ar X iv : c on d - m at / 9 50 71 32 v 1 3 0 Ju l 1 99 5 Does Fully - Developed Turbulence Exist ? Reynolds Number Independence versus Asymptotic Covariance

ar X iv : c on d - m at / 9 50 80 62 v 1 3 1 Ju l 1 99 5 QUANTUM THEORY OF LARGE SYSTEMS OF NON - RELATIVISTIC MATTER

Does fully developed turbulence exist? Reynolds number independence versus asymptotic covariance

By analogy with recent arguments concerning the mean velocity profile of wall-bounded turbulent shear flows, we suggest that there may exist corrections to the 3 law of Kolmogorov, which are proportional to (ln Re)-’ at large Re. Such corrections to K41 are the only ones permitted if one insists that the functional form of statistical averages at large Re be invariant under a natural redefiniti...

ar X iv : c on d - m at / 9 60 72 14 v 1 3 0 Ju l 1 99 6 Spontaneous vortex phase discovered ?

It is argued that a spontaneous vortex phase may exist in the recently discovered compound ErN i 2 B 2 C at temperature below 2.3K. The consequences of this proposal are discussed. In particular the magnetic response of the system are studied both above and below 2.3K and further experiments proposed.

ar X iv : c on d - m at / 9 50 71 07 v 1 2 5 Ju l 1 99 5 Two interacting particles in an effective 2 - 3 – d random potential

We study the effect of coherent propagation of two interacting particles in an effective 2-3-d disordered potential. Our numerical data demonstrate that in dimension d > 2, interaction can lead to two–particles delocalization below one–particle delocalization border. We also find that the distance between the two delocalized particles (pair size) grows logarithmically with time. As a result pai...

ar X iv : m at h / 99 07 18 5 v 1 [ m at h . M G ] 2 9 Ju l 1 99 9 Higher dimensional flexible polyhedra ∗

It is show that sphere homeomorphic flexible polyhedra (with self intersections) do really exist in n-dimensional Euclidean, Lobachevskij and spherical spaces for each n ≥ 3. 1991 Mathematics Subject Classification: 52C25, 52B11.