Convective Nonlinearity in Non-Newtonian Fluids

In the limit of infinite yield time for stresses, the hydrodynamic equations for viscoelastic, Non-Newtonian liquids such as polymer melts must reduce to that for solids. This piece of information suffices to uniquely determine the nonlinear convective derivative, an ongoing point of contention in the rheology literature.Comment: 4 page

Metamagnetism in the 2D Hubbard Model with easy axis

Although the Hubbard model is widely investigated, there are surprisingly few attempts to study the behavior of such a model in an external magnetic field. Using the Projector Quantum Monte Carlo technique, we show that the Hubbard model with an easy axis exhibits metamagnetic behavior if an external field is turned on. For the case of intermediate correlations strength $U$, we observe a smooth transition from an antiferromagnetic regime to a paramagnetic phase. While the staggered magnetization will decrease linearly up to a critical field $B_c$, uniform magnetization develops only for fields higher than $B_c$.Comment: RevTeX 5 pages + 2 postscript figures (included), accepted for PRB Rapid Communication

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