Microwave Induced Instability Observed in BSCCO 2212 in a Static Magnetic Field

We have measured the microwave dissipation at 10 GHz through the imaginary part of the susceptibility, $\chi^"$, in a BSCCO 2212 single crystal in an external static magnetic field $H$ parallel to the c-axis at various fixed temperatures. The characteristics of $\chi^"(H)$ exhibit a sharp step at a field $H_{step}$ which strongly depends on the amplitude of the microwave excitation $h_{ac}$. The characteristics of $h_{ac}$ vs. $H_{step}$, qualitatively reveal the behavior expected for the magnetic field dependence of Josephson coupling.Comment: 4 pages, 3 Postscript figure

Universality of Tip Singularity Formation in Freezing Water Drops

A drop of water deposited on a cold plate freezes into an ice drop with a pointy tip. While this phenomenon clearly finds its origin in the expansion of water upon freezing, a quantitative description of the tip singularity has remained elusive. Here we demonstrate how the geometry of the freezing front, determined by heat transfer considerations, is crucial for the tip formation. We perform systematic measurements of the angles of the conical tip, and reveal the dynamics of the solidification front in a Hele-Shaw geometry. It is found that the cone angle is independent of substrate temperature and wetting angle, suggesting a universal, self-similar mechanism that does not depend on the rate of solidification. We propose a model for the freezing front and derive resulting tip angles analytically, in good agreement with observations.Comment: Letter format, 5 pages, 3 figures. Note: authors AGM and ORE contributed equally to the pape

SOS model partition function and the elliptic weight functions

We generalize a recent observation [arXiv:math/0610433] that the partition function of the 6-vertex model with domain-wall boundary conditions can be obtained by computing the projections of the product of the total currents in the quantum affine algebra $U_{q}(\hat{\mathfrak{sl}}_{2})$ in its current realization. A generalization is proved for the the elliptic current algebra [arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of total currents are calculated explicitly and are represented as integral transforms of the product of the total currents. We prove that the kernel of this transform is proportional to the partition function of the SOS model with domain-wall boundary conditions.Comment: 21 pages, 5 figures, requires iopart packag

Boundary Heisenberg algebras and their deformations

We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and Heisenberg circle plus mitt algebras which arise as symmetry algebras in three-dimensional gravity theories. As a result of the deformation procedure we find a large class of algebras. While some of these algebras are new, some of them have already been obtained as asymptotic and boundary symmetry algebras, supporting the idea that symmetry algebras associated to diverse boundary conditions and spacetime loci are algebraically interconnected through deformation of algebras. The deformation/contraction relationships between the new algebras are investigated. In addition, it is also shown that the deformation procedure reaches new algebras inaccessible to the Sugawara construction. As a byproduct of our analysis, we obtain that Heisenberg circle plus mitt and the asymptotic symmetry algebra Weyl-bms(3) are not connected via single deformation but in a more subtle way

Random walks in random Dirichlet environment are transient in dimension d≥3d\ge 3

We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On $\Z^d$, RWDE are parameterized by a $2d$-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension $d\ge 3$. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and applies for example to finitely generated symmetric transient Cayley graphs. In terms of reinforced random walks it implies that directed edge reinforced random walks are transient for $d\ge 3$.Comment: New version published at PTRF with an analytic proof of lemma

Gastrointestinal tract size, total-tract digestibility, and rumen microflora in different dairy cow genotypes

peer-reviewedThe superior milk production efficiency of Jersey (JE) and Jersey × Holstein-Friesian (JE × HF) cows compared with Holstein-Friesian (HF) has been widely published. The biological differences among dairy cow genotypes, which could contribute to the milk production efficiency differences, have not been as widely studied however. A series of component studies were conducted using cows sourced from a longer-term genotype comparison study (JE, JE × HF, and HF). The objectives were to (1) determine if differences exist among genotypes regarding gastrointestinal tract (GIT) weight, (2) assess and quantify whether the genotypes tested differ in their ability to digest perennial ryegrass, and (3) examine the relative abundance of specific rumen microbial populations potentially relating to feed digestibility. Over 3 yr, the GIT weight was obtained from 33 HF, 35 JE, and 27 JE × HF nonlactating cows postslaughter. During the dry period the cows were offered a perennial ryegrass silage diet at maintenance level. The unadjusted GIT weight was heavier for the HF than for JE and JE × HF. When expressed as a proportion of body weight (BW), JE and JE × HF had a heavier GIT weight than HF. In vivo digestibility was evaluated on 16 each of JE, JE × HF, and HF lactating dairy cows. Cows were individually stalled, allowing for the total collection of feces and were offered freshly cut grass twice daily. During this time, daily milk yield, BW, and dry matter intake (DMI) were greater for HF and JE × HF than for JE; milk fat and protein concentration ranked oppositely. Daily milk solids yield did not differ among the 3 genotypes. Intake capacity, expressed as DMI per BW, tended to be different among treatments, with JE having the greatest DMI per BW, HF the lowest, and JE × HF being intermediate. Production efficiency, expressed as milk solids per DMI, was higher for JE than HF and JE × HF. Digestive efficiency, expressed as digestibility of dry matter, organic matter, N, neutral detergent fiber, and acid detergent fiber, was higher for JE than HF. In grazing cows (n = 15 per genotype) samples of rumen fluid, collected using a transesophageal sampling device, were analyzed to determine the relative abundance of rumen microbial populations of cellulolytic bacteria, protozoa, and fungi. These are critically important for fermentation of feed into short-chain fatty acids. A decrease was observed in the relative abundance of Ruminococcus flavefaciens in the JE rumen compared with HF and JE × HF. We can deduce from this study that the JE genotype has greater digestibility and a different rumen microbial population than HF. Jersey and JE × HF cows had a proportionally greater GIT weight than HF. These differences are likely to contribute to the production efficiency differences among genotypes previously reported

A geometric study of the dispersionless Boussinesq type equation

We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney-Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in . The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators that send conservation laws and symmetries to each other but are neither Hamiltonian, nor symplectic. These operators give rise to a noncommutative infinite-dimensional algebra of recursion operators

Dispersionful analogues of Benney's equations and NN-wave systems

We recall Krichever's construction of additional flows to Benney's hierarchy, attached to poles at finite distance of the Lax operator. Then we construct a ``dispersionful'' analogue of this hierarchy, in which the role of poles at finite distance is played by Miura fields. We connect this hierarchy with $N$-wave systems, and prove several facts about the latter (Lax representation, Chern-Simons-type Lagrangian, connection with Liouville equation, $\tau$-functions).Comment: 12 pages, latex, no figure