Filtered screens and augmented Teichm\"uller space

We study a new bordification of the decorated Teichm\"uller space for a multiply punctured surface F by a space of filtered screens on the surface that arises from a natural elaboration of earlier work of McShane-Penner. We identify necessary and sufficient conditions for paths in this space of filtered screens to yield short curves having vanishing length in the underlying surface F. As a result, an appropriate quotient of this space of filtered screens on F yields a decorated augmented Teichm\"uller space which is shown to admit a CW decomposition that naturally projects to the augmented Teichm\"uller space by forgetting decorations and whose strata are indexed by a new object termed partially oriented stratum graphs.Comment: Final version to appear in Geometriae Dedicat

Climate change - The cloud conundrum

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62779/1/432962a.pd

Topology of RNA-RNA interaction structures

The topological filtration of interacting RNA complexes is studied and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that for two interacting RNAs, called interaction structures, there exist for fixed genus only finitely many irreducible shadows. This implies that for fixed genus there are only finitely many classes of interaction structures. In particular the simplest case of genus zero already provides the formalism for certain types of structures that occur in nature and are not covered by other filtrations. This case of genus zero interaction structures is already of practical interest, is studied here in detail and found to be expressed by a multiple context-free grammar extending the usual one for RNA secondary structures. We show that in $O(n^6)$ time and $O(n^4)$ space complexity, this grammar for genus zero interaction structures provides not only minimum free energy solutions but also the complete partition function and base pairing probabilities.Comment: 40 pages 15 figure

Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral

In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the reciprocal of the order of the automorphism group of a tiling of a Riemann surface. The second method is based on the classical analysis of orthogonal polynomials. A rigorous asymptotic method is established, and a special case of the matrix integral is computed in terms of the Riemann $\zeta$-function. The third method is derived from a formula for the $\tau$-function solution to the KP equations. This method leads us to a new class of solutions of the KP equations that are \emph{transcendental}, in the sense that they cannot be obtained by the celebrated Krichever construction and its generalizations based on algebraic geometry of vector bundles on Riemann surfaces. In each case a mathematically rigorous way of dealing with asymptotic series in an infinite number of variables is established

Comparison of a global-climate model simulation to a cloud-system resolving model simulation for long-term thin stratocumulus clouds

A case of thin, warm marine-boundary-layer (MBL) clouds is simulated by a cloud-system resolving model (CSRM) and is compared to the same case of clouds simulated by a general circulation model (GCM). In this study, the simulation by the CSRM adopts higher resolutions which are generally used in large-eddy simulations (LES) and more advanced microphysics as compared to those by the GCM, enabling the CSRM-simulation to act as a benchmark to assess the simulation by the GCM. Explicitly simulated interactions among the surface latent heat (LH) fluxes, buoyancy fluxes, and cloud-top entrainment lead to the deepening-warming decoupling and thereby the transition from stratiform clouds to cumulus clouds in the CSRM. However, in the simulation by the GCM, these interactions are not resolved and thus the transition to cumulus clouds is not simulated. This leads to substantial differences in liquid water content (LWC) and radiation between simulations by the CSRM and the GCM. When stratocumulus clouds are dominant prior to the transition to cumulus clouds, interactions between supersaturation and cloud droplet number concentration (CDNC) (controlling condensation) and those between rain evaporation and cloud-base instability (controlling cloud dynamics and thereby condensation) determine LWC and thus the radiation budget in the simulation by the CSRM. These interactions result in smaller condensation and thus smaller LWC and reflected solar radiation by clouds in the simulation by the CSRM than in the simulation by the GCM where these interactions are not resolved. The resolved interactions (associated with condensation and the transition to cumulus clouds) lead to better agreement between the CSRM-simulation and observation than that between the GCM-simulation and observation

Examination of the aerosol indirect effect under contrasting environments during the ACE-2 experiment

International audienceThe Active Tracer High-resolution Atmospheric Model (ATHAM) has been adopted to examine the aerosol indirect effect in contrasting clean and polluted cloudy boundary layers during the Second Aerosol Characterization Experiment (ACE-2). Model results are in good agreement with available in-situ observations, which provides confidence in the results of ATHAM. Sensitivity tests have been conducted to examine the response of the cloud fraction (CF), cloud liquid water path (LWP), and cloud optical depth (COD) to changes in aerosols in the clean and polluted cases. It is shown for two cases that CF and LWP would decrease or remain nearly constant with an increase in aerosols, a result which shows that the second aerosol indirect effect is positive or negligibly small in these cases. Further investigation indicates that the background meteorological conditions play a critical role in the response of CF and LWP to aerosols. When large-scale subsidence is weak as in the clean case, the dry overlying air above the cloud is more efficiently entrained into the cloud, and in so doing, removes cloud water more efficiently, and results in lower CF and LWP when aerosol burden increases. However, when the large-scale subsidence is strong as in the polluted case, the growth of the cloud top is suppressed and the entrainment drying makes no significant difference when aerosol burden increases. Therefore, the CF and LWP remain nearly constant. In both the clean and polluted cases, the COD tends to increase with aerosols, and the total aerosol indirect effect (AIE) is negative even when the CF and LWP decrease with an increase in aerosols. Therefore, the first AIE dominates the response of the cloud to aerosols

M‐BLANK: a program for the fitting of X‐ray fluorescence spectra

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148382/1/jsy2rv5095.pd

Global 2-D intercomparison of sectional and modal aerosol modules

International audienceWe present an intercomparison of several aerosol modules, sectional and modal, in a global 2-D model in order to differentiate their behavior for tropospheric and stratospheric applications. We model only binary sulfuric acid-water aerosols in this study. Three versions of the sectional model and three versions of the modal model are used to test the sensitivity of background aerosol mass and size distribution to the number of bins or modes and to the prescribed width of the largest mode. We find modest sensitivity to the number of bins (40 vs. 150) used in the sectional model. Aerosol mass is found to be reduced in a modal model if care is not taken in selecting the width of the largest lognormal mode, reflecting differences in sedimentation in the middle stratosphere. The size distributions calculated by the sectional model can be better matched by a modal model with four modes rather than three modes in most but not all situations. A simulation of aerosol decay following the 1991 eruption of Mt. Pinatubo shows that the representation of the size distribution can have a signficant impact on model-calculated aerosol decay rates in the stratosphere. Between 1991 and 1995, aerosol extinction and surface area density calculated by two versions of the modal model adequately match results from the sectional model. Calculated effective radius for the same time period shows more intermodel variability, with a 20-bin sectional model performing much better than any of the modal models