Mixing by polymers: experimental test of decay regime of mixing

By using high molecular weight fluorescent passive tracers with different diffusion coefficients and by changing the fluid velocity we study dependence of a characteristic mixing length on the Peclet number, $Pe$, which controls the mixing efficiency. The mixing length is found to be related to $Pe$ by a power law, $L_{mix}\propto Pe^{0.26\pm 0.01}$, and increases faster than expected for an unbounded chaotic flow. Role of the boundaries in the mixing length abnormal growth is clarified. The experimental findings are in a good quantitative agreement with the recent theoretical predictions.Comment: 4 pages,5 figures. accepted for publication in PR

Free-energy transition in a gas of non-interacting nonlinear wave-particles

We investigate the dynamics of a gas of non-interacting particle-like soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by employing methods of the statistical mechanics of chaos. In particular, we show that a suitable free energy undergoes a metamorphosis as the input excitation is increased, thereby developing a first order phase transition whose measurable manifestation is the formation of shock waves. This demonstrates that even the simplest phase-space dynamics, involving independent (uncoupled) degrees of freedom, can sustain critical phenomena.Comment: 4 pages, 3 figure

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Nonlinear management of the angular momentum of soliton clusters

We demonstrate an original approach to acquire nonlinear control over the angular momentum of a cluster of solitary waves. Our model, derived from a general description of nonlinear energy propagation in dispersive media, shows that the cluster angular momentum can be adjusted by acting on the global energy input into the system. The phenomenon is experimentally verified in liquid crystals by observing power-dependent rotation of a two-soliton cluster.Comment: 4 pages, 3 figure

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

High field x-ray diffraction study on a magnetic-field-induced valence transition in YbInCu4

We report the first high-field x-ray diffraction experiment using synchrotron x-rays and pulsed magnetic fields exceeding 30 T. Lattice deformation due to a magnetic-field-induced valence transition in YbInCu4 is studied. It has been found that the Bragg reflection profile at 32 K changes significantly at around 27 T due to the structural transition. In the vicinity of the transition field the low-field and the high-field phases are observed simultaneously as the two distinct Bragg reflection peaks: This is a direct evidence of the fact that the field-induced valence state transition is the first order phase transition. The field-dependence of the low-field-phase Bragg peak intensity is found to be scaled with the magnetization.Comment: 5 pages, 6 figures, submitted to J. Phys. Soc. Jp

On the universality of the Discrete Nonlinear Schroedinger Equation

We address the universal applicability of the discrete nonlinear Schroedinger equation. By employing an original but general top-down/bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely applicable and the simplest possible model, revealing that the discrete nonlinear Schroedinger equation is ``universally'' fit to describe light propagation even in discrete tensorial nonlinear systems and in the presence of nonparaxial and vectorial effects.Comment: 6 Pages, to appear in Phys. Rev.

Sous-groupes alg\'ebriques du groupe de Cremona

We give a complete classification of maximal algebraic subgroups of the Cremona group of the plane and provide algebraic varieties that parametrize the conjugacy classes. ----- Nous donnons une classification compl\`ete des sous-groupes alg\'ebriques maximaux du groupe de Cremona du plan et explicitons les vari\'et\'es qui param\`etrent les classes de conjugaison.Comment: Text in French, Translated introduction, 35 pages, 1 figure, to appear in Transform. Group

Pasquale del Pezzo, Duke of Caianello, Neapolitan mathematician

This article is dedicated to a reconstruction of some events and achievements, both personal and scientific, in the life of the Neapolitan mathematician Pasquale del Pezzo, Duke of Caianello