Selective Principal Component Extraction and Reconstruction: A Novel Method for Ground Based Exoplanet Spectroscopy

Context: Infrared spectroscopy of primary and secondary eclipse events probes the composition of exoplanet atmospheres and, using space telescopes, has detected H2O, CH4 and CO2 in three hot Jupiters. However, the available data from space telescopes has limited spectral resolution and does not cover the 2.4 - 5.2 micron spectral region. While large ground based telescopes have the potential to obtain molecular-abundance-grade spectra for many exoplanets, realizing this potential requires retrieving the astrophysical signal in the presence of large Earth-atmospheric and instrument systematic errors. Aims: Here we report a wavelet-assisted, selective principal component extraction method for ground based retrieval of the dayside spectrum of HD 189733b from data containing systematic errors. Methods: The method uses singular value decomposition and extracts those critical points of the Rayleigh quotient which correspond to the planet induced signal. The method does not require prior knowledge of the planet spectrum or the physical mechanisms causing systematic errors. Results: The spectrum obtained with our method is in excellent agreement with space based measurements made with HST and Spitzer (Swain et al. 2009b; Charbonneau et al. 2008) and confirms the recent ground based measurements (Swain et al. 2010) including the strong 3.3 micron emission.Comment: 4 pages, 3 figures; excepted for publication by A&

Key Issues in the Analysis of Remote Sensing Data: A report on the workshop

The procedures of a workshop assessing the state of the art of machine analysis of remotely sensed data are summarized. Areas discussed were: data bases, image registration, image preprocessing operations, map oriented considerations, advanced digital systems, artificial intelligence methods, image classification, and improved classifier training. Recommendations of areas for further research are presented

Bayesian classification in a time-varying environment

The problem of classifying a pattern based on multiple observation made in a time-varying environment is analyzed. The identity of the pattern may itself change. A Bayesian solution is derived, after which the conditions of the physical situation are invoked to produce a cascade classifier model. Experimental results based on remote sensing data demonstrate the effectiveness of the classifier

Implementation and evaluation of ILLIAC 4 algorithms for multispectral image processing

Data concerning a multidisciplinary and multi-organizational effort to implement multispectral data analysis algorithms on a revolutionary computer, the Illiac 4, are reported. The effectiveness and efficiency of implementing the digital multispectral data analysis techniques for producing useful land use classifications from satellite collected data were demonstrated

Contact angles on heterogeneous surfaces; a new look at Cassie's and Wenzel's laws

We consider a three dimensional liquid drop sitting on a rough and chemically heterogeneous substrate. Using a novel minimization technique on the free energy of this system, a generalized Young's equation for the contact angle is found. In certain limits, the Cassie and Wenzel laws, and a new equivalent rule, applicable in general, are derived. We also propose an equation in the same spirit as these results but valid on a more `microscopic' level. Throughout we work under the presence of gravity and keep account of line tension terms.Comment: 10 pages RevTeX, 2 EPS figures. A few minor corrections mad

Wetting between structured surfaces: Liquid bridges and induced forces

Wetting phenomena are theoretically studied for a slab geometry consisting of a wetting phase confined between two chemically patterned substrates. Each of these is decorated by an array of stripes whose composition alternates between two different surface phases. For a single pair of opposing stripes, the wetting phase may either form a bridge spanning from one surface to the other or it may break up into two separate channels. The bridge state induces an effective interaction between the two substrates. This leads to the bridge itself having a preferred contact angle and the substrates having a preferred separation. In the case of many stripes, one has a whole sequence of morphological transitions with the number of bridges decreasing as the surface separation grows

The Influence of Substrate Structure on Membrane Adhesion

We consider a membrane both weakly and strongly adhering to a geometrically structured substrate. The interaction potential is assumed to be local, via the Deryagin approximation, and harmonic. Consequently, we can analytically describe a variety of different geometries: as well as randomly rough self-affine surfaces, smooth substrates interrupted by an isolated cylindrical pit, a single elongated trench or a periodic array of trenches are investigated. We present more general expressions for the adhesion energy and membrane configuration in Fourier space and find that, compared to planar surfaces, the adhesion energy decreases. We also highlight the possibility of overshoots occurring in the membrane profile and look at its degree of penetration into surface indentations.Comment: 41 pages LaTex, 12 EPS figure

Corrugation-Induced First-Order Wetting: An Effective Hamiltonian Study

We consider an effective Hamiltonian description of critical wetting transitions in systems with short-range forces at a corrugated (periodic) wall. We are able to recover the results obtained previously from a `microscopic' density-functional approach in which the system wets in a discontinuous manner when the amplitude of the corrugations reaches a critical size A*. Using the functional renormalization group, we find that A* becomes dependent on the wetting parameter \omega in such a way as to decrease the extent of the first-order regime. Nevertheless, we still expect wetting in the Ising model to proceed in a discontinuous manner for small deviations of the wall from the plane.Comment: 9 pages RevTex with 2 EPS figures. To appear in Eur. Phys. J.

An exact solution for two dimensional wetting with a corrugated wall

An exact solution of a two dimensional RSOS model of wetting at a corrugated (periodic) wall is found using transfer matrix techniques. In contrast to mean-field analysis of the same problem the wetting transition remains second-order and occurs at a lower temperature than that of the planar system. Comparison with numerical studies and other analytical approaches is made.Comment: 11 pages LaTex with 1 eps figure. To appear in J.Phys.

Coupled Hamiltonians and Three Dimensional Short-Range Wetting Transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate \ell representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting respectively which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. We investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i we show that arbitrary two-field models H[X_1,X_2] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set of Hamiltonians based on proper collective coordinates s near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,\ell] in which the degree of coupling is controlled by an angle-like variable, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility \chi_1 is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalized critical amplitude \theta in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.Comment: 34 pages, RevTex, 8 eps figures. To appear in Physica