Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.

Quantitative analysis of crystal/grain sizes and their distributions in 2D and 3D

We review methods to estimate the average crystal (grain) size and the crystal (grain) size distribution in solid rocks. Average grain sizes often provide the base for stress estimates or rheological calculations requiring the quantification of grain sizes in a rock's microstructure. The primary data for grain size data are either 1D (i.e. line intercept methods), 2D (area analysis) or 3D (e.g., computed tomography, serial sectioning). These data have been used for different data treatments over the years, whereas several studies assume a certain probability function (e.g., logarithm, square root) to calculate statistical parameters as the mean, median, mode or the skewness of a crystal size distribution. The finally calculated average grain sizes have to be compatible between the different grain size estimation approaches in order to be properly applied, for example, in paleo-piezometers or grain size sensitive flow laws. Such compatibility is tested for different data treatments using one- and two-dimensional measurements. We propose an empirical conversion matrix for different datasets. These conversion factors provide the option to make different datasets compatible with each other, although the primary calculations were obtained in different ways. In order to present an average grain size, we propose to use the area-weighted and volume-weighted mean in the case of unimodal grain size distributions, respectively, for 2D and 3D measurements. The shape of the crystal size distribution is important for studies of nucleation and growth of minerals. The shape of the crystal size distribution of garnet populations is compared between different 2D and 3D measurements, which are serial sectioning and computed tomography. The comparison of different direct measured 3D data; stereological data and direct presented 20 data show the problems of the quality of the smallest grain sizes and the overestimation of small grain sizes in stereological tools, depending on the type of CSD. (C) 2011 Published by Elsevier Ltd.

Controls of heavy minerals and grain size in a holocene regressive barrier (Ilha Comprida, southeastern Brazil)

Ilha Comprida is a regressive barrier island located in southeastern Brazil that was formed essentially by Quaternary sandy sediments. Ilha Comprida sediments were analyzed to assess heavy mineral indices and grain size variables. The spatial variation of heavy minerals and grain size was interpreted in terms of the present barrier dynamics and the barrier`s evolution since the Middle Holocene. These analyses allowed for the identification of the main factors and processes that control the variation of heavy minerals and grain size on the barrier. Rutile and zircon (RZi) and tourmaline and hornblende (THi) are significantly sensitive to provenance and exhibit the contributions of the Ribeira de Iguape River sediments, which reach the coast next to the northeastern end of Ilha Comprida. In addition to the influence of provenance, TZi responds mainly to hydraulic sorting processes. This agrees with a sediment transport pattern characterized by a divergence of two resultant net alongshore drifts southwest of the barrier. The sediments from the Ribeira de Iguape River reach the barrier directly through the river mouth and indirectly after temporary storage in the inner shelf. The combination of grain size and heavy mineral analyses is a reliable method for determining sediment transport patterns and provenance. (C) 2010 Elsevier Ltd. All rights reserved.

Grain-size distribution, carbon and calcium carbonate at DSDP Leg 63 Holes

Sand-silt-clay distribution was determined at Scripps on samples collected at the time the cores were split and described. The sediment classification used here is that of Shepard (1954); sand, silt, and clay boundaries are determined on the basis of the Wentworth (1922) scale. Thus the sand, silt, and clay fractions are composed of particles whose diameters range from 2000 to 62.5 µm, 62.5 to 3.91 µm, and less than 3.91 µm, respectively. This classification is applied regardless of sediment type and origin.

Grain-size, carbon and calcium carbonate at DSDP Leg 77 Holes

Sand-silt-clay distribution was determined on 10-cm**3 sediment samples collected at the time the cores were split and described.

Grain-size, carbona and calcium carbonate at DSDP Leg 58 Holes

Sand-silt-clay distribution was determined on 10-cm**3 sediment samples collected at the time the cores were split and described. The sediment classification used here is that of Shepard (1954), with the sand, silt, and clay boundaries based on the Wentworth (1922) scale. Thus the sand, silt, and clay fractions are composed of particles whose diameters are 2000 to 62.5 µm, 62.5 to 3.91 µm, and less than 3.91 µm, respectively. This classification is applied without regard to sediment type and origin; therefore, the sediment names used in this table may differ from those used elsewhere in this volume; e.g., a silt composed of nannofossils may be called a nannofossil ooze in a site chapter.

Grain size composition and age of ODP Hole 167-1017E sediments

Siliciclastic sedimentation at Ocean Drilling Program Site 1017 on the southern slope of the Santa Lucia Bank, central California margin, responded closely to oceanographic and climatic change over the past ~130 ka. Variation in mean grain-size and sediment sorting within the ~25-m-thick succession from Hole 1017E show Milankovitch-band to submillenial-scale variation. Mean grain size of the "sortable silt" fraction (10-63 µm) ranges from 17.6 to 33.9 µm (average 24.8 µm) and is inversely correlated with the degree of sorting. Much of the sediment has a bimodal or trimodal grain-size distribution that is composed of distinct fine silt, coarse silt to fine sand, and clay-size components. The position of the mode and the sorting of each component changes through the succession, but the primary variation is in the presence or abundance of the coarse silt fraction that controls the overall mean grain size and sorting of the sample. The occurrence of the best-sorted, finest grained sediment at high stands of sea level (Holocene, marine isotope Substages 5c and 5e) reflect the linkage between global climate and the sedimentary record at Site 1017 and suggest that the efficiency of off-shelf transport is a key control of sedimentation on the Santa Lucia Slope. It is not clear what proportion of the variation in grain size and sorting may also be caused by variations in bottom current strength and in situ hydrodynamic sorting.

Grain-size distribution, sedimentation rate and x-ray fluorescence data of four sediment cores off the Senegal River estuary

Fine-grained sediment depocenters on continental shelves are of increased scientific interest since they record environmental changes sensitively. A north-south elongated mud depocenter extends along the Senegalese coast in mid-shelf position. Shallow-acoustic profiling was carried out to determine extent, geometry and internal structures of this sedimentary body. In addition, four sediment cores were retrieved with the main aim to identify how paleoclimatic signals and coastal changes have controlled the formation of this mud depocenter. A general paleoclimatic pattern in terms of fluvial input appears to be recorded in this depositional archive. Intervals characterized by high terrigenous input, high sedimentation rates and fine grain sizes occur roughly contemporaneously in all cores and are interpreted as corresponding to intensified river discharge related to more humid conditions in the hinterland. From 2750 to 1900 and from 1000 to 700 cal a BP, wetter conditions are recorded off Senegal, an observation which is in accordance with other records from NW-Africa. Nevertheless, the three employed proxies (sedimentation rate, grain size and elemental distribution) do not always display consistent inter-core patterns. Major differences between the individual core records are attributed to sediment remobilization which was linked to local hydrographic variations as well as reorganizations of the coastal system. The Senegal mud belt is a layered inhomogeneous sedimentary body deposited on an irregular erosive surface. Early Holocene deceleration in the rate of the sea-level rise could have enabled initial mud deposition on the shelf. These favorable conditions for mud deposition occur coevally with a humid period over NW-Africa, thus, high river discharge. Sedimentation started preferentially in the northern areas of the mud belt. During mid-Holocene, a marine incursion led to the formation of an embayment. Afterwards, sedimentation in the north was interrupted in association with a remarkable southward shift in the location of the active depocenter as it is reflected by the sedimentary architecture and confirmed by radiocarbon dates. These sub-recent shifts in depocenters location are caused by migrations of the Senegal River mouth. During late Holocene times, the weakening of river discharge allowed the longshore currents to build up a chain of beach barriers which have forced the river mouth to shift southwards.

Grain size analysis of sediment core GeoB1510-2

Detailed information about the sediment properties and microstructure can be provided through the analysis of digital ultrasonic P wave seismograms recorded automatically during full waveform core logging. The physical parameter which predominantly affects the elastic wave propagation in water-saturated sediments is the P wave attenuation coefficient. The related sedimentological parameter is the grain size distribution. A set of high-resolution ultrasonic transmission seismograms (-50-500 kHz), which indicate downcore variations in the grain size by their signal shape and frequency content, are presented. Layers of coarse-grained foraminiferal ooze can be identified by highly attenuated P waves, whereas almost unattenuated waves are recorded in fine-grained areas of nannofossil ooze. Color -encoded pixel graphics of the seismograms and instantaneous frequencies present full waveform images of the lithology and attenuation. A modified spectral difference method is introduced to determine the attenuation coefficient and its power law a = kF. Applied to synthetic seismograms derived using a "constant Q" model, even low attenuation coefficients can be quantified. A downcore analysis gives an attenuation log which ranges from -700 dB/m at 400 kHz and a power of n=1-2 in coarse-grained sands to few decibels per meter and n :s; 0.5 in fine-grained clays. A least squares fit of a second degree polynomial describes the mutual relationship between the mean grain size and the attenuation coefficient. When it is used to predict the mean grain size, an almost perfect coincidence with the values derived from sedimentological measurements is achieved.

Eolian mass-accumulation rates and grain size at DSDP Sites 86-576 and 86-578

The mass-accumulation rate and grain size of the total eolian component of North Pacific pelagic clays at Deep Sea Drilling Project Sites 576 and 578 have been used to evaluate changes in eolian sedimentation and the intensity of atmospheric circulation that have occurred during the past 70 m.y. Eolian deposition, an indicator of source area aridity, was low in the Paleocene, Eocene, and Oligocene, apparently reflecting the humid environments of that time as well as the lack of glacial erosion products. A general increase in eoiian accumulation in the Miocene apparently reflects the relative increase in global aridity during the latter part of the Cenozoic. A dramatic increase in eolian accumulation rates in the Pliocene reflects the increased aridity and availability of glacial erosion products associated with Northern Hemisphere glaciation 2.5 m.y. ago. Eolian grain size, an indicator of wind intensity, suggests that Late Cretaceous wind strength was comparable to present-day wind strength. A sharp decrease in eolian grain size across the Paleocene/Eocene boundary is not readily interpreted, but may indicate a significant reduction in the intensity of atmospheric circulation at that time. Fine eolian grain size and low accumulation rates in the Eocene and early Oligocene are in agreement with low early Tertiary thermal gradients and less vigorous atmospheric circulation. Large increases in grain size during the Oligocene, mid-to-late Miocene, and Pliocene appear to be a response to steepening thermal gradients resulting from increasing polar isolation.

Temperatures, salinity, wind speed, grain sizes and foraminifera abundance in the Great Belt Channel, western Baltic Sea

The Great Belt, the largest inlet to the Baltic Sea, has a deep and well defined channel system. A distinct thermohaline layer at roughly 18 to 20 m of water depth separates the saltier and generally cooler deeper North Sea water from the brackish and warmer surface water. It is practically a current dominated area, with the strongest bottom currents due to prolonged west winds. The size and shape of the surface sediments and their grain size distributions show a close relationship with the prevailing hydrographical conditions. Southerly current marks predominate while northerly directions are confined to 10 to 14 m of water depth. The degree of bioturbation is highest in the uppermost sedimentary cover where practically all original stratification has been destroyed. Various bioturbate structures have been identified with the fauna. Coiling ratios of Ammonia beccarii (Linnaeus) have been successfully applied for correlation in the postglacial sediments of the early Littorina Transgression. The succession shows that in the Boreal brackish water conditions were probably followed by peat and limnic sediments as the sea regressed. With the Littorina Transgression, the sea again entered the area and high sedimentation rates resulted in the major deposits of the Great Belt. At least for the last 4000 years, sedimentation rates had been very low. Present day currents sweep out the sediments, mainly to the southern marginal areas.

The effect of grain refinement and silicon content on grain formation in hypoeutectic Al-Si alloys

The effect of increasing the amount of added grain refiner on grain size and morphology has been investigated for a range of hypoeutectic Al-Si alloys. The results show a transition in grain size at a silicon concentration of about 3 wt% in unrefined alloys; the grain size decreasing with silicon content before the transition, and increasing beyond the transition point. A change in morphology also occurs with increased silicon content. The addition of grain refiner leads to greater refinement for silicon contents below the transition point than for those contents above the transition point, while the transition point seems to remain unchanged. The slope of the grain size versus silicon content curve after the transition seems to be unaffected by the degree of grain refinement. The results are related to the competitive processes of nucleation and constitutional effects during growth and their impact on nucleation kinetics. (C) 1999 Elsevier Science S.A. All rights reserved.