Summary Trace-element data for mid-ocean ridge basalts (MORBs) and ocean island basalts (OIB) are used to formulate chemical systematics for oceanic basalts. The data suggest that the order of trace-element incompatibility in oceanic basalts is Cs ≈ Rb ≈ (≈ Tl) ≈ Ba(≈ W) > Th > U ≈ Nb = Ta ≈ K > La > Ce ≈ Pb > Pr (≈ Mo) ≈ Sr > P ≈ Nd (> F) > Zr = Hf ≈ Sm > Eu ≈ Sn (≈ Sb) ≈ Ti > Dy ≈ (Li) > Ho = Y > Yb. This rule works in general and suggests that the overall fractionation processes operating during magma generation and evolution are relatively simple, involving no significant change in the environment of formation for MORBs and OIBs. In detail, minor differences in element ratios correlate with the isotopic characteristics of different types of OIB components (HIMU, EM, MORB). These systematics are interpreted in terms of partial-melting conditions, variations in residual mineralogy, involvement of subducted sediment, recycling of oceanic lithosphere and processes within the low velocity zone. Niobium data indicate that the mantle sources of MORB and OIB are not exact complementary reservoirs to the continental crust. Subduction of oceanic crust or separation of refractory eclogite material from the former oceanic crust into the lower mantle appears to be required. The negative europium anomalies observed in some EM-type OIBs and the systematics of their key element ratios suggest the addition of a small amount (⩽1% or less) of subducted sediment to their mantle sources. However, a general lack of a crustal signature in OIBs indicates that sediment recycling has not been an important process in the convecting mantle, at least not in more recent times (⩽2 Ga). Upward migration of silica-undersaturated melts from the low velocity zone can generate an enriched reservoir in the continental and oceanic lithospheric mantle. We propose that the HIMU type (eg St Helena) OIB component can be generated in this way. This enriched mantle can be re-introduced into the convective mantle by thermal erosion of the continental lithosphere and by the recycling of the enriched oceanic lithosphere back into the mantle.

Chemical and isotopic systematics of oceanic basalt : implications for mantle composition and processes

Chemical and isotopic systematics of oceanic basalts. Implications for Mantle Composition and Processes

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

/pdf/power-law-distributions-in-empirical-data-4dybihkltl.pdf

Power-Law Distributions in Empirical Data

A comprehensive and quantitative study of the fundamental aspects of plate tectonics. Provides an introduction to heat flow, elasticity and flexure, fluid mechanics, faulting, gravity, and flow in porous media, with a wide range of geological applications. Contains detailed coverage of mantle convection and mantle rheology. Includes a wide variety of practical problems.

Geodynamics applications of continuum physics to geological problems

This book introduces the fundamental concepts of fractal geometry and chaotic dynamics These concepts are then related to a variety of geological and geophysical problems, illustrating just what chaos theory and fractals really tell us and how they can be applied to the earth sciences Petroleum and mineral reserves, earthquakes, mantle convection and magnetic field generation are among the earth's properties that come under scrutiny This is the first book that covers these topics at an accessible level; the concepts are introduced at the lowest possible level of mathematics and are consistently understandable, so that the reader requires only a background in basic physics and mathematics Problems are also included for the reader to solve

Fractals and Chaos in Geology and Geophysics

The concept of self-organized criticality was introduced to explain the behaviour of the sandpile model. In this model, particles are randomly dropped onto a square grid of boxes. When a box accumulates four particles they are redistributed to the four adjacent boxes or lost off the edge of the grid. Redistributions can lead to further instabilities with the possibility of more particles being lost from the grid, contributing to the size of each ‘avalanche’. These model ‘avalanches’ satisfied a power-law frequency‐area distribution with a slope near unity. Other cellular-automata models, including the slider-block and forest-fire models, are also said to exhibit self-organized critical behaviour. It has been argued that earthquakes, landslides, forest fires, and species extinctions are examples of self-organized criticality in nature. In addition, wars and stock market crashes have been associated with this behaviour. The forest-fire model is particularly interesting in terms of its relation to the critical-point behaviour of the sitepercolation model. In the basic forest-fire model, trees are randomly planted on a grid of points. Periodically in time, sparks are randomly dropped on the grid. If a spark drops on a tree, that tree and adjacent trees burn in a model fire. The fires are the ‘avalanches’ and they are found to satisfy power-law frequency‐area distributions with slopes near unity. This forest-fire model is closely related to the site-percolation model, that exhibits critical behaviour. In the forest-fire model there is an inverse cascade of trees from small clusters to large clusters, trees are lost primarily from model fires that destroy the largest clusters. This quasi steady-state cascade gives a power-law frequency‐area distribution for both clusters of trees and smaller fires. The site-percolation model is equivalent to the forest-fire model without fires. In this case there is a transient cascade of trees from small to large clusters and a power-law distribution is found only at a critical density of trees.

/pdf/self-organized-criticality-4v87dkoa15.pdf

Self-organized criticality

Landslides are generally associated with a trigger, such as an earthquake, a rapid snowmelt or a large storm. The landslide event can include a single landslide or many thousands. The frequency–area (or volume) distribution of a landslide event quantifies the number of landslides that occur at different sizes. We examine three well-documented landslide events, from Italy, Guatemala and the USA, each with a different triggering mechanism, and find that the landslide areas for all three are well approximated by the same three-parameter inverse-gamma distribution. For small landslide areas this distribution has an exponential ‘roll-over’ and for medium and large landslide areas decays as a power-law with exponent −2·40. One implication of this landslide distribution is that the mean area of landslides in the distribution is independent of the size of the event. We also introduce a landslide-event magnitude scale mL = log(NLT), with NLT the total number of landslides associated with a trigger. If a landslide-event inventory is incomplete (i.e. smaller landslides are not included), the partial inventory can be compared with our landslide probability distribution, and the corresponding landslide-event magnitude inferred. This technique can be applied to inventories of historical landslides, inferring the total number of landslides that occurred over geologic time, and how many of these have been erased by erosion, vegetation, and human activity. We have also considered three rockfall-dominated inventories, and find that the frequency–size distributions differ substantially from those associated with other landslide types. We suggest that our proposed frequency–size distribution for landslides (excluding rockfalls) will be useful in quantifying the severity of landslide events and the contribution of landslides to erosion. Copyright © 2004 John Wiley & Sons, Ltd.

Landslide inventories and their statistical properties

The use of renormalization group techniques on fragmentation problems is examined. The equations which represent fractals and the size-frequency distributions of fragments are presented. Method for calculating the size distributions of asteriods and meteorites are described; the frequency-mass distribution for these interplanetary objects are due to fragmentation. The application of two renormalization group models to fragmentation is analyzed. It is observed that the models yield a fractal behavior for fragmentation; however, different values for the fractal dimension are produced . It is concluded that fragmentation is a scale invariant process and that the fractal dimension is a measure of the fragility of the fragmented material.

Donald L. Turcotte

Papers

Geodynamics applications of continuum physics to geological problems

Fractals and Chaos in Geology and Geophysics

Self-organized criticality

Landslide inventories and their statistical properties

Fractals and fragmentation