Factorization of the Universal R-matrix for Uq(sl^2)U_q(\hat{sl}_2)

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential equations on the factors of the universal ${\cal R}$-matrix, which allow to construct uniquely these factors in the integral form.Comment: 28 pages, LaTeX 2.09 using amssym.def and amssym.te

Time-Resolved Studies of Stick-Slip Friction in Sheared Granular Layers

Sensitive and fast force measurements are performed on sheared granular layers undergoing stick-slip motion, along with simultaneous imaging. A full study has been done for spherical particles with a +-20% size distribution. Stick-slip motion due to repetitive fluidization of the layer occurs for low driving velocities. Between major slip events, slight creep occurs that is variable from one event to the next. The effects of changing the stiffness k and velocity V of the driving system are studied in detail. The stick-slip motion is almost periodic for spherical particles over a wide range of parameters, but becomes irregular when k is large and V is relatively small. At larger V, the motion becomes smoother and is affected by the inertia of the upper plate bounding the layer. Measurements of the period T and amplitude A of the relative motion are presented as a function of V. At a critical value Vc, a transition to continuous sliding motion occurs that is discontinuous for k not too large. The time dependence of the instantaneous velocity of the upper plate and the frictional force produced by the granular layer are determined within individual slipping events. The force is a multi-valued function of the instantaneous velocity, with pronounced hysteresis and a sudden drop prior to resticking. Measurements of vertical displacement reveal a small dilation of the material (about one tenth of the mean particle size in a layer 20 particles deep) associated with each slip event. Finally, optical imaging reveals that localized microscopic rearrangements precede (and follow) each slip event. The behavior of smooth particles is contrasted with that of rough particles.Comment: 20, pages, 17 figures, to appear in Phys. Rev.

Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory

Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of N=6 superconformal Chern-Simons theory from osp(6|4) superconformal symmetry. For the osp(4|2) sector, we prove integrability through a Yangian construction. We argue that integrability extends to the full planar two-loop dilatation generator, confirming the applicability of the Bethe equations at weak coupling. Further confirmation follows from an analytic computation of the two-loop twist-one spectrum.Comment: 45 pages, v2: typos in (D.9) fixed, reference added, many small change

The Circadian Rhythm of Blood Pressure During Pregnancy

To review the literature on the circadian rhythm of blood pressure during pregnancy. Data Sources : Computerized searches on MEDLINE, CINAHL, and MIRLYN. Study Selection : Selected studies from 1969 to 1997 were evaluated. Data Extraction : Data were extracted and information was organized under the following areas: definition of and the interconnection between circadian rhythm and blood pressure; the circadian variability of blood pressure throughout the trimesters; the patterns of the circadian rhythm of blood pressure in pregnancies defined as normal and those complicated by chronic hypertension and preeclampsia; and clinical implications. Data Synthesis : The circadian rhythm of blood pressure in pregnancy is the same as in the nonpregnant state, with a nocturnal decrease, especially during sleep. In patients with chronic hypertension, the nocturnal fall in blood pressure may be steeper. Patients with mild preeclampsia may experience a less pronounced nocturnal decrease in blood pressure. Patients with severe preeclampsia may display a reversed circadian rhythm, with no decrease and/or an increase in nocturnal blood pressure. Conclusions : The patterns of the circadian rhythm of blood pressure during normal pregnancy and pregnancies complicated by chronic hypertension and preeclampsia warrant consideration when monitoring patients and implementing management plans.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71412/1/j.1552-6909.2000.tb02771.x.pd

Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity.

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects