64.70.Nd Structural transitions in nanoscale materials. We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelctrolyte mixture that includes both complexation and incompatibility. 1

Abstract. The integrable system is introduced based on the Poisson rs-matrix structure. This is a generalization of the Gaudin magnet, and in SL(2) case isomorphic to the generalized Neumann model. The separation of variables is discussed for both classical and quantum case. Short title: BC-type Gaudin Magnet

An example is given of a plane topological torsion defect representing a cosmic wall double wall in teleparallel gravity.The parallel planar walls undergone a repulsive gravitational force due to Cartan torsion.This is the first example of a non-Riemannian double cosmic wall.It is shown that the walls oscillate with a speed that depends on torsion and on the surface density of the wall.Cartan torsion acts also as a damping force reducing the speed of oscillation when it is stronger.

The equations of in-medium gluodynamics are proposed. Their classical lowest order solution is explicitly shown for a color charge moving with constant speed. For nuclear permittivity larger than 1 it describes emission of Cherenkov gluons resembling results of classical electrodynamics. The values of the real and imaginary parts of the nuclear permittivity are obtained from the fits to experimental data on the double-humped structure around the away-side jet obtained at RHIC. The dispersion of the nuclear permittivity is predicted by comparing the RHIC, SPS and cosmic ray data. This is important for LHC experiments. Cherenkov gluons may be responsible for the asymmetry of dilepton mass spectra near ρ-meson observed in the SPS experiment with excess in the low-mass wing of the resonance. This feature is predicted to be common for all resonances. The ”color rainbow ” quantum effect might appear according to higher order terms of in-medium QCD if the nuclear permittivity depends on color. 1

Total spectrum of photon emission by an ultra-relativistic positron channelling in a periodically bent crystal. ‡

In this work is shown that standard dynamical equations of the chaotic inflation for a massive real scalar field hold an especial local gauge symmetry. Given symmetry admits that inflation field mass can be considered as an especial ”charge”. Also, it is shown that given equations except expected CPT symmetry, hold surprisingly, C 1 2P 1 2T 1 2 symmetry too. Key words: chaotic inflation- massive scalar field- CPT symmetry In this work will be shown that standard dynamical equations of the chaotic inflation for a massive real scalar field hold an especial, local gauge symmetry. Given symmetry admits that inflation field mass can be considered as an especial ”charge”. Also, it is shown that given equations except CPT symmetry, hold C 1 2P 1 2T 1 2 symmetry too. As it is well-known [1]-[7], chaotic inflation dynamics for a real scalar field with mass m can be generally presented by two usual differential equations d2φ + 31 dt2 a ( 1 da a dt)2 + k 4π a2 da dφ dt dt = −m2φ (1) 3m 2 P ( ( dφ dt)2 + m 2 φ 2). (2) Here φ represents the real scalar field depending of the time t, mP- Planck’s mass, a- scale factor of the universe, k- curvature constant (that equals 1 for closed, 0 for flat and-1 for open universe). 1 Define the following operator Dt = d − im (3) dt representing an especial covariant differentiation so that it is satisfied Dt(e imt φ) = e imtdφ. (4) dt By use of (3), (4) equation (1) can be presented in an equivalent form DtDt(e imt φ) + 3 1 da a dt Dt(e imt φ) = −m 2 (e imt φ) (5) or after complex conjugation, ∗, in other equivalent form D ∗ tD ∗ t (e−imtφ) + 3 1 da a dt D ∗ t (e−imtφ) = −m 2 (e −imt φ) (6) Also, by use (3), (4) equation (2) can be presented in an equivalent form ( 1 da a dt)2 + k 4π

We present a proof of the positivity of the Bondi energy in Einstein-Maxwell axion dilaton gravity, being the low-energy limit of the heterotic string theory. We consider the spacelike hypersurface which asymptotically approaches a null cone and on which the equations of the theory under consideration are given. Next, we generalize the proof allowing the hypersurface having inner boundaries. 1

Assumption of nonvanishingness of vacuum expectation of the scalar field for spontaneous symmetry breaking is superfluous

In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical transformations which lead to the adiabatic invariant of the system and to the first order non linear correction to its Hannay angle. Then, applying the same transformations to the 1-D quartic damped oscillator we show that this oscillator is canonically equivalent to the linear generalized harmonic oscillator for finite values of the damping parameter (which implies no correction to the linear Hannay angle) whereas, in an appropriate weak damping limit, it becomes equivalent to the quartic generalized oscillator (which implies a non linear correction to this angle). 2 INTRODUCTION The Hannay’s angle [1] (classical counterpart of the Berry’s

framework rationalize data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks. PACS numbers: 05.70.Ln, 05.50.+q Typeset using REVT E X 1 Many social, biological, and communication systems can be properly described by complex