
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 JWalking Monte Carlo code
(during the visit of the EPCC under the TRACS program, MarchMay 2000).
The code enables us to carry out a Monte Carlo simulation efficiently in
a multiprocessor computing environment.
Up to now, we have used the code to simulate 59 molecule TeF_{6} clusters at different
temperatures to compute the heat capacity of the first orderphase transition,
which is known from the MD simulations to be a structural, disordertopartially ordered
transition.
 Jwalking 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 MT19937 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 nanosized 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 twodimensional melting
of harddisks systems. By studying various properties of the system  diffusion coefficient,
density of state distribution, bondorientation distribution, pressuredensity phase diagram  we
have confirmed that the liquidsolid transition is discontinuous, which can be detected even in very
small systems with the help of LeeKosterlitz histogram method. This result is important for the
study of the diffusion and sinter of free metallic clusters deposited onto a noninteracting 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 "TheoreticalGroup Approach to Phase Transitions" (1999)
The dynamic orientational orderdisorder transition of clusters consisting
of octahedral AF_{6} molecules is formulated in terms of
symmetryadapted rotator functions.
The transition from a highertemperature
bodycenteredcubic, orientationally disordered phase to a
lowertemperature,
monoclinic, orientationallyordered phase is a twostep process. The
highertemperature transition has two local minima in the free energy,
like a finitesystem counterpart of a firstorder
transition. Simulations show the lowertemperature transition
is continuous. Analytic theory predicts a temperature of 27K for this
transition, for a 59molecule cluster of TeF_{6}, in
good agreement with the ~30K result of canonical Monte Carlo
calculations.
 D. Nikolova "Shorttime 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]]+(1A{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 forthordered RungeKutta method for solving Ordinary Differential equations is
applied in finding onedimensional 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 onedimensionional 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 twodimensional 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



