Preliminary investigation of pressure influence on multiphase heat transfer report no. ii

Pressure and surface condition in multiphase boiling heat transfe

Growth of fat slits and dispersionless KP hierarchy

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte

Observation of vortex dipoles in an oblate Bose-Einstein condensate

We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics, finding that the vortex cores of opposite charge can exist for many seconds and that annihilation is inhibited in our highly oblate trap geometry. For sufficiently rapid flow velocities we find that clusters of like-charge vortices aggregate into long-lived dipolar flow structures.Comment: 4 pages, 4 figures, 1 EPAPS fil

Applications of p-deficiency and p-largeness

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich for the remaining primes. We also generalise a result of Grigorchuk on Coxeter groups to odd primes.Comment: 23 page

Surface plasmon toy-model of a rotating black hole

Recently introduced surface plasmon toy black hole model has been extended in order to emulate a rotating black hole (Kerr metric). Physical realization of this model involves a droplet of an optically active liquid on the metal surface which supports propagation of surface plasmons. Such droplets are shown to exhibit giant optical activity in the frequency range near the surface plasmon resonance of a metal-liquid interface.Comment: 4 pages, 4 figure

On the Radial Distribution of White Dwarfs in the Globular Cluster NGC 6397

We have examined the radial distribution of white dwarfs over a single HST/ACS field in the nearby globular cluster NGC 6397. In relaxed populations, such as in a globular cluster, stellar velocity dispersion, and hence radial distribution, is directly dependent on stellar masses. The progenitors of very young cluster white dwarfs had a mass of ~0.8 solar masses, while the white dwarfs themselves have a mass of ~0.5 solar masses. We thus expect young white dwarfs to have a concentrated radial distribution (like that of their progenitors) that becomes more extended over several relaxation times to mimic that of ~0.5 solar mass main-sequence stars. However, we observe young white dwarfs to have a significantly extended radial distribution compared to both the most massive main sequence stars in the cluster and also to old white dwarfs.Comment: 13 pages including 1 table and 3 figures. Accepted for publication in the MNRAS Letter

Darboux Transformations, Infinitesimal Symmetries and Conservation Laws for Nonlocal Two-Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connections between the solutions of overdetermined linear systems and their expansions in series at singular points neighborhood are presented. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained.Comment: 12 pages, infinitesimal symmetries and conservation laws are adde