Annual Report 2004
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A new algorithm Jetfinder based on a wavelet analysis has been developed in the framework of the VBLHE-LIT collaboration that realizes a jet reconstruction under conditions of intensive background. The algorithm works in the space of pseudorapidity versus , using as weights transverse momenta for STAR TPC or ECAL energy. The main advantages of the Jetfinder algorithm, as compared to the standard procedure LUCELL (UA1) which uses tree parameters, are in using the only control parameter and remarkable robustness of this algorithm. Besides the Jetfinder analyzes all scales automatically by one pass of the algorithm .
Simulation of the processes of multifragmentation and spallation in reactions of separated Sn isotopes with proton and deuteron beams at the energies 0.6, 3.5 and 8.1 GeV/nucleon has been performed. Results of the simulation are compared with experimental data obtained at VBLHE synchrophasotron .
A visualization package for observation of the profile of a primary beam and its location on the target for effective operation of the fragment-separator COMBAS was developed. The package allows one to visualize data both in on-line and off-line modes. When starting the package, a window containing a central field of survey of the beam profile and two auxiliary fields for its projections onto axes X and Y appear (Fig. 3). By small modifications the package can be used for a broad spectrum of set-ups which use accelerator beams .
Fig. 3. Visualization of the beam profile
In the framework of the Glauber-Sitenko microscopic optical-limit model, calculations are made of the nucleus-nucleus total reaction cross sections. Satisfactory agreement with existing experimental data at energies higher than 50 MeV/nucleon is obtained without introducing any free parameters. On the basis of the model, calculations of the 6,8He + 28Si total reaction cross sections at intermediate energies have been performed. The results of the calculations are compared with the existing experimental data (Fig. 4). The effects of the density tails of the projectile nuclei, as well as the role of shell admixtures and short-range correlations, are analyzed .
Fig. 4. Total cross section for reaction 6He + 28Si (a) and 8He + 28Si (b) calculated in the framework of the high-energy approximation
A phenomenological and semimicroscopic analysis of data acquired in experiments on elastic and inelastic scattering of 50-MeV alpha particles resulted from their collisions with 112,114,120,124Sn nuclei has been carried out within the optical potential approach and techniques of distorted waves and coupled channels .
Anomalous decays , in the framework of the three-flavor Nambu-Jona-Lasinio [NJL] model, in the vacuum and in quark matter in equilibrium are studied. It is found that the behavior of the relevant observables essentially reflects a manifestation of the partial restoration of chiral symmetry, in non-strange and strange sectors. The probability of such decays decreases with density, showing that anomalous mesonic interactions are significantly affected by the medium .
Phase transitions in hot and dense matter and the in-medium behavior of pseudoscalar mesons are investigated, in the framework of the three flavor Nambu-Jona-Lasinio model, including the 't Hooft interaction, which breaks the UA(1) symmetry. It is found that the appearance of strange quarks, above certain densities, leads to meaningful changes in different observables, especially in matter with in equilibrium. The behaviour of mesons in the plane is analyzed in connection with possible signatures of restoration of symmetries .
The photon-proton scattering reactions
are investigated via the field-theoretical one-particle
-meson, nucleon and
-isobar exchange model .
The solutions of Klein-Gordon equation in the gravitational field of a massive point source in GR were considered for the first time. The basic bounded quantum state and the next few states in the discrete spectrum for different values of the orbital momentum were examined numerically. A novel feature of the solutions under consideration is the essential dependence of their physical properties upon the gravitational mass defect of the point source. It yields a repulsion or an attraction of the quantum levels and to their quasi-crossing .
On the basis of the separated form-factor model, parameters of the polydispersed unilamellar DMPC vesicle population are analyzed. The neutron scattering length density across the membrane is simulated on the basis of a fluctuated model of a lipid bilayer. The hydration of vesicle is described by sigmoid distribution function of water molecules. The results of fitting (Fig. 5) the experimental data obtained at the small-angle spectrometer SANS-I, PSI (Switzerland) are as follows: average vesicle radius (272 0.4) , radius polydispersity 27%, membrane thickness (50.6 0.8) , thickness of hydrocarbon chain region (21.4 2.8) , number of water molecules per one DMPC molecule 13 1, area per one DMPC (59 2) 2. The calculated water distribution function across the bilayer directly explains why the lipid membrane is easily penetrated by water molecules .
Fig. 5. The results of fitting the experimental data obtained at the small-angle spectrometer SANS-I, PSI (Switzerland)
Algorithms and codes have been developed for constructing stationary regular solutions to the Yang-Mills-dilaton system and obtaining unstable eigenmodes of those solutions. Corresponding problems (boundary value problem and Sturm-Liouville matrix problem) were solved on the basis of the continuous analogue of Newton's method. An effective algorithm has been developed and a program complex has been designed for solving a system of nonlinear wave equations .
Based on the principles of classical hydrodynamics and Newtonian gravity, the theory of hydrogravity formulated in the manner of hydromagnetic theory has been developed to provide constructive account of the gravitational effect of global pulsations of a neutron star on the motions of ambient gas-dust interstellar medium. Particular attention was given to gas-dynamical oscillations generated by a pulsating neutron star in an unbounded spherical shell of gas and dust promoted by circumstellar gravitational stresses and damped by viscosity of the interstellar matter. Computed in the long wavelength approximation, the periods of these gravity-driven shear modes, referred to as quasistatic modes of hydrogravity, are found to be proportional to periods of the gravity modes in the neutron star bulk .
A system of equations for electron gas and lattice around and along the trajectory of a 700-ĢeV uranium heavy ion in nickel at the constants of heat capacity and heat conductivity taken at room temperature is solved numerically in the cylindrical axial-symmetric coordinate system. Based on the temperature dependence upon radius and depth around the ion trajectory, one can conclude that the ionizing energy loss is enough for the melting and evaporation processes in the target (Fig. 6). The maximal sizes of radius and depth in target where the melting and evaporation processes can take place have been estimated .
Fig. 6. Time dependence of the temperature of electron gas (a) and lattice (b) on the surface (z=0) of nickel irradiated with uranium ions for various distances from the track axis. Time dependences of temperatures of electron gas (c) and lattices (d) in the place of passing a uranium ion through a surface (r=0) for different depths z in the target. The shaded straight lines on panels b and d show the temperatures of melting Tmelt and evaporation Tevap
Coherent modes of trapped Bose gases were investigated. The conditions of appearing resonance excitations of the modes have been figured out .
A traditional two-day Workshop on Computer Algebra was held in Dubna on 25-26 May 2004. The workshop was dedicated to the memory of the outstanding Russian physicist and organizer of science M.Mescheryakov.
An efficient parallelization of algorithms for computing involutive polynomial bases of Janet type and with integer coefficients of unbound length was demonstrated. Apart from Janet bases, the parallel version of the algorithm can also be applied for computing reduced Groebner bases. In so doing, there are no needs in extra reductions, since reduced Groebner bases form internally fixed subsets of involutive bases .
It was argued that the most general and universal algorithmic approach to reduction of multiloop Feynman integrals to basic integrals was based on computation of Groebner bases for recurrence relations derived from the integration by parts method. In this connection, one considers generic recurrence relations when propagators have arbitrary integer powers treated as symbolic variables (indices) for the relations .
A number of discrete algorithms for symbolic computation of topological phases in optical interference microscopy were designed and analyzed. These algorithms have been implemented as Maple and Mathematica packages .
The problem of solving the Schroedinger equation for bound states in space of dimension D was investigated for the central potentials of a polynomial type and the coefficients dependent of 2q of arbitrary constants. By a numerical-analytical solving of the algebraic system of equations that is equivalent to the Schroedinger equation (the Magjari system), some interesting laws in distribution and behaviour of the roots of that system were found out depending on value D. In particular, at great enough values of D, the energy spectrum gets equidistant .
With the help of the program implementing an original algorithm, cohomologies of the limited Lie algebras of Hamiltonian vector fields were investigated. Such algebras (or Lie p algebras) of vector fields are finite dimensional analogs, determined over fields of positive characteristic p, of corresponding classical algebras. Their finite dimensionality removes a number of difficulties, arising at calculation of cohomologies of classical Lie algebras of vector fields .
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