Monte Carlo methods

The purpose of this paper is to introduce Monte Carlo methods and to describe some significant applications of these methods. By computations on random numbers, Monte Carlo methods provide solutions of analytic and probabilistic problems

Heat Flow in the Arctic

Defines heat flow as the flux at the earth's solid surface of heat conducted from the interior; the heat-flow-unit (hfu) is on the order of 1-millionth calorie through each sq cm of the surface/sec, which is enough to melt a 4-mm layer of ice over the earth's surface/yr. Earth heat originates from radioactive decay of U, Th and K in the crust and mantle. Although land heat-flow measurements in the Arctic are too few for regional interpretation, those from Cape Thompson, Barrow and Cape Simpson, Northern Alaska are discussed and figured to show what they contribute to understanding of permafrost, climatic change and shoreline movements. Measuring thermal conductivity and gradient is much simpler in ocean basins than on land. Locations of such measurements are mapped, the results for the Alaskan quadrant in more detail. The sharp change in heat flow at the edge of the Alpha Cordillera, shown in a geothermal model, suggests that this feature is a huge accumulation of basalt, rather than mantle material or remnant of a foundering continent as previously postulated. Future Arctic heat flow studies are discussed

Non-contact infrared temperature measurements in dry permafrost boreholes

While planning the COAST Expedition to the Siberian Laptev Sea in 2005, the question of how to make a short equilibrium temperature measurement in a dry borehole arose. As a result, an infrared borehole tool was developed and used in three dry boreholes (up to 60.2 m deep) in the coastal transition zone from terrestrial to sub-sea permafrost near Mamontovy Klyk in the western Laptev Sea. A depth versus temperature profile was acquired with equilibration times of 50 × 10−3 s at each depth interval. Comparison with a common resistor string revealed an offset due to limitations of accuracy of the infrared technique and the influence of the probe's massive steel housing. Therefore it was necessary to calibrate the infrared sensor with a high precision temperature logger in each borehole. The results of the temperature measurements show a highly dynamic transition zone with temperature gradients up to −0.092°C/m and heat flow of −218 mW/m. A period of submergence of only 600 years the drilled sub-sea permafrost is approaching the overlying seawater temperature at −1.61°C with a temperature gradient of 0.021°C/m and heat flow of 49 mW/m. Further offshore, 11 km from the coastline, a temperature gradient of 0.006°C/m and heat flow of 14 mW/m occur. Thus the sub-sea permafrost in the Mamontovy Klyk region has reached a critical temperature for the presence of interstitial ice. The aim of this article is to give a brief feasibility study of infrared downhole temperature measurements and to present experiences and results of its successful application

Heat flow in southernmost California and the origin of the Salton Trough

Heat flow in the Imperial Valley and adjacent crystalline rocks is very high (∼140 mW m−2). Gravity and seismic studies suggest the crust is about 23.5 km thick with the lower half composed of gabbro and the upper fourth composed of low-density sediments. Conduction through such a crust resting directly on asthenosphere would give the observed heat flow if there were no extension or sedimentation. However, both processes must have been active, as the Imperial Valley is part of the Salton Trough, a pull-apart sedimentary basin that evolved over the past 4 or 5 m.y. To investigate the interrelations of these factors, we consider a one-dimensional model of basin formation in which the lower crustal gabbro and upper crustal sediments accumulated simultaneously as the crust extended and sedimentation kept pace with isostatic subsidence. For parameters appropriate for the Salton Trough, increasing the extension rate has little effect on surface heat flow because it increases effects of heating by intrusion and cooling by sedimentation in a compensating manner; it does, however, result in progressively increasing lower crustal temperatures. Analytical results suggest that the average extensional strain rate during formation of the trough was ∼20–50%/m.y. (∼1014 s−1); slower rates are inadequate to account for the present composition of the crust, and faster rates would probably cause massive crustal melting. To achieve the differential velocities of the Pacific plate at one end of the trough and North American plate at the other with this strain rate, extension must have, on the average, been distributed (or shifted about) over a spreading region ∼150 km wide. This is about 10 times wider than the present zone of active seismicity, suggesting that the seismic pattern is ephemeral on the time scale for the trough's formation. Narrow spreading zones are typical where sustained spreading is compensated by basaltic intrusion to form the thin oceanic crust, but where such spreading occurs in thicker continental crust, broader zones of distributed extension (with smaller strain rates) may be required for heat balance. The Salton Trough model suggests that distributed extension can be associated with substantial magmatic additions to the crust; their effect on crustal buoyancy has important implications for the relation between crustal extension and subsidence

A Study of Lean Body Mass in Estimating Basal Metabolic Rate

The primary purpose of the study was to determine if measured LBM could be used as a more powerful predictor of BMR than could surface area (SA) as calculated by the formula of DuBois and DuBois (1916). It was also of interest to develop a prediction equation for BMR using multiple regression analysis. Data from 82 women and 76 men were included in the study. Pearson product-moment correlations indicated that LBM was a better predictor for BMR than SA on either of the principal SA prediction equations, those of Aub and DuBois (1917) and Harris and Benedict (1919). Age, sex, and fat weight were not found to contribute significantly to prediction when included by multiple regression analyses. Linear equations for BMR as a function of LBM were developed for each sex. Tables based on these equations were also generated as a quick reference for clinicians

A 200-year 210Pb record from Greenland

A continuous profile of 210Pb activity extending back to 1766 has been developed for a firn/ice core collected at Site D in central Greenland in 1984. Unexpectedly high activities of 210Pb were found at the base of this core (0.032 pCi kg−1 in samples more than 200 years old), calling into question the common assumption that supported 210Pb can be neglected when constructing chronologies in glacial snow and ice. It is problematic to assert that all of the 210Pb measured at depth should be attributed to the supported fraction, given previous estimates of dust loading in Greenland ice cores. However, even if an estimated constant value of 0.032 pCi supported210Pb kg−1 is subtracted from the measured values to estimate excess 210Pb, the 210Pb chronology for Site D yields ages that are significantly younger (mean accumulation rate too high) than an independent depth-age scale based on annual layer counting. It is apparent that the flux of excess and/or supported 210Pb to this site must have decreased over the past 2 centuries, with decreasing trends in both fractions most likely. Previously published 210Pb profiles for cores from Summit and Dye 3, Greenland, show similar trends, which had been interpreted as decreasing fluxes of excess 210Pb only. For all three sites, it is not possible to separate variations in the fluxes of the excess and supported fractions of 210Pb, but variations in the total 210Pb flux will impact 210Pb-based chronologies generally if these variations have not been restricted to the Greenland ice sheet

Physical models as an aid for teaching wood anatomy

Student activities and instructor-made models are described to facilitate and encourage other instructors to develop their own appropriate activities and models for teaching the three-dimensional structure of wood. The teaching activities include making several annual rings with straws pushed into clay, drawing wood’s structure onto a piece of paper that is folded to resemble a wedge, and assigning students to make an anatomical model to present in class. Plans are given for instructor-made models (1:500 scale) of tracheids, vessel elements, and a hardwood ‘fiber’ to demonstrate their relative dimensions and geometries. These models also include a set of outerwood and corewood tracheids onto which the microfibril angle is traced, and one tracheid on which bordered and cross-field pitting are shown. Plans are then given for a bordered pit pair with its membrane (1:6300 scale). The last model demonstrates the Hagen-Poiseuille equation with an array of 16 conduits that together have the same potential flow as one conduit of two times their diameter. The use of these models has enlivened the classroom and helped students to more readily grasp wood anatomy and function

An Experimental Investigation of the Scaling of Columnar Joints

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.Comment: 12 pages, 11 figures, for supporting online movies, go to http://www.physics.utoronto.ca/nonlinear/movies/starch_movies.htm