Monte Carlo Group Home Page Head of the group:
Prof. Dr. Ana Proykova
Atomic Physics Department, room V25
tel: (++359 2) 8161-828
Educational projects




Research projects:

    Structural Phase Transitions in Molecular Clusters:

  • R. Radev - "Parallel Monte Carlo Simulation of Critical Behaviour in Molecular Clusters"
    We have developed a parallel J-Walking Monte Carlo code (during the visit of the EPCC under the TRACS program, March-May 2000). The code enables us to carry out a Monte Carlo simulation efficiently in a multi-processor computing environment. Up to now, we have used the code to simulate 59 molecule TeF6 clusters at different temperatures to compute the heat capacity of the first order-phase transition, which is known from the MD simulations to be a structural, disorder-to-partially ordered transition.
    • J-walking procedure for sampling the multi dimensional phase space of 59 TeF6 molecules clusters has been implemented to solve the problem arising from weakly connected local minimma; a code writen in C has been developed.
    • The developed code has been parallelized with MPI to solve the problem with ergodicity and computaion time. It is not possible to retrieve information about more then one cluster simultaneously in sequentional code.
    • Parallelisation of MT-19937 Random Number Generator.
  • E. Daykova - "The Influence of Hydrophobic Guest Molecules on the Hydrogen Bond Network in Water Clusters"
    We analytically investigate both the effects of the guest molecule concentration and the free surface on the different melting and freezing points that appear in nano-sized water clusters. The Molecular Dynamics simulations performed up to now show that the melting starts around the guest molecules and the cluster surface. Having in mind that the properties of water systems (bulk and clusters) are governed by the hydrogen bond network (HBN) we address the question: What is the influence of the guest hydrophobic molecules and the surface onto the local and global HBN reorganization? There are experimental indications that the hydrogen bonds become stiffer around the guest molecules. It is known as well that the water warms when hydrophobic molecules like methane are being added. A possible explanation is to include the rotation of both the guest molecule and neighboring water molecules. However, it is not clear in advance if the global network is more or less ordered. To study the order we adopt a microscopic point of view, in which the spatial arrangements (specifically, hydrogen- bond network dynamics) and the motion of solvent and solute molecules play the central role. We suggest a statistical method based on the Weber and Stillinger melting theory to compute the entropy contribution of the guest molecules to the HBN.
    Potential Energy Surface analysis:

  • S. Pisov
Educational projects:

  • P. Michailov "Entropy driven phase transition" (1999)
    A constant pressure Monte Carlo method has been used to simulate the two-dimensional melting of hard-disks systems. By studying various properties of the system - diffusion coefficient, density of state distribution, bond-orientation distribution, pressure-density phase diagram - we have confirmed that the liquid-solid transition is discontinuous, which can be detected even in very small systems with the help of Lee-Kosterlitz histogram method. This result is important for the study of the diffusion and sinter of free metallic clusters deposited onto a non-interacting surface. Usually, the number of clusters is very small and the region where the clusters stick together is restricted to a small spot.

  • D. Nikolova "Theoretical-Group Approach to Phase Transitions" (1999)
    The dynamic orientational order-disorder transition of clusters consisting of octahedral AF6 molecules is formulated in terms of symmetry-adapted rotator functions. The transition from a higher-temperature body-centered-cubic, orientationally disordered phase to a lower-temperature, monoclinic, orientationally-ordered phase is a two-step process. The higher-temperature transition has two local minima in the free energy, like a finite-system counterpart of a first-order transition. Simulations show the lower-temperature transition is continuous. Analytic theory predicts a temperature of 27K for this transition, for a 59-molecule cluster of TeF6, in good agreement with the ~30K result of canonical Monte Carlo calculations.

  • D. Nikolova "Short-time memory in 1D" (1998)
    We reconsider the deterministic nonlinear dynamical system which is able to encode multiple memories during a transient period, but retains no more than two memories for long times. A simple discrete diffusion equation describes the system dynamics: x{j}[t+1]=x{j}[t]+int{sum{i(nn)}}{{k[x{i}[t]-x{j}[t]]+(1-A{t})}} where the sum is over the nearest neighbours having position indices i,j, and t is the time index. The memory is provoked by applying the sequence of forces At onto the system.

  • E. Daykova "Runge Cutta" (1998)
    The forth-ordered Runge-Kutta method for solving Ordinary Differential equations is applied in finding one-dimensional integral. The errors of the integration of smooth and peak functions are compared for RKM, trapezia and Monte Carlo for the same number of steps.The convergence of RKM and trapezia is a power function of order 4.37 and 2.20 .For one-dimensionional integration the MC is worst.This result is for the smooth functions.RKM and MC are bad for the sase of peak functins because of the small interval where the function is nonezero.

  • R. Radev "Special Projection Method" (1997)
    The 3D orientational distribution of the molecules is projected onto a two-dimensional spherical surface with the help of the method which we have developed to reveal the mechanism of ordering process in plastic clusters. The time evolution of the cluster at a given temperature is animated by using successive time frames. The animation is accomplished in Java. This presentation elucidates the process of the structural phase change from a more orientationally disordered to a more ordered phase that is characterized with an alignment of the molecular symmetry axes along a particular direction.

  • R. Radev "Random Walk in 2D" (1996)
    Random number sequences are intended for a general use in different kind of problems - immanently stochastic processes like the quantum particle scattering or deterministic processes whose equations are solved by implementation of stochastic methods. The random numbers can be produced by chance with the help of a suitable random process or can be generated by a completely specified rule which should be so devised that the tests would detect no significant departure from randomness. However, the production of the random numbers should not affect the person who has to used them, since the question is not "where are these numbers coming from?" but "are these numbers correctly distributed?". This last question is answered by statistical tests on the numbers themselves. This approach requires, strictly speaking, production of infinitely many random numbers and make a lot of statistical tests on them to ensure fully that they meet all the requirements. In practice we produce only finite sequences of random numbers, subject them to several tests, and expect that they would have satisfied the rest of the tests. It is much better to create a run test that simulates a model with a known output.

Last updated: March 14 2003 10:30:33 AM   by H. Iliev or S. Pisov