Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Dissipative dynamics of vortex arrays in trapped Bose-condensed gases: neutron stars physics on μ\muK scale

We develop a theory of dissipative dynamics of large vortex arrays in trapped Bose-condensed gases. We show that in a static trap the interaction of the vortex array with thermal excitations leads to a non-exponential decay of the vortex structure, and the characteristic lifetime depends on the initial density of vortices. Drawing an analogy with physics of pulsar glitches, we propose an experiment which employs the heating of the thermal cloud in the course of the decay of the vortex array as a tool for a non-destructive study of the vortex dynamics.Comment: 4 pages, revtex; revised versio

Earth Radiation Budget Experiment (ERBE) scanner instrument anomaly investigation

The results of an ad-hoc committee investigation of in-Earth orbit operational anomalies noted on two identical Earth Radiation Budget Experiment (ERBE) Scanner instruments on two different spacecraft busses is presented. The anomalies are attributed to the bearings and the lubrication scheme for the bearings. A detailed discussion of the pertinent instrument operations, the approach of the investigation team and the current status of the instruments now in Earth orbit is included. The team considered operational changes for these instruments, rework possibilities for the one instrument which is waiting to be launched, and preferable lubrication considerations for specific space operational requirements similar to those for the ERBE scanner bearings

Coherent Evolution of Bouncing Bose-Einstein Condensates

We investigate the evolution of Bose-Einstein condensates falling under gravity and bouncing off a mirror formed by a far-detuned sheet of light. After reflection, the atomic density profile develops splitting and interference structures which depend on the drop height, on the strength of the light sheet, as well as on the initial mean field energy and size of the condensate. We compare experimental results with simulations of the Gross-Pitaevski equation. A comparison with the behaviour of bouncing thermal clouds allows to identify quantum features specific for condensates.Comment: 4 page

Evaporative Cooling of a Two-Component Degenerate Fermi Gas

We derive a quantum theory of evaporative cooling for a degenerate Fermi gas with two constituents and show that the optimum cooling trajectory is influenced significantly by the quantum statistics of the particles. The cooling efficiency is reduced at low temperatures due to Pauli blocking of available final states in each binary collision event. We compare the theoretical optimum trajectory with experimental data on cooling a quantum degenerate cloud of potassium-40, and show that temperatures as low as 0.3 times the Fermi temperature can now be achieved.Comment: 6 pages, 4 figure

Zero-temperature phase diagram of binary boson-fermion mixtures

We calculate the phase diagram for dilute mixtures of bosons and fermions at zero temperature. The linear stability conditions are derived and related to the effective boson-induced interaction between the fermions. We show that in equilibrium there are three possibilities: a) a single uniform phase, b) a purely fermionic phase coexisting with a purely bosonic one and c) a purely fermionic phase coexisting with a mixed phase.Comment: 8 pages, revtex, 3 postscript figures; NORDITA-1999/71 C

Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II

The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the plane and hyperbolic analogues to the spherical symmetric case. For spherically symmetric static models the set of equations is reduced to the Tolman-Oppenheimer-Volkoff equation only. Some new non-stationary and inhomogeneous solutions with shear, expansion, and acceleration of the fluid are presented. Among these are a class of temporally self-similar solutions with equation of state given by $p=(\gamma-1)\mu, 1<\gamma<2$, and a class of solutions characterized by $\sigma=-\Theta/6$. We give an example of geometry where the Riemann tensor and the Ricci rotation coefficients are not sufficient to give a complete description of the geometry. Using an extension of the method, we find the full metric in terms of curvature quantities.Comment: 24 pages, 1 figur

Stellar and Gas properties of High HI Mass-to-Light Ratio Galaxies in the Local Universe

We present a multi-wavelength study (BVRI band photometry and HI line interferometry) of nine late-type galaxies selected from the HIPASS Bright Galaxy Catalog on the basis of apparently high HI mass-to-light ratios (3 M_sun/L_sun < M_HI/L_B < 27 M_sun/L_sun). We found that most of the original estimates for M_HI/L_B based on available photographic magnitudes in the literature were too high, and conclude that genuine high HI mass-to-light ratio (>5 M_sun/L_sun) galaxies are rare in the Local Universe. Extreme high M_HI/L_B galaxies like ESO215-G?009 appear to have formed only the minimum number of stars necessary to maintain the stability of their HI disks, and could possibly be used to constrain galaxy formation models. They may to have been forming stars at a low, constant rate over their lifetimes. The best examples all have highly extended HI disks, are spatially isolated, and have normal baryonic content for their total masses but are deficent in stars. This suggests that high M_HI/L_B galaxies are not lacking the baryons to create stars, but are underluminous as they lack either the internal or external stimulation for more extensive star formation.Comment: 29 Pages, 59 Figures. Accepted for publication in AJ (to be published ~April 2006

Intravenous Polyethylene Glycol Inhibits the Loss of Cerebral Cells after Brain Injury

We have tested the effectiveness of polyethylene glycol (PEG) to restore the integrity of neuronal membranes after mechanical damage secondary to severe traumatic brain injury (TBI) produced by a standardized head injury model in rats. We provide additional detail on the standardization of this model, particularly the use and storage of foam bedding that serves to both support the animal during the impact procedure and to dampen the acceleration of the brass weight. Further, we employed a dye exclusion technique using ethidium bromide (EB; quantitative evaluation) and horseradish peroxidase (HRP; qualitative evaluation). Both have been successfully used previously to evaluate neural injury in the spinal cord since they enter cells when their plasma membranes are damaged. We quantified EB labeling (90 M in 110 L of sterile saline) after injection into the left lateral ventricle of the rat brain 2 h after injury. At six h after injection and 8 h after injury, the animals were sacrificed and the brains were analyzed. In the injured rat brain, EB entered cells lining and medial to the ventricles, particularly the axons of the corpus callosum. There was minimal EB labeling in uninjured control brains, limited to cells lining the luminal surfaces of the ventricles. Intravenous injections of PEG (1 cc of saline, 30% by volume, 2000 MW) immediately after severe TBI resulted in significantly decreased EB uptake compared with injured control animals. A similar result was achieved using the larger marker, HRP. PEG-treated brains closely resembled those of uninjured animals

Atomic Deuterium Adsorbed on the Surface of Liquid Helium

We investigate deuterium atoms adsorbed on the surface of liquid helium in equilibrium with a vapor of atoms of the same species. These atoms are studied by a sensitive optical method based on spectroscopy at a wavelength of 122 nm, exciting the 1S-2P transition. We present a direct measurement of the adsorption energy of deuterium atoms on helium and show evidence for the existence of resonantly enhanced recombination of atoms residing on the surface to molecules.Comment: 6 pages 4 figure