**Title:**
The role of angular momentum conservation law in statistical mechanics
**Author(s):**

I.M.Dubrovskii (Institute for Metal Physics, 36 Vernadsky Str., Kyiv 03680, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 585, EnglishWithin the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation does not change the density of probability distribution in both cases, just as it is assumed in the conventional theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation law changes the density of distribution of the system only in case the full angular momentum of a system is not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206,

9, 23]. Two-dimensional gas of charged particles located within a section of an endless strip filled with gas in magnetic field is considered. Under such conditions the angular momentum is not conserved. Directional particle flows take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics method, it was suggested to consider near-boundary trajectories relative to a reference system that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field. Only the average velocity of near-boundary particles that form near-boundary electric currents creating the paramagnetic moment turn out to be essential.

DOI:10.5488/CMP.11.4.585

**Title:**
On the kinetics of phase transformation of small particles in Kolmogorov's model
**Author(s):**

N.V.Alekseechkin (Akhiezer Institute for Theoretical Physics, National Science Centre "Kharkov Institute of Physics and Technology", Akademicheskaya Str. 1, Kharkov 61108, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 597, EnglishThe classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory is generalized to the case of a finite-size system. The problem of calculating the new-phase volume fraction in a spherical domain is solved within the framework of geometrical-probabilistic approach. The solutions are obtained for both homogeneous and heterogeneous nucleations. It is shown that the finiteness property results in a qualitative distinction of the volume-fraction time dependence from that in infinite space: the Avrami exponent in the process of homogeneous nucleation decreases with time from 4 to 1, i.e. a slowing down of the transformation process takes place. The obtained results can be used, in particular, for controlling the crystallization kinetics in amorphous powders.

DOI:10.5488/CMP.11.4.597

**Title:**
Molecular dynamics simulations of ultrathin water film confined between flat diamond plates
**Author(s):**

A.V.Khomenko (Sumy State University, 2 Rimskiy-Korsakov Str., 40017 Sumy, Ukraine) , | |

N.V.Prodanov (Sumy State University, 2 Rimskiy-Korsakov Str., 40017 Sumy, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 615, EnglishMolecular dynamics simulations of ultrathin water film confined between atomically flat rigid diamond plates are described. Films with thickness of one and two molecular diameters are concerned and TIP4P model is used for water molecules. Dynamical and equilibrium characteristics of the system for different values of the external load and shear force are investigated. An increase of the external load causes the transition of the film to a solidlike state. This is manifested in a decrease of the diffusion constant and in the ordering of the liquid molecules into quasidiscrete layers. For two-layer film under high loads, the molecules also become ordered parallel to the surfaces. Time dependencies of the friction force and the changes of its average value with the load are obtained. In general, the behaviour of the studied model is consistent with the experimental results obtained for simple liquids with spherical molecules.

DOI:10.5488/CMP.11.4.615

**Title:**
Electronic structure and x-ray magnetic circular dichroism in the Heusler alloy Co_{2}FeSi
**Author(s):**

V.N.Antonov (Institute for Metal Physics of the National Academy of Sciences of Ukraine, 36 Vernadsky Str., 03142 Kiev) , | |

D.A.Kukusta (Institute for Metal Physics of the National Academy of Sciences of Ukraine, 36 Vernadsky Str., 03142 Kiev) , | |

A.P.Shpak (Institute for Metal Physics of the National Academy of Sciences of Ukraine, 36 Vernadsky Str., 03142 Kiev) , | |

A.N.Yaresko (Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 627, EnglishThe electronic structure and x-ray magnetic circular dichroism (XMCD) spectra of the Heusler alloy Co

_{2}FeSi were investigated theoretically from first principles, using the fully relativistic Dirac linear MT-orbital (LMTO) band structure method. Densities of valence states, orbital and spin magnetic moments as well as polarization of the electronic states at the Fermi level are analyzed and discussed. The origin of the XMCD spectra in the Co_{2}FeSi compound is examined. The calculated results are compared with available experimental data.

DOI:10.5488/CMP.11.4.627

**Title:**
Semi-infinite metal: perturbative treatment based on semi-infinite jellium
**Author(s):**

P.P.Kostrobij (Lviv Polytechnic National University, 12, S. Bandera Str., Lviv 79013, Ukraine) , | |

B.M.Markovych (Lviv Polytechnic National University, 12, S. Bandera Str., Lviv 79013, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 641, EnglishEnergy of electronic subsystem of semi-infinite metal is presented in the form of an expansion in powers of pseudo-potential. It is shown that generally electron many-particle density matrices are necessary for the energy calculation, whereas in case of a local pseudo-potential only diagonal elements (electron distribution functions) are necessary. In a specific case of a local pseudo-potential within the first order of perturbation theory, our results for energy coincide with those widely applicable in the density functional theory.

DOI:10.5488/CMP.11.4.641

**Title:**
The effect of polarization charges on energy of univalent and bivalent donors in a spherical quantum dot
**Author(s):**

V.I.Boichuk (Department of Theoretical Physics, Ivan Franko Drohobych State Pedagogical University, 24 Ivan Franko Str., 82100 Drohobych, Ukraine) , | |

I.V.Bilynskyi (Department of Theoretical Physics, Ivan Franko Drohobych State Pedagogical University, 24 Ivan Franko Str., 82100 Drohobych, Ukraine) , | |

R.Ya.Leshko (Department of Theoretical Physics, Ivan Franko Drohobych State Pedagogical University, 24 Ivan Franko Str., 82100 Drohobych, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 653, EnglishThe energy of electrons of univalent and bivalent impurity of a spherical

β-HgS/CdS nanoheterostructure is calculated as a function of quantum dot radius by the variation technique in the case of finite and infinite wells in the effective mass approximation. The effect of polarization charges which arise at the separation boundary of the media is studied taking into account both the existence and the absence of an intermediate layer, where dielectric permittivity depends on the coordinate.

DOI:10.5488/CMP.11.4.653

**Title:**
Phase transitions in the lattice model of intercalation
**Author(s):**

T.S.Mysakovych (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) , | |

V.O.Krasnov (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) , | |

I.V.Stasyuk (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 663, EnglishThe lattice model which can be employed for the description of intercalation of ions in crystals is considered in this work. Pseudospin formalism is used in describing the interaction of electrons with ions. The possibility of hopping of intercalated ions between different positions is taken into account. The thermodynamics of the model is investigated in the mean field approximation. Phase diagrams are built. It is shown that at high values of the parameter of ion transfer, the phase transition to a modulated phase disappears.

DOI:10.5488/CMP.11.4.663

**Title:**
Modelling of cycling of lithium battery with microporous carbon electrode
**Author(s):**

D.Portnyagin (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 669, EnglishCharge/discharge cycles of lithium cell with microporous carbon electrode under potentiodynamic control have been modelled. Predictions of the models with variable and constant diffusion coefficient neglecting the electric field inside the particle (CPM, DFM) are compared to the predictions of the models with variable and constant diffusion coefficient in which electrostatic interaction inside the particles of carbon electrode (CPME, DFME) is taken into account. There is observed a considerable difference between both. Electrostatic interactions of lithium ions with each other and the charge distributed inside the particle promote intercalation during the discharge of the cell and deintercalation during the charge. The dependance of the effect of hysteresis during the cycling of the cell on the rate of change of the applied voltage is studied. The larger is the speed of change of the applied voltage the more effective is hysteresis. We have also obtained concentration profiles at different stages of charge/discharge process.

DOI:10.5488/CMP.11.4.669

**Title:**
Analysis of thermal expansivity of solids at extreme compression
**Author(s):**

J.Shanker (Department of Physics, Institute of Basic Sciences, Khandari, Agra (U.P.) INDIA 282002) , | |

B.P.Singh (Department of Physics, Institute of Basic Sciences, Khandari, Agra (U.P.) INDIA 282002) , | |

K.Jitendra (Department of Physics, Institute of Basic Sciences, Khandari, Agra (U.P.) INDIA 282002) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 681, EnglishThermodynamics of solids in the limit of infinite pressure formulated by Stacey reveals that the thermal expansivity (alpha) of solids tends to zero at infinite pressure. The earlier models for the volume dependence of thermal expansivity do not satisfy the infinite pressure behaviour of thermal expansivity. The expressions for the volume dependence of the isothermal Anderson- Grüneisen parameter (delta T) considered in the derivation of earlier formulations for alpha (V) have been found to be inadequate. A formulation for the volume dependence of delta T is presented here which is similar to the model due to Burakovsky and Preston for the volume dependence of the Grüneisen parameter. The new formulation for alpha (V) reveals that delta T infinity must be greater than zero for satisfying the thermodynamic result according to which alpha tends to zero at infinite pressure. It is found that our model fits well the experimental data on thermal expansivity alpha (V) for hcp iron corresponding to a wide range of pressures (0-360 GPa).

DOI:10.5488/CMP.11.4.681

**Title:**
Annihilation operators associated with unstable vacua in non-equilibrium thermo-field dynamics
**Author(s):**

K.Yoshida (Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Ibaraki 305-8571, Japan) , | |

T.Arimitsu (Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Ibaraki 305-8571, Japan) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 687, EnglishOut of thermal equilibrium state, the vacuum is unstable and evolves in time. Consequently, the annihilation operators associated with the unstable vacuum depend on time. This dissipative time-evolution of quantum systems can be systematically treated, within the canonical operator formalism referred to as non-equilibrium thermo-field dynamics. Given is an alternative route to derive the time-dependent annihilation operators within the formalism. As an example, time-dependent annihilation operators for the systems of bosonic and fermionic semi-free fields are derived.

DOI:10.5488/CMP.11.4.687

**Title:**
Non-equilibrium stochastic dynamics in continuum: The free case
**Author(s):**

Y.Kondratiev (Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, D-33501 Bielefeld, Germany; Institute of Mathematics, Kiev, Ukraine; BiBoS, Univ. Bielefeld, Germany) , | |

E.Lytvynov (University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.) , | |

M.Röckner (Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, D-33501 Bielefeld, Germany; BiBoS, Univ. Bielefeld, Germany) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 701, EnglishWe study the problem of identification of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a fixed Markov process

Mon a Riemannian manifoldX. The main problem arising here is a possible collapse of the system, in the sense that, though the initial configuration of particles is locally finite, there could exist a compact set inXsuch that, with probability one, infinitely many particles will arrive at this set at some timet>0. We assume thatXhas infinite volume and, for eachα≥1, we consider the set Θ_{α}of all infinite configurations inXfor which the number of particles in a compact set is bounded by a constant times theα-th power of the volume of the set. We find quite general conditions on the processMwhich guarantee that the corresponding infinite particle process can start at each configuration from Θ_{α}, will never leave Θ_{α}, and has cadlag (or, even, continuous) sample paths in the vague topology. We consider the following examples of applications of our results: Brownian motion on the configuration space, free Glauber dynamics on the configuration space (or a birth-and-death process inX), and free Kawasaki dynamics on the configuration space. We also show that ifX=, then for a wide class of starting distributions, the (non-equilibrium) free Glauber dynamics is a scaling limit of (non-equilibrium) free Kawasaki dynamics.R^{d}

DOI:10.5488/CMP.11.4.701

**Title:**
On matrices associated to prime factorization of odd integers
**Author(s):**

T.Bier (DOMAS, Faculty of Science, Sultan Qaboos University, Muscat 123, Al-Khod PO Box, Oman; Twiskenweg 43 B, D-26129 Oldenburg, Germany) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 723, EnglishIn this paper we introduce in section 5 integral matrices

M(n)for any factorization of an odd integernintordistinct odd primes. The matrices appear in several versions according to a parameterρ∈[0,1], they have size 2^{r}×2^{r}and their rank satisfies e.g. forρ=1/2 the inequalities of theorem 4:r+1≤rank(M(n))≤ 2^{r-1}+1, which are obtained using theorem 1 discussed separately in the first few sections. The casesρ=0,1,1/2 are analyzed in some detail, and various counterexamples forρ≠0,1,1/2 are included. There are several main results, theorem 5 is a duality between the casesρ=0 andρ=1, and theorem 6 is a periodicity theorem. The most important result perhaps is theorem 8 (valid forρ=1/2 only) on the existence of odd squarefree integersnwithrodd prime factors such that rank(M(n))=r+1 attains the lower bound shown previously.

DOI:10.5488/CMP.11.4.723

**Title:**
On the application of strong approximation to weak convergence of products of sums for dependent random variables
**Author(s):**

P.Matuła (Maria Curie-Skłodowska University, pl. M.C.-Skłodowskiej 1, 20-031 Lublin, Poland) , | |

I.Stępień (Maria Curie-Skłodowska University, pl. M.C.-Skłodowskiej 1, 20-031 Lublin, Poland) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 749, EnglishWe present the application of the strong approximation theorems to the study of weak convergence of products of sums of positive random variables. We focus our attention on sequences of dependent random variables such as associated and mixing sequences.

DOI:10.5488/CMP.11.4.749

**Title:**
Local solutions to Darboux problem with a discontinuous right-hand side
**Author(s):**

P.Pikuta (Marie Curie-Skłodowska University, Institute of Mathematics pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 755, EnglishThe existence of a local solution to the Darboux problem

u,_{xy}(x,y)=g(u(x,y))u(x,0)=u(0,y)=0, wheregis Lebesgue measurable and has at most polynomial growth, is proved.

DOI:10.5488/CMP.11.4.755

**Title:**
Information and data protection within a RDBMS
**Author(s):**

Y.Khmelevsky (Computer Science Department, Okanagan College, 1000 KLO Road, Kelowna, BC, V1Y 4X8, Canada) |

Condensed Matter Physics, 2008, vol. 11, No. 4(56), p. 761, EnglishSecurity issues for some special large data, such as binary and image files, as well as video and audio files and streams still require a special development, especially for the industrial database systems (Oracle, MS SQL, DB2, etc). New encryption methods should be used additionally to traditional encryption methods and other protection solutions, such as authentication, authorization, access control, security monitoring and audit. The purpose of this article is to present the research results regarding information security and data protection, as well as some practical aspects of the encryption by CrypTIM algorithm, developed by Prof. V.~Ustimenko in the last decade [Ustimenko~V., Lecture Notes In Computer Science, 2001,

278, 2227]. This text additionally proposes a practical utilization of the Model Driven system design for large objects (LOB) encryptions within a database, used to store some special large binary files, such as images, sound files, movies, special binary files in order to improve maintenance and data protection. Novel problems and trends in providing security against criminal activities in the current Cyberspace are analyzed.

DOI:10.5488/CMP.11.4.761

**
AUTHOR INDEX OF VOLUME 11 (2008)
**

**
IX Workshop and Competition for young scientists in
the field of statistical physics and condensed
matter theory**

**
3-rd Conference "Statistical
Physics: Modern Trends and Applications"**