The saturation of decaying counterflow turbulence in helium II

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L \sim t^{-1}$. Schwarz and Rozen [Phys. Rev. Lett. {\bf 66}, 1898 (1991); Phys. Rev. B {\bf 44}, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek and collaborators [Phys. Rev. E {\bf 67}, 047302 (2003)] found an initial transient followed by the same classical $t^{-3/2}$ scaling observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.Comment: 19 pages, 5 figure

Scattering length of Andreev reflection from quantized vortices in 3^3He-BB

Andreev reflection of thermal quasiparticles from quantized vortices is an important technique to visualize quantum turbulence in low temperature $^3$He-$B$. We revisit a problem of Andreev reflection from the isolated, rectilinear vortex line. For quasiparticle excitations whose impact parameters, defined as distances of the closest approach to the vortex core, do not exceed some arbitrary value, $b$, we calculate exactly the reflected fraction of the total flux of excitations incident upon the vortex in the direction orthogonal to the vortex line. We then define and calculate exactly, as a function of $b$, the scattering length, that is the scattering cross-section per unit length of the vortex line. We also define and calculate the scattering lengths for the flux of energy carried by thermal excitations, and for the net energy flux resulting from a (small) temperature gradient, and analyze the dependence of these scattering lengths on temperature.Comment: 8 pages, 4 figure

Coherent vortex structures in quantum turbulence

This report addresses an important question discussed by the quantum turbulence community during the last decade: do quantized vortices form, in zero-temperature superfluids, coherent structures similar to vortex tubes in ordinary, viscous turbulence? So far the evidence provided by numerical simulations is that bundles of quantized vortices appear in finite-temperature superfluids, but from the interaction with existing coherent structures in the turbulent (viscous) normal fluid, rather than due to the intrinsic superfuid dynamics. In this report we show that, in very intense quantum turbulence (whose simulation was made possible by a tree algorithm), the vortex tangle contains small coherent vortical structures (bundles of quantized vortices) which arise from the Biot-Savart dynamics alone, and which are similar to the coherent structures observed in classical viscous turbulence.Comment: 6 pages, 6 figure

vol.17 奥付・裏表紙

protein atomic structure predicted using homology modelin

Spherical geometry and integrable systems

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.Comment: 15 pages, 5 figure