More Torsion in the Homology of the Matching Complex

A matching on a set $X$ is a collection of pairwise disjoint subsets of $X$ of size two. Using computers, we analyze the integral homology of the matching complex $M_n$, which is the simplicial complex of matchings on the set $\{1, >..., n\}$. The main result is the detection of elements of order $p$ in the homology for $p \in \{5,7,11,13\}$. Specifically, we show that there are elements of order 5 in the homology of $M_n$ for $n \ge 18$ and for $n \in {14,16}$. The only previously known value was $n = 14$, and in this particular case we have a new computer-free proof. Moreover, we show that there are elements of order 7 in the homology of $M_n$ for all odd $n$ between 23 and 41 and for $n=30$. In addition, there are elements of order 11 in the homology of $M_{47}$ and elements of order 13 in the homology of $M_{62}$. Finally, we compute the ranks of the Sylow 3- and 5-subgroups of the torsion part of $H_d(M_n;Z)$ for $13 \le n \le 16$; a complete description of the homology already exists for $n \le 12$. To prove the results, we use a representation-theoretic approach, examining subcomplexes of the chain complex of $M_n$ obtained by letting certain groups act on the chain complex.Comment: 35 pages, 10 figure

FEM-Based Thermal Analysis of Underground Power Cables Located in Backfills Made of Different Materials

Выполнен предварительный расчет температурного поля в подземных высоковольтных линиях электропередач, которые планируется использовать в электростанции мощностью 600 МВт. Исследуется система из трех силовых кабелей, размещенных в трубах из полиэтилена низкого давления, с многослойной засыпкой (грунт и термоизолирующие материалы). Рассматриваются различные конфигурации размещения слоев засыпки. Глубина размещения силовых кабелей, измеряемая от реперной точки (0,5 м ниже уровня грунта), варьируется от 2 до 6 м, что оказывает влияние на температурное распределение в грунте, изоляционном и проводящем слоях кабелей. С использованием метода конечных элементов выполнен численный расчет установившихся температурных полей. Для дополнительного учета влияния сформированной так называемой “сухой зоны” на распределение температуры постулируется зависимость теплопроводности грунта от температуры.Виконано попередній розрахунок температурного поля в підземних високовольтних лініях електропередач, які планується використовувати в електростанції потужністю 600 МВт. Досліджується система з трьох силових кабелів, що розміщені в трубах із поліетилену низького тиску, з багатошаровою засипкою (ґрунт і термоізольовані матеріали). Розглядаються різні конфігурації розміщення шарів засипки. Глибина розміщення силових кабелів, що вимірюється від реперної точки (0,5 м нижче рівня ґрунту), варіюється від 2 до 6 м, що впливає на температурний розподіл у ґрунті, ізоляційному і провідному кабелях. Із використанням методу скінченних елементів виконано числовий розрахунок усталених температурних полів. Для додаткового врахування впливу сформованої так званої “сухої зони” на розподіл температури постулюється залежність теплопровідності ґрунту від температури

Highly Variable Recurrence of Tsunamis In the 7,400 Years Before the 2004 Indian Ocean Tsunami

The devastating 2004 Indian Ocean tsunami caught millions of coastal residents and the scientific community off-guard. Subsequent research in the Indian Ocean basin has identified prehistoric tsunamis, but the timing and recurrence intervals of such events are uncertain. Here we present an extraordinary 7,400 year stratigraphic sequence of prehistoric tsunami deposits from a coastal cave in Aceh, Indonesia. This record demonstrates that at least 11 prehistoric tsunamis struck the Aceh coast between 7,400 and 2,900 years ago. The average time period between tsunamis is about 450 years with intervals ranging from a long, dormant period of over 2,000 years, to multiple tsunamis within the span of a century. Although there is evidence that the likelihood of another tsunamigenic earthquake in Aceh province is high, these variable recurrence intervals suggest that long dormant periods may follow Sunda megathrust ruptures as large as that of the 2004 Indian Ocean tsunami

Typhoon Haiyan Overwash Sediments From Leyte Gulf Coastlines Show Local Spatial Variations With Hybrid Storm and Tsunami Signatures

Marine inundation associated with the 5 to 8 m storm surge of Typhoon Haiyan in 2013 left overwash sediments inland on the coastal plains of the northwestern shores of Leyte Gulf, Philippines. The Haiyan overwash deposit provides a modern sedimentary record of storm surge deposition from a Category 5 landfalling typhoon. We studied overwash sediments at two locations that experienced similar storm surge conditions but represent contrasting sedimentological regimes, namely a siliciclastic coast and a mixed siliciclastic-carbonate coast. The contrasting local geology is significantly reflected in the differences in sediment grain size, composition and sorting at the two sites. The Haiyan overwash sediments are predominantly sand and silt and can be traced up to ~ 1.6 km inland, extending farther beyond the previously reported \u3c 300 m inland limit of sedimentation. Sites with similar geology, topographic relief, and overland flow conditions show significant spatial variability of sediment thickness and inland extent. We infer that other local factors such as small-scale variations in topography and the type of vegetation covermight influence the spatial distribution of overwash sediments. The Haiyan overwash deposits exhibit planar stratification, a coarsening upward sequence, a non-systematic landward fining trend, and a sharp depositional (rarely erosional) basal contact with the underlying substrate. Overall, the Haiyan deposits have sedimentologic and stratigraphic characteristics that show a hybrid signature common to both storm and tsunami deposits

The Conley Index and Rigorous Numerics for Attracting Periodic Orbits

Despite the enormous number of papers devoted to the problem of the exis-tence of periodic trajectories of differential equations, the theory is still far from being satisfactory, especially when concrete differential equations are concerned, because the necessary conditions formulated in many theoretica

Micropaleontology of the 2013 Typhoon Haiyan Overwash Sediments from the Leyte Gulf, Philippines

Coastal geologic records allow for the assessment of long-term patterns of tropical cyclone variability. However, the accuracy of geologic reconstructions of tropical cyclones is limited by the lack of modern analogues. We describe the microfossil (foraminifera and testate amoebae) assemblages contained within overwash sediments deposited by Typhoon Haiyan when it made landfall on the islands of Leyte and Samar in the Philippines on 7 November 2013 as a Category 5 super typhoon. The overwash sediments were transported up to 1.7 km inland at four study sites. The sediments consisted of light brown medium sand in a layer \u3c1 to 8 cm thick. We used Partitioning Around a Medoid (PAM) cluster analysis to identify lateral and vertical changes in the foraminiferal and testate amoebae data. The presence of intertidal and subtidal benthic, and planktic foraminifera that were variably unaltered and abraded identify the microfossil signature of the overwash sediments. Agglutinated mangrove foraminifera and testate amoebae were present within the overwash sediments at many locations and indicate terrestrial scouring by Haiyan\u27s storm surge. PAM cluster analysis subdivided the Haiyan microfossil dataset into two assemblages based on depositional environment: (1) a low-energy mixed-carbonate tidal flat located on Samar Island (Basey transect); and (2) a higher-energy clastic coastline near Tanauan on Leyte Island (Santa Cruz, Solano, and Magay transects). The assemblages and the taphonomy suggest a mixed provenance, including intertidal and subtidal sources, as well as a contribution of sediment sourced from deeper water and terrestrial environments. (C) 2016 Elsevier B.V. All rights reserved

Stratigraphic evidence of two historical tsunamis on the semi-arid coast of north-central Chile

On September 16, 2015, a Mw 8.3 earthquake struck the north-central Chile coast, triggering a tsunami observed along 500 km of coastline, between Huasco (28.5°S) and San Antonio (33.5°S). This tsunami provided a unique opportunity to examine the nature of tsunami deposits in a semi-arid, siliciclastic environment where stratigraphic and sedimentological records of past tsunamis are difficult to distinguish. To improve our ability to identify such evidence, we targeted one of the few low-energy, organic-rich depositional environments in north-central Chile: Pachingo marsh in Tongoy Bay (30.3°S).We found sedimentary evidence of the 2015 and one previous tsunami as tabular sand sheets. Both deposits are composed of poorly to moderately sorted, gray-brown, fine-to medium-grained sand and are distinct from underlying and overlying organic-rich silt. Both sand beds thin (from ∼20 cm to \u3c1 \u3ecm) and fine landward, and show normal grading. The older sand bed is thicker and extends over 125 m further inland than the 2015 tsunami deposit. To model the relative size of the tsunamis that deposited each sand bed, we employed tsunami flow inversion. Our results show that the older sand bed was produced by higher flow speeds and depths than those in 2015. Anthropogenic evidence along with 137Cs and 210Pb dating constrains the age of the older tsunami to the last ∼110 years. We suggest that the older sand bed was deposited by the large tsunami in 1922 CE sourced to the north of our study site. This deposit represents the first geologic evidence of a pre-2015 tsunami along the semi-arid north-central Chile coast and highlights the current and continuing tsunami hazard in the region

Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory

We present a computational tool that can be used to obtain the "spatial" homology groups of a causal set. Localisation in the causal set is seeded by an inextendible antichain, which is the analog of a spacelike hypersurface, and a one parameter family of nerve simplicial complexes is constructed by "thickening" this antichain. The associated homology groups can then be calculated using existing homology software, and their behaviour studied as a function of the thickening parameter. Earlier analytical work showed that for an inextendible antichain in a causal set which can be approximated by a globally hyperbolic spacetime region, there is a one parameter sub-family of these simplicial complexes which are homological to the continuum, provided the antichain satisfies certain conditions. Using causal sets that are approximated by a set of 2d spacetimes our numerical analysis suggests that these conditions are generically satisfied by inextendible antichains. In both 2d and 3d simulations, as the thickening parameter is increased, the continuum homology groups tend to appear as the first region in which the homology is constant, or "stable" above the discreteness scale. Below this scale, the homology groups fluctuate rapidly as a function of the thickening parameter. This provides a necessary though not sufficient criterion to test for manifoldlikeness of a causal set.Comment: Latex, 46 pages, 43 .eps figures, v2 numerous changes to content and presentatio