Mars' atmosphere: The sister planet, our statistical twin

Satellite-based Martian reanalyses have allowed unprecedented comparisons between our atmosphere and that of our sister planet, underlining various similarities and differences in their respective dynamics. Yet by focusing on large scale structures and deterministic mechanisms they have improved our understanding of the dynamics only over fairly narrow ranges of (near) planetary scales. However, the Reynolds numbers of the flows on both planets are larger than 1011 and dissipation only occurs at centimetric (Mars) or millimetric scales (Earth) so that over most of their scale ranges, the dynamics are fully turbulent. In this paper, we therefore examine the high-level, statistical, turbulent laws for the temperature, horizontal wind, and surface pressure, finding that Earth and Mars have virtually identical statistical exponents so that their statistics are very similar over wide ranges. Therefore, it would seem that with the exception of certain aspects of the largest scales (such as the role of dust in atmospheric heating on Mars, or of water in its various phases on Earth), that the nonlinear dynamics are very similar. We argue that this is a prediction of the classical laws of turbulence when extended to planetary scales and that it supports our use of turbulent laws on both planetary atmospheres

Verification and Control of Partially Observable Probabilistic Real-Time Systems

We propose automated techniques for the verification and control of probabilistic real-time systems that are only partially observable. To formally model such systems, we define an extension of probabilistic timed automata in which local states are partially visible to an observer or controller. We give a probabilistic temporal logic that can express a range of quantitative properties of these models, relating to the probability of an event's occurrence or the expected value of a reward measure. We then propose techniques to either verify that such a property holds or to synthesise a controller for the model which makes it true. Our approach is based on an integer discretisation of the model's dense-time behaviour and a grid-based abstraction of the uncountable belief space induced by partial observability. The latter is necessarily approximate since the underlying problem is undecidable, however we show how both lower and upper bounds on numerical results can be generated. We illustrate the effectiveness of the approach by implementing it in the PRISM model checker and applying it to several case studies, from the domains of computer security and task scheduling

Tissue multifractality and Born approximation in analysis of light scattering: a novel approach for precancers detection

Multifractal, a special class of complex self-affine processes, are under recent intensive investigations because of their fundamental nature and potential applications in diverse physical systems. Here, we report on a novel light scattering-based inverse method for extraction/quantification of multifractality in the spatial distribution of refractive index of biological tissues. The method is based on Fourier domain pre-processing via the Born approximation, followed by the Multifractal Detrended Fluctuation Analysis. The approach is experimentally validated in synthetic multifractal scattering phantoms, and tested on biopsy tissue slices. The derived multifractal properties appear sensitive in detecting cervical precancerous alterations through an increase of multifractality with pathology progression, demonstrating the potential of the developed methodology for novel precancer biomarker identification and tissue diagnostic tool. The novel ability to delineate the multifractal optical properties from light scattering signals may also prove useful for characterizing a wide variety of complex scattering media of non-biological origin

An Amazonian rainforest and its fragments as a laboratory of global change

We synthesize findings from one of the world’s largest and longest-running experimental investigations, the Biological Dynamics of Forest Fragments Project (BDFFP). Spanning an area of ~1,000 km2 in central Amazonia, the BDFFP was initially designed to evaluate the effects of fragment area on rainforest biodiversity and ecological processes. However, over its 38-year history to date the project has far transcended its original mission, and now focuses more broadly on landscape dynamics, forest regeneration, regional- and global-change phenomena, and their potential interactions and implications for Amazonian forest conservation. The project has yielded a wealth of insights into the ecological and environmental changes in fragmented forests. For instance, many rainforest species are naturally rare and hence are either missing entirely from many fragments or so sparsely represented as to have little chance of long-term survival. Additionally, edge effects are a prominent driver of fragment dynamics, strongly affecting forest microclimate, tree mortality, carbon storage and a diversity of fauna. Even within our controlled study area, the landscape has been highly dynamic: for example, the matrix of vegetation surrounding fragments has changed markedly over time, succeeding from large cattle pastures or forest clearcuts to secondary regrowth forest. This, in turn, has influenced the dynamics of plant and animal communities and their trajectories of change over time. In general, fauna and flora have responded differently to fragmentation: the most locally extinction-prone animal species are those that have both large area requirements and low tolerance of the modified habitats surrounding fragments, whereas the most vulnerable plants are those that respond poorly to edge effects or chronic forest disturbances, and that rely on vulnerable animals for seed dispersal or pollination. Relative to intact forests, most fragments are hyperdynamic, with unstable or fluctuating populations of species in response to a variety of external vicissitudes. Rare weather events such as droughts, windstorms and floods have had strong impacts on fragments and left lasting legacies of change. Both forest fragments and the intact forests in our study area appear to be influenced by larger-scale environmental drivers operating at regional or global scales. These drivers are apparently increasing forest productivity and have led to concerted, widespread increases in forest dynamics and plant growth, shifts in tree-community composition, and increases in liana (woody vine) abundance. Such large-scale drivers are likely to interact synergistically with habitat fragmentation, exacerbating its effects for some species and ecological phenomena. Hence, the impacts of fragmentation on Amazonian biodiversity and ecosystem processes appear to be a consequence not only of local site features but also of broader changes occurring at landscape, regional and even global scales

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

Nonlinear Measures for Characterizing Rough Surface Morphologies

We develop a new approach to characterizing the morphology of rough surfaces based on the analysis of the scaling properties of contour loops, i.e. loops of constant height. Given a height profile of the surface we perform independent measurements of the fractal dimension of contour loops, and the exponent that characterizes their size distribution. Scaling formulas are derived and used to relate these two geometrical exponents to the roughness exponent of a self-affine surface, thus providing independent measurements of this important quantity. Furthermore, we define the scale dependent curvature and demonstrate that by measuring its third moment departures of the height fluctuations from Gaussian behavior can be ascertained. These nonlinear measures are used to characterize the morphology of computer generated Gaussian rough surfaces, surfaces obtained in numerical simulations of a simple growth model, and surfaces observed by scanning-tunneling-microscopes. For experimentally realized surfaces the self-affine scaling is cut off by a correlation length, and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to [email protected]

Minutes 1877

https://place.asburyseminary.edu/freemethodistminutesyearbooks/1015/thumbnail.jp

The Buffer Gas Beam: An Intense, Cold, and Slow Source for Atoms and Molecules

Beams of atoms and molecules are stalwart tools for spectroscopy and studies of collisional processes. The supersonic expansion technique can create cold beams of many species of atoms and molecules. However, the resulting beam is typically moving at a speed of 300-600 m/s in the lab frame, and for a large class of species has insufficient flux (i.e. brightness) for important applications. In contrast, buffer gas beams can be a superior method in many cases, producing cold and relatively slow molecules in the lab frame with high brightness and great versatility. There are basic differences between supersonic and buffer gas cooled beams regarding particular technological advantages and constraints. At present, it is clear that not all of the possible variations on the buffer gas method have been studied. In this review, we will present a survey of the current state of the art in buffer gas beams, and explore some of the possible future directions that these new methods might take