Mathematical modelling of a laminar suspension flow in the flat inclined channel

The laminar flow of a suspension consisting of viscous incompressible fluid with solid spherical particles of the same size in a flat inclined channel is investigated in this work. The mathematical model is formulated in a one-fluid approximation in a three-dimensional statement and solved in the OpenFOAM software package. The results of mathematical modeling are compared with experimental data. The study of the dynamics of the distribution of solid spherical particles in the flow and sedimentation along the length of the channel depending on the size of particles and the angle of inclination of the channel relative to the horizon is carried out.

The Dynamics of Flow Discharge and Suspension Flow Discharge in Volcano Watershed with Agroforestry Land Cover

The suspension flow from the upper part of a volcano watershed, which has a very thick soil condition, is sensitive to landuse form. Agroforestry is the dominant landuse form in the volcanic landscape of Indonesia. There is a lack of detailed studies about suspension flow in the upper watershed where agroforestry is the land cover. This research, performed in agroforestry area, covered the correspondence between flow discharge and suspension flow discharge, the time lag of initial rain events and the formation of suspension flow; and the characteristics of the grain size of the suspensions during the flow. The suspension flow was measured at the outlet of a gully in key watershed areas, which yielded a total of 436 suspension data. The measurement analysis was conducted at every rain event in the field and in the laboratory. The crop characteristics in the rain catchment area were recorded in details during the field survey. The characteristics of the channels converging toward the gully system were observed during the field survey. There were three relationship patterns between the peak flow discharge and the peak suspension discharge, namely (1) the peak flow discharge corresponded to the peak suspension discharge, (2) the peak flow discharge preceded the peak suspension discharge, (3) the peak flow discharge occurred after the peak suspension discharge. The average time interval between the rain events and the occurrence of suspension flow was 17.7 minutes. The peak suspension content varied from 0.0016 g/L up to 4.71 g/L with an average of 1.03 g/L. The grain size of the suspension was dominated by 71-76% of clay fraction with an average of 73% at the rising phase and 68-71% of clay fraction with an average of 69% at the falling stage

On Sinaĭ Billiards on Flat Surfaces with Horns

We show that certain billiard flows on planar billiard tables with horns can be modeled as suspension flows over Young towers (Ann. Math. 147:585–650, 1998) with exponential tails. This implies exponential decay of correlations for the billiard map. Because the height function of the suspension flow itself is polynomial when the horns are Torricelli-like trumpets, one can derive Limit Laws for the billiard flow, including Stable Limits if the parameter of the Torricelli trumpet is chosen in (1, 2).

Numerical modelling of igneous processes

<p>Magma matters. From magmatic differentiation of terrestrial planets into core, mantle and crust, to magmatism modulating plate tectonics and deep volatile cycles that maintain a habitable Earth, and volcanism causing terrible hazards but also providing rich energy and mineral resources – igneous processes are integral to the evolution of Earth and other terrestrial planetary bodies. Our understanding of volcanoes and their deep magmatic roots derives from a range of disciplines including field geology, experimental petrology, geochemical analyses, geophysical imaging, and volcano monitoring. Observational and experimental studies, however, are hampered by incomplete access to processes that play out across scales ranging from sub-millimetre size to thousands of kilometres, and from seconds to billions of years. Computational modelling provides a tool kit for investigating igneous processes across these scales.</p><p>Over the past decade, my research has been focused on advancing the theoretical description and numerical application of multi-phase reaction-transport processes at the volcano to planetary scale. Mixture theory provides a framework to represent the spatially averaged behaviour of a large sample of microscopic phase constituents including mineral grains, melt films, fluid droplets, and vapour bubbles. The approach has been used successfully to model both porous flow of melt percolating through compacting rock, as well as suspension flow of crystals settling in convecting magma bodies. My recent work has introduced a new modelling framework that bridges the porous to mushy and suspension flow limits, and extends beyond solid-liquid systems to multi-phase systems including several solid, liquid, and vapour phases. Igneous process modelling can thus provide new insights into the generation and extraction of mantle melts, the dynamics of crustal magma processing, the outgassing and eruption of shallow magma reservoirs, and the generation of mineral resources by exsolution of enriched magmatic liquids.</p>