Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow

We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the nonintegrable perturbation. This type of chaotic advection, termed {\it resonance-induced diffusion\/}, is generic for a large class of flows.Comment: 4 pages, uuencoded compressed postscript file, to appear in Phys. Rev. Lett. Also available on the WWW from http://formentor.uib.es/~julyan/, or on paper by reques

An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.Comment: 5 pages, 3 figures, some modest revisions to previous version (esp. to the figures) to aid clarity; accepted for publication in Physical Review A (due out on January 1st 2003

Marginal Coral Populations: the Densest Known Aggregation of Pocillopora in the Galápagos Archipelago is of Asexual Origin

Coral populations at distributional margins frequently experience suboptimal and variable conditions. Recurrent El Niño-Southern Oscillation (ENSO) warming events have caused extensive mortality of reef-building corals in the Eastern Pacific, and particularly impacted branching pocilloporid corals in the Galápagos Islands. Pocillopora spp. were previously more common and formed incipient reefs at several locations in the archipelago but now occur as scattered colonies. Here, we report an unusually concentrated aggregation of colonies and evaluate their current genetic diversity. In particular we focus on a large population of 1614 live Pocillopora colonies found in a volcanic lagoon along the southern shore of Isabela Island. Forty seven colonies were sampled, primarily using a spatially explicit sampling design, and all colonies belonged to Pocillopora mitochondrial open reading frame lineage type 3a. Typing of additional Pocillopora samples (n = 40) from three other islands indicated that this stand is the only known representative of type 3a in the Galápagos Islands. The Isabela Pocillopora type 3a colonies harbored Symbiodinium ITS-2 clade C1d. Multilocus genotyping (n = 6 microsatellites) capable of resolving individual clones indicated that this stand is monogenotypic and thus the high density of colonies is a result of asexual reproduction, likely via fragmentation. Colony size distribution, while an imperfect measure, suggested the stand regrew from remnant colonies that survived the 1997/98 ENSO event but may postdate the 1982/83 ENSO. The community of Pocillopora colonies at Isabela is of particular ecological value due to its high density and support of associated organisms such as fish and benthic invertebrates. The Galapagos Pocillopora corals will continue to provide insights into the genetic structure and population dynamics of marginal coral populations

A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio

Water activity and activation diameters from hygroscopicity data - Part II: Application to organic species

International audienceA method has been developed for using particle hygroscopicity measurements made with a humidified tandem differential mobility analyzer (HTDMA) to determine water activity as a function of solute weight percent. In Part I, the method was tested for particles composed of sodium chloride and ammonium sulfate. Here, we report results for several atmospherically-relevant organic species: glutaric acid, malonic acid, oxalic acid and levoglucosan. Predicted water activities for aqueous dicarboxylic acid solutions are quite similar in some cases to published estimates and the simplified predictions of Köhler theory, while in other cases substantial differences are found, which we attribute primarily to the semivolatile nature of these compounds that makes them difficult to study with the HTDMA. In contrast, estimates of water activity for levoglucosan solutions compare very well with recently-reported measurements and with published data for aqueous glucose and fructose solutions. For all studied species, the critical dry diameters active at supersaturations between 0.2 and 1% that are computed with the HTDMA-derived water activities are generally within the experimental error (~20%) estimated in previously-published direct measurements using cloud condensation nuclei counters. For individual compounds, the variations in reported solution water activity lead to uncertainties in critical dry diameters of 5-25%, not significantly larger than the uncertainty in the direct measurements. To explore the impact of these uncertainties on modeled aerosol-cloud interactions, we incorporate the variations in estimates of solution water activities into the description of hygroscopic growth of aerosol particles in an adiabatic parcel model and examine the impact on the predicted drop number concentrations. For the limited set of initial conditions examined here, we find that the uncertainties in critical dry diameters for individual species lead to 0-21% changes in drop number concentration, with the largest effects at high aerosol number concentrations and slow updraft velocities. Ammonium sulfate, malonic acid and glutaric acid have similar activation behavior, while glutaric acid and levoglucosan are somewhat less hygroscopic and lead to lower drop number concentrations; sodium chloride is the most easily activated compound. We explain these behaviors in terms of a parameter that represents compound hygroscopicity, and conclude that this parameter must vary by more than a factor of 2 to induce more than a 15% change in activated drop number concentrations. In agreement with earlier studies, our results suggest that the number concentration of activated drops is more sensitive to changes in the input aerosol size and number concentrations and the applied updraft velocity than to modest changes in the aerosol composition and hygroscopic properties

Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility $\chi$ at the mobility edge, $\chi=\eta/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.Comment: 5 pages, RevTeX, 3 figures, Postscript, strongly revised version to be published in PR

E10 and a "small tension expansion" of M Theory

A formal ``small tension'' expansion of D=11 supergravity near a spacelike singularity is shown to be equivalent, at least up to 30th order in height, to a null geodesic motion in the infinite dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10(R). For the proof we make use of a novel decomposition of E10 into irreducible representations of its SL(10,R) subgroup. We explicitly show how to identify the first four rungs of the E10 coset fields with the values of geometric quantities constructed from D=11 supergravity fields and their spatial gradients taken at some comoving spatial point.Comment: 4 page

Hyperbolic billiards of pure D=4 supergravities

We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz (BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find that just as for the cases N=0 and N=8 investigated previously, these billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature arises, however, which is that the relevant Kac-Moody algebra can be the Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of this property is provided by showing that the data relevant for determining the billiards are the restricted root system and the maximal split subalgebra of the finite-dimensional real symmetry algebra characterizing the toroidal reduction to D=3 spacetime dimensions. To summarize: split symmetry controls chaos.Comment: 21 page

Orthogonality Catastrophe in Parametric Random Matrices

We study the orthogonality catastrophe due to a parametric change of the single-particle (mean field) Hamiltonian of an ergodic system. The Hamiltonian is modeled by a suitable random matrix ensemble. We show that the overlap between the original and the parametrically modified many-body ground states, $S$, taken as Slater determinants, decreases like $n^{-k x^2}$, where $n$ is the number of electrons in the systems, $k$ is a numerical constant of the order of one, and $x$ is the deformation measured in units of the typical distance between anticrossings. We show that the statistical fluctuations of $S$ are largely due to properties of the levels near the Fermi energy.Comment: 12 pages, 8 figure

Spectral statistics near the quantum percolation threshold

The statistical properties of spectra of a three-dimensional quantum bond percolation system is studied in the vicinity of the metal insulator transition. In order to avoid the influence of small clusters, only regions of the spectra in which the density of states is rather smooth are analyzed. Using finite size scaling hypothesis, the critical quantum probability for bond occupation is found to be $p_q=0.33\pm.01$ while the critical exponent for the divergence of the localization length is estimated as $\nu=1.35\pm.10$. This later figure is consistent with the one found within the universality class of the standard Anderson model.Comment: REVTeX, 4 pages, 5 figures, all uuencoded, accepted for publication in PRB (Rapid Communication