On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

Kinematics of disk galaxies in (proto-)clusters at z=1.5

We observed star-forming galaxies at z~1.5 selected from the HyperSuprimeCam Subaru Strategic Program. The galaxies are part of two significant overdensities of [OII] emitters identified via narrow-band imaging and photometric redshifts from grizy photometry. We used VLT/KMOS to carry out Halpha integral field spectroscopy of 46 galaxies in total. Ionized gas maps, star formation rates and velocity fields were derived from the Halpha emission line. We quantified morphological and kinematical asymmetries to test for potential gravitational (e.g. galaxy-galaxy) or hydrodynamical (e.g. ram-pressure) interactions. Halpha emission was detected in 36 targets. 34 of the galaxies are members of two (proto-)clusters at z=1.47, confirming our selection strategy to be highly efficient. By fitting model velocity fields to the observed ones, we determined the intrinsic maximum rotation velocity Vmax of 14 galaxies. Utilizing the luminosity-velocity (Tully-Fisher) relation, we find that these galaxies are more luminous than their local counterparts of similar mass by up to ~4 mag in the rest-frame B-band. In contrast to field galaxies at z<1, the offsets of the z~1.5 (proto-)cluster galaxies from the local Tully-Fisher relation are not correlated with their star formation rates but with the ratio between Vmax and gas velocity dispersion sigma_g. This probably reflects that, as is observed in the field at similar redshifts, fewer disks have settled to purely rotational kinematics and high Vmax/sigma_g ratios. Due to relatively low galaxy velocity dispersions (sigma_v < 400 km/s) of the (proto-)clusters, gravitational interactions likely are more efficient, resulting in higher kinematical asymmetries, than in present-day clusters. (abbr.)Comment: Accepted for publication in A&A. 11 pages, 8 figures, 1 tabl

Filtering techniques for the detection of Sunyaev-Zel'dovich clusters in multifrequency CMB maps

The problem of detecting Sunyaev-Zel'dovich (SZ) clusters in multifrequency CMB observations is investigated using a number of filtering techniques. A multifilter approach is introduced, which optimizes the detection of SZ clusters on microwave maps. An alternative method is also investigated, in which maps at different frequencies are combined in an optimal manner so that existing filtering techniques can be applied to the single combined map. The SZ profiles are approximated by the circularly-symmetric template $\tau (x) = [1 +(x/r_c)^2]^{-\lambda}$, with $\lambda \simeq \tfrac{1}{2}$ and $x\equiv |\vec{x}|$, where the core radius $r_c$ and the overall amplitude of the effect are not fixed a priori, but are determined from the data. The background emission is modelled by a homogeneous and isotropic random field, characterized by a cross-power spectrum $P_{\nu_1 \nu_2}(q)$ with $q\equiv |\vec{q}|$. The filtering methods are illustrated by application to simulated Planck observations of a $12.8^\circ \times 12.8^\circ$ patch of sky in 10 frequency channels. Our simulations suggest that the Planck instrument should detect $\approx 10000$ SZ clusters in 2/3 of the sky. Moreover, we find the catalogue to be complete for fluxes $S > 170$ mJy at 300 GHz.Comment: 12 pages, 7 figures; Corrected figures. Submitted to MNRA

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.Comment: 5 pages, 1 table, 1 figur

Time Dependent Development of the Coulomb Gap

We show that the time development of the Coulomb gap in a Coulomb glass can involve very long relaxation times due to electron rearrangement and hopping. We find that an applied magnetic field reduces the rate of electron hopping and, hence, Coulomb gap formation. These results are consistent with recent conductance experiments on thin semiconducting and metallic films.Comment: 4 pages, Latex, 3 encapsulated postscript figure

Physiological requirements for carbonate precipitation during biofilm development of Bacillus subtilis etfA mutant

Although the implications of calcium carbonate (CaCO(3)) precipitation by microorganisms in natural environments are quite relevant, the physiology and genetics of this phenomenon are poorly understood. We have chosen Bacillus subtilis 168 as our model to study which physiological aspects are associated with CaCO(3) (calcite) formation during biofilm development when grown on precipitation medium. A B. subtilis eftA mutant named FBC5 impaired in calcite precipitation was used for comparative studies. Our results demonstrate that inactivation of etfA causes a decrease in the pH of the precipitation medium during biofilm development. Further analysis demonstrated that eftA extrudes an excess of 0.7 mol H(+) L(-1) with respect to B. subtilis 168 strain. Using media buffered at different pH values, we were able to control calcite formation. Because etfA encodes the alpha-subunit of a putative flavoprotein involved in fatty acid metabolism, we compared the intracellular levels of NADH among strains. Our physiological assay showed that FBC5 accumulated up to 32 times more NADH than the wild-type strain. We propose that the accumulation of NADH causes a deregulation in the generation of the proton motive force (DeltamicroH(+)) in FBC5 producing the acidification

Peaks in the Cosmic Microwave Background: flat versus open models

We present properties of the peaks (maxima) of the CMB anisotropies expected in flat and open CDM models. We obtain analytical expressions of several topological descriptors: mean number of maxima and the probability distribution of the gaussian curvature and the eccentricity of the peaks. These quantities are calculated as functions of the radiation power spectrum, assuming a gaussian distribution of temperature anisotropies. We present results for angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are relevant for the MAP and COBRAS/SAMBA space missions and the ground-based interferometer experiments. Our analysis also includes the effects of noise. We find that the number of peaks can discriminate between standard CDM models, and that the gaussian curvature distribution provides a useful test for these various models, whereas the eccentricity distribution can not distinguish between them.Comment: 13 pages latex file using aasms4.sty + 3 tables + 2 postscript figures, to appear in ApJ (March 1997

Quasi-classical cyclotron resonance of Dirac fermions in highly doped graphene

Cyclotron resonance in highly doped graphene has been explored using infrared magnetotransmission. Contrary to previous work, which only focused on the magneto-optical properties of graphene in the quantum regime, here we study the quasi-classical response of this system. We show that it has a character of classical cyclotron resonance, with an energy which is linear in the applied magnetic field and with an effective cyclotron mass defined by the position of the Fermi level m = E_F/v_F^2.Comment: 6 pages, 4 figure