57 < l < 0.39 and is due to the efficient packing of two layers of short rods inside one smectic layer of long rods. Our theoretical predictions for the three smectic structures are in close agreement with the smectic phase behaviour of a binary mixture of short and long helical polysilanes (Okoshi et al., Macromolecules 42, 3443 (2009)). It seems reasonable that the helical polysilanes can be considered as an ideal system for testing the hard-body theories. Finally, it is interesting that the stabilisation process of the columnar phase with respect to the smectic ordering with decreasing length ratio turns over at l = 0.3.
Varga Sz., Gabor A., Velasco E., Mederos L. and Vesely F. J.:
"Demixed and ordered phases in hard-rod mixtures".
Mol. Phys. 106/15 (2008) 1939
We analyse demixing and ordering transitions in systems of hard cylindrical particles. The second virial approximation of Onsager and a bifurcation analysis, as introduced by Koda and Kimura, are used to evaluate the free energies, pressures, and density distribution functions in mixtures of equally long but differently wide cylinders. The spatial density distribution along the one relevant coordinate is of particular importance as it provides more detailed information concerning the nature of the phase transition than the bare bifurcation diagnosis. Detailed results are given for the nematic–nematic spinodal and the nematic–smectic transitions. Allowing for the absence of an isotropic phase, our results are in good qualitative agreement with those for freely orienting rods reported previously, and indicate a complex sequence of phase diagrams as the diameter dissimilarity of the two components is increased, with upper and lower critical points bounding nematic and smectic demixing regions. However, experimental results on colloidal rods show that nematic demixing occurs at a diameter ratio much smaller than ours or those for freely rotating fluids, indicating that Onsager-type theories may be insufficient to reproduce this phenomenon in a quantitative manner and, consequently, that more sophisticated approaches, presumably incorporating particle flexibility and additional interactions, are required.
Vesely, Franz J.:
"Lennard-Jones sticks: A new model for linear molecules".
J. Chem. Phys. 125, (2006) 214106
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.
Vesely, Franz J.:
"Smectic phases in hard particle mixtures: Koda's theory".
Molecular Physics, Vol. 103, No. 5 (2005), 679
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.
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.
Kastenmeier, Thomas, and Vesely, Franz J.:
robot kinematics based on stochastic and molecular simulation
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.
"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