Torstein Jøssang

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.

A Simulation Model for Meandering Rivers

A computer model for the dynamics of meandering rivers has been used to study the interplay between the migrating river and the changing sedimentary environment created by the meandering river itself. The model is based on the theory of Ikeda et al. [1981] and is closely related to that proposed by Howard [1983]. Coarser sands, which are often associated with high credibility, are deposited in the point bars formed when the river migrates away from its former bank. Fine-grained material eventually fills the oxbow lakes created by cutoff processes and forms erosion-resistant plugs. In the simulations, geometric forms of individual meanders observed in different natural sedimentary environments have been reproduced by changing the credibility of the corresponding sedimentary materials, such as point bar deposits, flood plain deposits, and oxbow lake deposits. The simulations indicate that the typical meander wavelength is determined mainly by hydraulic factors such as the flow in the channel and the inclination of the underlying flood plain and is independent of the difference in the credibilities of sedimentary deposits. The computational approach permits exploration of long-term changes in the floodplain geology, mediated by the meandering river. As an initial demonstration, the formation of meander belts is investigated using the model. The results suggest that a meander belt will be formed by a rivers own cutoff loops only if the characteristic time of deposition and solidification of an oxbow lake is longer than the typical time that it takes the river to migrate downstream over the distance of a meander-loop wavelength.

The fractal nature of geochemical landscapes

Abstract Fractals are shapes that look basically the same on all scales of magnification — they are self-like. Numerous natural phenomena have this property, and fractal geometry has contributed significantly to their analysis. Geochemical maps and other geochemical data from the literature indicate that geochemical dispersion patterns (geochemical landscapes) may have fractal dimensions because they appear similar at all scales of magnitude from microscopic to continental, in agreement with diverse geological processes of varying rapidity and spatial extent ranging from chemical reactions to continental movements. Analysis of variogrammes and other tests carried out on geochemical dispersion patterns (contents of 21 acid soluble elements in 6000 samples of stream sediment) with a 250,000 km2 survey area in northern Fennoscandia indicates a fractal dimension of between 2.1 and 2.9 for 10 elements (Al, Ba, Ca, Fe, Li, Mg, Sc, Sr, V and Zn), while the remaining 11 (Ag, Ce, Co, Cr, Cu, La, Mn, Mo, Ni, P and Zr) give inconclusive results presumably due, mainly, to inadequate precision of the chemical analyses. These fractal dimensions were found to exist between distances of 5 and 150 km, which are the linear limits set by the sample spacing and the size of the survey area respectively. It is proposed that various sets of geochemical, geophysical and other types of data from around the world be analyzed for their fractal properties, collecting evidence as to whether fractal dimensions are a general quality of geochemical dispersion patterns. If it can be shown that geochemical landscapes are usually true fractals analogoues to topographic landscapes, the impact on applied geochemistry may be profound. One practical consequence in mineral exploration could be the possible existence of numerous economically interesting regional to continental geochemical provinces on earth. Such provinces could be detected at relatively low cost through analysis of wide-spread samples. Consecutive denser sampling within the disclosed provinces would reveal subprovinces, which again could be investigated further by successively more intensive sampling. This type of systematic survey employing the principles of fractal geometry for stepwise selection and progressively more thorough examination of subareas of decreasing size, would apply to any survey area of interest and could improve cost-efficiency in mineral exploration.

A computer model for meandering rivers with multiple bed load sediment sizes: 1. Theory

A computer model for meandering rivers that couples water flow, bed topography, the sorting of sediments with different grain sizes, and channel migration has been developed using the linear theory of Johannesson and Parker [1989] for the dynamics of meandering rivers and the theory of Parker and Andrews [1985] for bed load sediment transport and sorting in meander bends. The equations for single-size sediment transport used in the linear theory of Johannesson and Parker were replaced by multiple-size sediment transport and sorting equations obtained from the theory of Parker and Andrews. This paper is the first of a pair. In this paper, the theoretical framework of the model is presented, and the derivation of the theory from the earlier theories is detailed. It is shown that there are five different regions in the two-dimensional model parameter space [ϵ(G1 − 3), (π/2)2 G2], where G1 is a measure of the coupling of the longitudinal sediment flow to the longitudinal water flow, ϵ is the rescaled bed friction coefficient, and G2 characterizes the coupling of the transverse (cross channel) sediment flow to the transverse component of the bed inclination. The model is not stable in two of the regions (regions 1 and 2). Alternating bars develop in region 4 but propagate along the channel with damped amplitudes, and no alternating bars develop in region 5. In region 3, which is the boundary between regions 2 and 4, alternating bars develop and propagate undamped throughout the entire channel. Increasing the floodplain inclination, channel width/depth ratio, average sediment size, or the breadth of the sediment size distribution in the model increases the tendency toward a transition from a stable meandering state to an unstable, presumably braided, state.

Photon correlation spectroscopy of human IgG.

The translational diffusion coefficient D20,w0, of monomeric human immunoglobulin G (IgG) has been studied by photon-correlation spectroscopy as a function of pH and protein concentration. At pH 7.6, we find D20,w0=3.89×10−7±0.02 cm2/sec, in good agreement with the value determined by classic mehods. This value corresponds to an effective hydrodynamic radius R, of 55.1±0.3 Å. As pH is increased to 8.9; with the same ionic strength, the molecule appears to expand slightly (3.5% increase in hydrodynamic radius). The concentration dependence of the IgG diffusion constant is interpreted in terms of solution electrostatic effects and shows that long-range repulsive interactions are negligible in the buffer used. The diffusion coefficient for dimeric IgG has also been determined to be D20,w=2.81×10−7±0.04 cm2/sec at 1.6 mg/ml, which corresponds to a hydrodynamic radius of 75 Å. For light-scattering studies of protein molecules in the dimension range of 5–10 nm (Mr=105−107) we find monomeric horse spleen ferritin well suited as a reference standard. Ferritin is a spherical molecule with a hydrodynamic radius R of 6.9±0.1 nm and is stable for years in our standard Tris-HCl-NaCl buffer even at room temperature.

TRACER DISPERSION IN A SELF-ORGANIZED CRITICAL SYSTEM

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette et al., Nature (London) 379, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a 1D cellular automaton modeling the experiment.

A computer model for meandering rivers with multiple bed load sediment sizes: 2. Computer simulations

The theory for flow and sediment transport in a curved channel that was presented by Sun et al. [this issue], paper 1 of this two-part study, was used to develop a computer model for meandering rivers with multiple sediment grain sizes. The model, which is based on the linear theory of Johannesson and Parker [1989] for meandering rivers, takes into account the effects of alternate bars. Therefore this is one of the first models that can be used to simulate bar-bend interactions and their relationships with both the initial growth and the long-term development of meandering rivers. Unlike the previous theoretical studies of Blondeaux and Seminara [1985] and Johannesson and Parker [1989], the results show that the initial growth of meandering rivers is controlled primarily by the curvature-related instabilities, and the influence of alternate bars on the initial development of meander loops appears to be negligible. The simulations also show that under certain conditions, meandering rivers do evolve toward a “resonant” state. It appears that finite amplitude perturbations are needed to enhance the initial development of alternate bars in the channel in order for the river to develop toward a bar-bend resonance state. The model includes the transport and sorting of sediment with a distribution of grain sizes. Heterogeneities in the sedimentary material deposited in the floodplain, as a result of meandering river migration, are realistically simulated.

Slow two-phase flow in artificial fractures: Experiments and simulations

The slow displacement of a wetting fluid by a nonwetting fluid in models of a single fracture was studied experimentally and by computer simulations on identical geometries. The fracture was modeled by the gap between a rough plate and a smooth transparent plate, both oriented horizontally. Two different rough plates were used, a textured glass plate and a polymethyl methacrylate plate with a computer-generated pattern. A nonwetting fluid (air) was injected slowly through an inlet into the model and displaced a wetting fluid (water) initially filling the model. The aperture fields of the artifical fractures were measured using a light absorption technique. The experiments were simulated using modified invasion percolation models, making use of the measured aperture fields. The simulation models captured invasion bursts and fragmentation and redistribution of the invading air. Experiments and simulations were compared step by step, and good qualitative and quantitative agreement was found.

Invasion percolation and secondary migration: experiments and simulations

Abstract Experiments have been carried out to study the displacement of wetting fluids by immiscible non-wetting fluids in quasi-two-dimensional and three-dimensional granular porous media. These experiments included a systematic investigation of the effects of gravity acting on the density difference between the two fluids. The simple invasion percolation model provides a surprisingly realistic simulation of the slow fluid–fluid displacement process in the absence of gravity, and a simple extension of the model can be used to simulate the most important features of gravity stabilized and destabilized fluid–fluid displacement processes. The dimensionless Bond number Bo (the ratio between buoyancy forces and capillary forces on the pore scale) can be used to compare experiments and simulations carried out using different (geometrically similar) porous media, different fluid–fluid interfacial tensions and different fluid densities. The complex patterns generated by gravity stabilized and gravity destabilized fluid–fluid displacement processes can be described in terms of a pattern of blobs of size ξ that have a fractal structure on length scales l in the range ϵ≤l≤ξ, where ϵ is the characteristic porous medium grain size. The blob size ξ is related to the Bond number by the simple scaling relationship ξ∼Bo−ν/(1+ν), which was first derived by Wilkinson, 1984 , Wilkinson, 1996 ) for gravity-stabilized displacement. Here, ν is the percolation theory correlation length exponent (ν=4/3 in two-dimensional systems and ν≈0.88 in three-dimensional systems). The experiments and simulations have been extended to include fluid–fluid displacement in fracture apertures and the effects of flow of the wetting fluid under the influence of a hydraulic potential gradient. These experimental and simulation results have important implications for our understanding of secondary migration. They indicate that the residual hydrocarbon saturation in the enormous volume of porous sedimentary rock (carrier rocks) between the hydrocarbon source and the reservoir can be very low, thus allowing significant quantities of oil and gas to reach the reservoir. Simulations have been carried out to explore the effects of heterogeneities on gravity destabilized fluid–fluid displacement processes and fluid–fluid displacement in fracture apertures. However, the structure of the carrier rocks is highly dynamic on the time scales over which secondary migration takes place (of the order of 108 years, in many cases). A better understanding of the pore structure of the carrier rocks and its dynamics on long time scales is needed to more accurately model secondary migration.

On the determination of stacking fault energies from extended dislocation node measurements

Abstract A method based on the continuum theory of dislocations is used to determine the relation between the stacking fault energy γ and the extension of dislocation nodes. Several procedures for determining γ from electron micrographs are presented. The accuracy of the method is estimated and the method is applied to the determination of γ for graphite and aluminum nitride.