On blowup for Yang-Mills fields

We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical and analytical methods we show in both cases that generic solutions starting with sufficiently large initial data blow up in finite time. The mechanism of singularity formation depends on the dimension: in $d=5$ the blowup is exactly self-similar while in $d=4$ the blowup is only approximately self-similar and can be viewed as the adiabatic shrinking of the marginally stable static solution. The threshold for blowup and the connection with critical phenomena in the gravitational collapse (which motivated this research) are also briefly discussed.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Skylab investigation of the upwelling off the Northwest coast of Africa

The upwelling off the NW coast of Africa in the vicinity of Cape Blanc was studied in February - March 1974 from aircraft and in September 1973 from Skylab. The aircraft study was designed to determine the effectiveness of a differential radiometer in quantifying surface chlorophyll concentrations. Photographic images of the S190A Multispectral Camera and the S190B Earth Terrain Camera from Skylab were used to study distributional patterns of suspended material and to locate ocean color boundaries. The thermal channel of the S192 Multispectral Scanner was used to map sea-surface temperature distributions offshore of Cape Blanc. Correlating ocean color changes with temperature gradients is an effective method of qualitatively estimating biological productivity in the upwelling region off Africa

THEORETICAL STUDY OF THE IR SPECTROSCOPY OF BENZENE-(WATER)N CLUSTERS

The local mode Hamiltonian that assigns RIDIR spectra for Bz-(H$_2$O)$_6$ and Bz-(H$_2$O)$_7$ is explored in detail for Bz-(H$_2$O)$_n$ with $n=3-7$. In addition to contributions from OH stretches, the Hamiltonian includes the anharmonic coupling of each water monomer's bend overtone and its OH stretch fundamentals, which is necessary for accurately modeling 3150-3300 cm$^{-1}$ region of the spectra. The parameters of the Hamiltonian can be calculated using either MP2 or density functional theory. The relative strengths and weaknesses of these two electronic structure approaches are examined to gain further physical understanding. Initial assignments of Bz-(H$_2$O)$_6$ and Bz-(H$_2$O)$_7$ were based on a linear scaling of M06-2X harmonic frequencies. In most cases, counterpoise-corrected MP2 calculations obtain similar frequencies (across all cluster sizes) if stretch anharmonicity is taken into account. Individual ``monomer Hamiltonians'' are constructed via the application of fourth order Van Vleck perturbation theory to MP2 potential energy surfaces. These calculations elucidate the sensitivity of intra-monomer couplings to chemical environment. The presence of benzene has particularly important consequences for the spectra of the Bz-(H$_2$O)$_{3-5}$ clusters, in which the symmetry of the water cycles is broken by $pi$-H-bonding to benzene. The nature of these perturbations is discussed

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.Comment: 4 pages, several minor modifications, title change

The role of quantum fluctuations in the optomechanical properties of a Bose-Einstein condensate in a ring cavity

We analyze a detailed model of a Bose-Einstein condensate trapped in a ring optical resonator and contrast its classical and quantum properties to those of a Fabry-P{\'e}rot geometry. The inclusion of two counter-propagating light fields and three matter field modes leads to important differences between the two situations. Specifically, we identify an experimentally realizable region where the system's behavior differs strongly from that of a BEC in a Fabry-P\'{e}rot cavity, and also where quantum corrections become significant. The classical dynamics are rich, and near bifurcation points in the mean-field classical system, the quantum fluctuations have a major impact on the system's dynamics.Comment: 11 pages, 11 figures, submitted to PR

From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity Ns of the inherent structures generically has a lognormal distribution. In addition, the large volume limit of ln/ differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.Comment: 10 pages, 9 figs, slightly improved presentation, more references, accepted for publication in Phys Rev

Energy landscape and rigidity

The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this effect. The model predicts a deviation from the Debye law at low temperatures. Then, the connection between the topography of the energy landscape, the topology of the phase space and the rigidity of a glass is explored. As a result, we relate the number of constraints and floppy modes with the statistics of the landscape. We apply these ideas to a simple model for which we provide an approximate expression for the number of energy basins as a function of the rigidity. This allows to understand certains features of the glass transition, like the jump in the specific heat or the reversible window observed in chalcogenide glasses.Comment: 1 text+3 eps figure