Abstract:
In the paper the nilpotent conditions of BRST operator for new superconformal string model were found. This string includes anticommutation $2-d$ fields additional to the standard Neveu-Schwarz superconformal set which carry quark quantum numbers. In this case the superconformal symmetry is realized by a non-linear way. In the superconformal composite string new constraints for 1 and 1/2 conformal dimension should be added to the standard system of Virasoro superalgebra constraints for 2 and 3/2 conformal dimensions. The number $N$ of the constraints and numbers $D$ and $D'$ of bosonic and fermionic $2-d$ fields are connected by a simple relationship $D'/2+D-3N-15=0.$ Also perspectives of the critical composite superconformal string are discussed.

Abstract:
The paper describes two Monte Carlo codes dedicated to muon simulations: MUSIC (MUon SImulation Code) and MUSUN (MUon Simulations UNderground). MUSIC is a package for muon transport through matter. It is particularly useful for propagating muons through large thickness of rock or water, for instance from the surface down to underground/underwater laboratory. MUSUN is designed to use the results of muon transport through rock/water to generate muons in or around underground laboratory taking into account their energy spectrum and angular distribution.

Abstract:
The ANTARES Collaboration is currently constructing a large neutrino telescope in the Mediterranean sea. The telescope will use a three-dimensional array of photomultiplier tubes (PMTs) to detect the Cherenkov light emitted in sea water by neutrino-induced muons. The array of 12 strings, which hold 900 PMTs, is planned to be deployed at a depth of about 2500 m near Toulon (France), 40 km off the coast. The scientific objective of ANTARES is to detect high-energy neutrinos, which may be produced at astrophysical sources -- sites of the cosmic-ray acceleration, such as quasars, gamma-ray bursters, microquasars and supernova remnants. The objectives also include the indirect search for WIMPs by looking for neutrinos from neutralino annihilations in the centres of the Sun, the Earth and the Galaxy. In 2003 two strings have been successfully deployed and connected to the electro-optical cable, which transmitted data to shore station.

Abstract:
The Boulby Dark Matter Collaboration (BDMC) is running several experiments for particle (WIMP) dark matter search in the Underground Boulby Laboratory. These include a liquid xenon detector (ZEPLIN I) and a low pressure gas TPC with directional sensitivity (DRIFT I). Next stage double-phase xenon detectors ZEPLIN II and ZEPLIN III, and a new TPC DRIFT II will be installed at Boulby in a few months. Recent results from the running experiments are discussed and future programme towards large-scale detectors is presented.

Abstract:
New string dynamics is formulated on the basis of the extended set of supergauge constraints including not only supergauge Virasoro conditions but also nilpotent supercurrent constraints . This approach arises from a natural generalization of the classical operator many-string vertices. The formulation of this model leads to three two-dimensional surfaces for description of hadron strings. It gives some dynamical generalization of Chan-Paton factor for string amplitudes in terms of operator vertices. Supersymmetry on the 2-d world surface is present but ten-dimensional supersymmetry is absent. In this approach two-dimensional fermion string fields make it possible to give a unified description of hadron and lepton degrees of freedom and of its dynamics. This model allows to solve the problem of elimination of the most part of parity twins in the baryon spectrum. One-loop (and many-loops perhaps) amplitudes in this model are finite due to the extended set of supergauge constraints and to the significant excess of the total number of fermion two-dimensional fields over the number of boson 2-d fields.

Abstract:
It is considered here the possibility of unitary spinor representations of the Virasoro and super-Virasoro algebras for conformal spin to be equal 1/k; k are integers.

Abstract:
Production of muon pairs by high-energy photons in electromagnetic and hadronic showers in atmosphere has been calculated. The effect of muon pair production in hadronic Extensive Air Showers (EAS) is unlikely to be seen by next generation detectors. Applications of muon pair production process in electromagnetic showers to the very high energy gamma-ray astronomy is discussed. It is shown that, although this process dominates over conventional pion and kaon decay above a few TeV in photon-initiated showers and provides a distinctive signature of photon-induced event (muon pair), it is practically impossible to discriminate such events statistically from the background of muon pairs produced in the hadronic EAS. The rate of events is very low and requires detectors of a huge size.

Abstract:
We consider a critical composite superconformal string model to desribe hadronic interactions. We present a new approach of introducing hadronic quantum numbers in the scattering amplitudes. The physical states carry the quantum numbers and form a common system of eigenfunctions of the operators in this string model. We give explicit constructions of the quantum number operators.

Abstract:
New generation dark matter experiments aim at exploring the 10e-9 - 10e-10 pb cross-section region for the WIMP-nucleon scalar interactions. Neutrons produced in the detector components are one of the main factors that can limit detector sensitivity. Estimation of the background from this source then becomes a crucial task for designing future large-scale detectors. Energy spectra and production rates for neutrons coming from radioactive contamination are required for all materials in and around the detector. In order to estimate neutron yields and spectra, the cross-sections of (a,n) reactions and probabilities of transitions to different excited states should be known. Cross-sections and transition probabilities have been calculated using Empire2.19 for several isotopes, and for some isotopes, a comparison with the experimental data is shown. The results have been used to calculate the neutron spectra from materials using the code Sources4A. Neutron background event rates from some detector components in a hypothetical dark matter detector based on Ge crystals have been estimated. Some requirements for the radiopurity of the materials have been deduced from the results of these simulations.

Abstract:
The process of collision of two parallel domain walls in a supersymmetric model is studied both in effective Lagrangian approximation and by numerical solving of the exact classical field problem. For small initial velocities we find that the walls interaction looks like elastic reflection with some delay. It is also shown that in such approximation internal parameter of the wall may be considered as a time-dependent dynamical variable.