A lattice grain model of hillslope evolution

Abstract. This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and baselevel lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of baselevel lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

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A lattice grain model of hillslope evolution

Earth Surface Dynamics ◽

10.5194/esurf-6-563-2018 ◽

2018 ◽

Vol 6 (3) ◽

pp. 563-582 ◽

Cited By ~ 2

Author(s):

Gregory E. Tucker ◽

Scott W. McCoy ◽

Daniel E. J. Hobley

Keyword(s):

Rock Weathering ◽

Additional Parameter ◽

Bare Rock ◽

Near Surface ◽

Weathering Rate ◽

Physical Weathering ◽

Stochastic Disturbance ◽

Base Level ◽

Hillslope Evolution ◽

Level Lowering

Abstract. This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. Cells representing near-surface soil material undergo stochastic disturbance events, in which initially stationary material is put into motion. Net downslope transport emerges from the greater likelihood for disturbed material to move downhill than to move uphill. Cells representing rock undergo stochastic weathering events in which the rock is converted into regolith. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and base-level lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of base-level lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

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Structural analysis of the photosynthetic membrane from Ectothiorhodospira halochloris

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010007727x ◽

1983 ◽

Vol 41 ◽

pp. 740-741

Author(s):

H. Engelhardt ◽

R. Guckenberger ◽

W. Baumeister

Keyword(s):

Lattice Structure ◽

Bacterial Species ◽

Hexagonal Lattice ◽

Reaction Centre ◽

Photosynthetic Membrane ◽

Rhodopseudomonas Viridis ◽

Photosynthetic Membranes ◽

Ectothiorhodospira Halochloris ◽

Main Components

Bacterial photosynthetic membranes contain, apart from lipids and electron transport components, reaction centre (RC) and light harvesting (LH) polypeptides as the main components. The RC-LH complexes in Rhodopseudomonas viridis membranes are known since quite seme time to form a hexagonal lattice structure in vivo; hence this membrane attracted the particular attention of electron microscopists. Contrary to previous claims in the literature we found, however, that 2-D periodically organized photosynthetic membranes are not a unique feature of Rhodopseudomonas viridis. At least five bacterial species, all bacteriophyll b - containing, possess membranes with the RC-LH complexes regularly arrayed. All these membranes appear to have a similar lattice structure and fine-morphology. The lattice spacings of the Ectothiorhodospira haloohloris, Ectothiorhodospira abdelmalekii and Rhodopseudomonas viridis membranes are close to 13 nm, those of Thiocapsa pfennigii and Rhodopseudomonas sulfoviridis are slightly smaller (∼12.5 nm).

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Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100076834 ◽

1983 ◽

Vol 41 ◽

pp. 646-647

Author(s):

Joseph A. Zasadzinski

Keyword(s):

Liquid Crystalline ◽

Freeze Fracture ◽

Continuum Theory ◽

Closed Surfaces ◽

Straight Line ◽

Low Weight ◽

Concentric Spheres ◽

Membrane Geometry ◽

Dupin Cyclides ◽

Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

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Electron Microscope study of commensurate-incommensurate phase transition in BaZnGeO4

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173996 ◽

1990 ◽

Vol 48 (4) ◽

pp. 172-173

Author(s):

Naoki Yamamoto ◽

Makoto Kikuchi ◽

Tooru Atake ◽

Akihiro Hamano ◽

Yasutoshi Saito

Keyword(s):

Phase Transition ◽

Electron Microscope Study ◽

Room Temperature ◽

Hexagonal Lattice ◽

Ferroelectric Materials ◽

Temperature Phase ◽

X Ray Diffraction ◽

X Ray ◽

Periodic Arrays ◽

Modulation Wave Vector

BaZnGeO4 undergoes many phase transitions from I to V phase. The highest temperature phase I has a BaAl2O4 type structure with a hexagonal lattice. Recent X-ray diffraction study showed that the incommensurate (IC) lattice modulation appears along the c axis in the III and IV phases with a period of about 4c, and a commensurate (C) phase with a modulated period of 4c exists between the III and IV phases in the narrow temperature region (—58°C to —47°C on cooling), called the III' phase. The modulations in the IC phases are considered displacive type, but the detailed structures have not been studied. It is also not clear whether the modulation changes into periodic arrays of discommensurations (DC’s) near the III-III' and IV-V phase transition temperature as found in the ferroelectric materials such as Rb2ZnCl4.At room temperature (III phase) satellite reflections were seen around the fundamental reflections in a diffraction pattern (Fig.1) and they aligned along a certain direction deviated from the c* direction, which indicates that the modulation wave vector q tilts from the c* axis. The tilt angle is about 2 degree at room temperature and depends on temperature.

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The need of electron microscopy in the study of domains and domain walls in ferroelectrics

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100170487 ◽

1994 ◽

Vol 52 ◽

pp. 550-551

Author(s):

Wenwu Cao

Keyword(s):

Domain Wall ◽

Domain Walls ◽

High Mobility ◽

Continuum Theory ◽

Polarization Vector ◽

Ferroelectric Materials ◽

Dielectric Constants ◽

Nonlocal Coupling ◽

Cubic Symmetry ◽

Gradient Energy

Domain structures play a key role in determining the physical properties of ferroelectric materials. The formation of these ferroelectric domains and domain walls are determined by the intrinsic nonlinearity and the nonlocal coupling of the polarization. Analogous to soliton excitations, domain walls can have high mobility when the domain wall energy is high. The domain wall can be describes by a continuum theory owning to the long range nature of the dipole-dipole interactions in ferroelectrics. The simplest form for the Landau energy is the so called ϕ model which can be used to describe a second order phase transition from a cubic prototype,where Pi (i =1, 2, 3) are the components of polarization vector, α's are the linear and nonlinear dielectric constants. In order to take into account the nonlocal coupling, a gradient energy should be included, for cubic symmetry the gradient energy is given by,

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Cryo-Electron Microscopy and Correlation Averaging of Frozen-Hydrated, Polymorphic 2D Crystals of the Mitochondrial Outer Membrane Channel

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179257 ◽

1990 ◽

Vol 48 (1) ◽

pp. 100-101

Author(s):

Xiao-Wei Guo

Keyword(s):

Outer Membrane ◽

Hexagonal Lattice ◽

Mitochondrial Outer Membrane ◽

Rectangular Lattice ◽

Electron Microscopic ◽

Cryo Electron Microscopy ◽

Voltage Dependent ◽

Outer Membrane Channel ◽

2D Crystals ◽

Vdac Channel

Voltage-dependent, anion-selective channels (VDAC) are formed in the mitochondrial outer membrane (mitOM) by a 30-kDa polypeptide. These channels form ordered 2D arrays when mitOMs from Neurospora crassa are treated with soluble phospholipase A2. We obtain low-dose electron microscopic images of unstained specimens of VDAC crystals preserved in vitreous ice, using a Philips EM420 equipped with a Gatan cryo-transfer stage. We then use correlation analysis to compute average projections of the channel crystals. The procedure involves Fourier-filtration of a region within a crystal field to obtain a preliminary average that is subsequently cross-correlated with the entire crystal. Subregions are windowed from the crystal image at coordinates of peaks in the cross-correlation function (CCF, see Figures 1 and 2) and summed to form averages (Figure 3).The VDAC channel forms several different types of crystalline arrays in mitOMs. The polymorph first observed during phospholipase treatment is a parallelogram array (a=13 run, b=11.5 run, θ==109°) containing 6 water-filled pores per unit cell. Figure 1 shows the CCF of a sub-field of such an “oblique” array used to compute the correlation average of Figure 3A. With increased phospholipase treatment, other polymorphs are observed, often co-existing within the same crystal. For example, two distinct (but closely related) types of lattices occur in the field corresponding to the CCF of Figure 2: a “contracted” version of the parallelogram lattice (a=13 run, b=10 run, θ=99°), and a near-rectangular lattice (a=8.5 run, b=5 nm). The pattern of maxima in this CCF suggests that a third, near-hexagonal lattice (a=4.5 nm) may also be present. The correlation averages of Figures 3B-D were computed from polycrystalline fields, using peak coordinates in regions of CCFs corresponding to each of the three lattice types.

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Microdiffraction analysis of precipitate crystallography and morphology in Al alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100177908 ◽

1990 ◽

Vol 48 (4) ◽

pp. 954-955

Author(s):

B.C. Muddle ◽

G.R. Hugo

Keyword(s):

Point Group ◽

Hexagonal Lattice ◽

Intersection Point ◽

Saed Pattern ◽

Point Symmetry ◽

Hexagonal Symmetry ◽

Precipitate Crystal ◽

The Matrix ◽

The Subject ◽

Electron Microdiffraction

Electron microdiffraction has been used to determine the crystallography of precipitation in Al-Cu-Mg-Ag and Al-Ge alloys for individual precipitates with dimensions down to 10 nm. The crystallography has been related to the morphology of the precipitates using an analysis based on the intersection point symmetry. This analysis requires that the precipitate form be consistent with the intersection point group, defined as those point symmetry elements common to precipitate and matrix crystals when the precipitate crystal is in its observed orientation relationship with the matrix.In Al-Cu-Mg-Ag alloys with high Cu:Mg ratios and containing trace amounts of silver, a phase designated Ω readily precipitates as thin, hexagonal-shaped plates on matrix {111}α planes. Examples of these precipitates are shown in Fig. 1. The structure of this phase has been the subject of some controversy. An SAED pattern, Fig. 2, recorded from matrix and precipitates parallel to a <11l>α axis is suggestive of hexagonal symmetry and a hexagonal lattice has been proposed on the basis of such patterns.

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Reconstruction of Chitin-Protein Complexes Using Correlation Averaging Methods: Ovipositor of the Ichneumon Fly Megarhyssa

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s1431927600000143 ◽

1980 ◽

Vol 38 ◽

pp. 38-39

Author(s):

L. T. Germinario ◽

J. Blackwell ◽

J. Frank

Keyword(s):

Protein Complexes ◽

Hexagonal Lattice ◽

Uranyl Acetate ◽

Optical Diffraction ◽

Insect Cuticle ◽

High Dose ◽

Wide Angle ◽

X Ray ◽

Averaging Methods ◽

Digital Correlation

This report describes the use of digital correlation and averaging methods 1,2 for the reconstruction of high dose electron micrographs of the chitin-protein complex from Megarhyssa ovipositor. Electron microscopy of uranyl acetate stained insect cuticle has demonstrated a hexagonal array of unstained chitin monofibrils, 2.4−3.0 nm in diameter, in a stained protein matrix3,4. Optical diffraction Indicated a hexagonal lattice with a = 5.1-8.3 nm3 A particularly well ordered complex is found in the ovipositor of the ichneumon fly Megarhyssa: the small angle x-ray data gives a = 7.25 nm, and the wide angle pattern shows that the protein consists of subunits arranged in a 61 helix, with an axial repeat of 3.06 nm5.

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