Diffusivity of a walk on fracture loops of a discrete torus

In this paper we study functions on the discrete torus which have a crystalline structure. This means that if we fix such a function and walk around the torus in a positive direction, the function increases on almost every step, except at a small number of steps where it must go down in order to meet the periodicity of the torus. It turns out that the down steps are organised into a small number of closed simple disjoint paths, the fracture lines of the crystal. We define a random walk on the resulting functions, the law of which is Brownian in the diffusive limit. We show that in the limit of the crystal structure becoming microscopic, the diffusivity is given by $\sigma^2=(1+2\operatorname{gcd}(\mathbf{n}_1,\mathbf{n}_2))^{-1}$, where $\mathbf{n}_1$ and $\mathbf{n}_2$ are the number of fractures in the horizontal and vertical direction respectively. This is the main result of this paper. The diffusivity of the corresponding one-dimensional model has already been studied by Espinasse, Guillotin-Plantard and Nadeau, and this paper generalises that model to two dimensions. However, the methodology involving an analysis of the fracture lines that we use to calculate the diffusivity is completely novel

Subsidization of the shipbuilding industry in the Federal Republic of Germany

German shipyards were hit extremely hard during World War II, and then again in the following years when the parts that had not been damaged were disassembled by the Allies. But World War II and its consequences proved to be a blessing in disguise as it opened possibilities for a very prosperous shipbuilding industry in the fifties. That is, the yards were rapidly rebuilt with modern equipment, partly through Marshal- Fund aid. Since many of the refugees front the eastern parts of Germany had settled in the coastal regions of West Germany, a qualified work force was readily available. Relatively high productivity and low wages made German shipyards highly competitive and, as a result, by the mid-fifties, German shipbuilding industry had grown to become number two in Europe after the UK; 17.3 p.c. of vessels completed worldwide in 1956 were built on yards of the Federal Republic.

River ice responses to a warming Arctic—recent evidence from Russian rivers

This paper looks at the response of river ice to recent warming in the Arctic at six major downstream gauges on large Russian rivers flowing to the Arctic Ocean. For the Severnaya Dvina, Ob, Yenisey, Lena, Yana and Kolyma we determine how river ice has changed in recent years and we try to understand the underlying causes of those changes. Long-term variability and trends in beginning and ending dates of ice events, duration of ice conditions, and maximum ice thickness were analyzed over 1955–2012. Significant changes in timing of ice events and a decrease in ice thickness were found for the five Siberian rivers. Duration of ice conditions decreased from 7 days for the Severnaya Dvina, Lena and Yenisey to almost 20 days for the Ob at Salekhard. The change in timing of ice events is consistent with changes in regional air temperature, which has significantly increased at each of these river gauges, except Lena-Kusur. The primary cause of the considerable increase in maximum ice thickness was not identified. Variation of mean winter air temperature and river discharge do not correlate well with maximum ice thickness and it is assumed the influence of specific local conditions can play a more important role in ice formation at these locations. Understanding this interrelationship across the Eurasian pan-Arctic using more comprehensive data archives for river ice and discharge is therefore needed

River Discharge, in Chapter 5, Arctic, State of the Climate in 2010

Several large-scale climate patterns influenced climate conditions and weather patterns across the globe during 2010. The transition from a warm El Niño phase at the beginning of the year to a cool La Niña phase by July contributed to many notable events, ranging from record wetness across much of Australia to historically low Eastern Pacific basin and near-record high North Atlantic basin hurricane activity. The remaining five main hurricane basins experienced below- to well-below-normal tropical cyclone activity. The negative phase of the Arctic Oscillation was a major driver of Northern Hemisphere temperature patterns during 2009/10 winter and again in late 2010. It contributed to record snowfall and unusually low temperatures over much of northern Eurasia and parts of the United States, while bringing above-normal temperatures to the high northern latitudes. The February Arctic Oscillation Index value was the most negative since records began in 1950

Record Russian river discharge in 2007 and the limits of analysis

The Arctic water cycle has experienced an unprecedented degree of change which may have planetary-scale impacts. The year 2007 in particular not only was unique in terms of minimum sea ice extent in the Arctic Ocean but also was a record breaking year for Eurasian river inflow to the Arctic Ocean. Over the observational period from 1936 to 2006, the mean annual river discharge for the six largest Russian rivers was 1796 km3 y−1, with the previous record high being 2080 km3 y−1, in 2002. The year 2007 showed a massive flux of fresh water from these six drainage basins of 2254 km3 y−1. We investigated the hydroclimatological conditions for such extreme river discharge and found that while that year\u27s flow was unusually high, the overall spatial patterns were consistent with the hydroclimatic trends since 1980, indicating that 2007 was not an aberration but a part of the general trend. We wanted to extend our hydroclimatological analysis of river discharge anomalies to seasonal and monthly time steps; however, there were limits to such analyses due to the direct human impact on the river systems. Using reconstructions of the naturalized hydrographs over the Yenisey basin we defined the limits to analysis due to the effect of reservoirs on river discharge. For annual time steps the trends are less impacted by dam construction, whereas for seasonal and monthly time steps these data are confounded by the two sources of change, and the climate change signals were overwhelmed by the human-induced river impoundments. We offer two solutions to this problem; first, we recommend wider use of algorithms to \u27naturalize\u27 the river discharge data and, second, we suggest the identification of a network of existing and stable river monitoring sites to be used for climate change analysis