Directed nonabelian sandpile models on trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs, unlike the well-known abelian sandpile model. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.Comment: 43 pages, 5 figures; introduction improve

Markov chains, R\mathscr R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJA

Advanced Uses for Carbon Nanotubes: A Spherical Sound Source and Hot-films as Microphones

Super-aligned carbon nanotube (CNT) thin-film is used to create thermophones. The thermal properties of CNT film allow it to rapidly heat and cool when supplied AC power producing temperature and pressure gradients and, therefore, audible sound. The advantages of CNT thermophones include eliminating all moving components of traditional speakers and reducing the weight of the speaker itself by using CNT film, which is nearly weightless. Additionally, the flexibility of CNT film provides the unique opportunity to construct loudspeakers of various sizes and geometries. In this work, a spherical CNT thermophone is designed, manufactured, and tested for directivity with the overall goal of creating a perfectly omnidirectional sound source over a wide frequency band. The spherical CNT thermophone is found to have significant directivity associated with it at the lowest and highest audible frequency bands, while performance is nearly omnidirectional at middle frequency bands. The second part of this work uses of the same CNT thin-film as a microphone through hot-film anemometry sensing the particle velocity in acoustic waves of pure frequency tones. The advantages of a CNT hot-film microphone are similar to those of CNT thermophones and include the ability to construct microphones of various sizes and shapes because the film is ultra-lightweight and flexible. The microphone’s sensitivity, power requirements, and frequency response were investigated. Results indicate that it may be feasible to use a CNT hot-film anemometer configuration as a microphone for detecting pure frequency tones across a large frequency range

On The Determination of MDI High-Degree Mode Frequencies

The characteristic of the solar acoustic spectrum is such that mode lifetimes get shorter and spatial leaks get closer in frequency as the degree of a mode increases for a given order. A direct consequence of this property is that individual p-modes are only resolved at low and intermediate degrees, and that at high degrees, individual modes blend into ridges. Once modes have blended into ridges, the power distribution of the ridge defines the ridge central frequency and it will mask the true underlying mode frequency. An accurate model of the amplitude of the peaks that contribute to the ridge power distribution is needed to recover the underlying mode frequency from fitting the ridge. We present the results of fitting high degree power ridges (up to l = 900) computed from several two to three-month-long time-series of full-disk observations taken with the Michelson Doppler Imager (MDI) on-board the Solar and Heliospheric Observatory between 1996 and 1999. We also present a detailed discussion of the modeling of the ridge power distribution, and the contribution of the various observational and instrumental effects on the spatial leakage, in the context of the MDI instrument. We have constructed a physically motivated model (rather than some ad hoc correction scheme) resulting in a methodology that can produce an unbiased determination of high-degree modes, once the instrumental characteristics are well understood. Finally, we present changes in high degree mode parameters with epoch and thus solar activity level and discuss their significance.Comment: 59 pages, 38 figures -- High-resolution version at http://www-sgk.harvard.edu:1080/~sylvain/preprints/ -- Manuscript submitted to Ap

Evaluating and improving the Community Land Model's sensitivity to land cover

Modeling studies have shown the importance of biogeophysical effects of deforestation on local climate conditions but have also highlighted the lack of agreement across different models. Recently, remote-sensing observations have been used to assess the contrast in albedo, evapotranspiration (ET), and land surface temperature (LST) between forest and nearby open land on a global scale. These observations provide an unprecedented opportunity to evaluate the ability of land surface models to simulate the biogeophysical effects of forests. Here, we evaluate the representation of the difference of forest minus open land (i.e., grassland and cropland) in albedo, ET, and LST in the Community Land Model version 4.5 (CLM4.5) using various remote-sensing and in situ data sources. To extract the local sensitivity to land cover, we analyze plant functional type level output from global CLM4.5 simulations, using a model configuration that attributes a separate soil column to each plant functional type. Using the separated soil column configuration, CLM4.5 is able to realistically reproduce the biogeophysical contrast between forest and open land in terms of albedo, daily mean LST, and daily maximum LST, while the effect on daily minimum LST is not well captured by the model. Furthermore, we identify that the ET contrast between forests and open land is underestimated in CLM4.5 compared to observation-based products and even reversed in sign for some regions, even when considering uncertainties in these products. We then show that these biases can be partly alleviated by modifying several model parameters, such as the root distribution, the formulation of plant water uptake, the light limitation of photosynthesis, and the maximum rate of carboxylation. Furthermore, the ET contrast between forest and open land needs to be better constrained by observations to foster convergence amongst different land surface models on the biogeophysical effects of forests. Overall, this study demonstrates the potential of comparing subgrid model output to local observations to improve current land surface models' ability to simulate land cover change effects, which is a promising approach to reduce uncertainties in future assessments of land use impacts on climate

La combustion des terrils

National audienceLa combustion des terrils est une spécificité des régions où du charbon est (ou a été) exploité - nous ne présenterons pas ici la combustion des stériles d'autres exploitations (schistes bitumineux...) ni de la combustion des résidus métallurgiques. Ce phénomène spectaculaire est relativement courant et suivi de près d'une part à cause des risques d'explosion qui lui sont liés et d'autre part à cause des conséquences environnementales. Du point de vue du pétrographe, des paragénèses inhabituelles de ultra-haute température à pression ambiante se développent, ainsi que des efflorescences de minéraux complexes, donnant ainsi des opportunités pour leur étude