Lithosphere-Scale Thermal Shear Zones

The shear-heating induced localisation of
lithosphere-scale deformation is suggested as a potentially important mechanism
for breaking the lithosphere. Yet, the physical parameters that control the onset of
this instability remain unclear. We therefore performed systematic 2-D simulations of
visco-elasto-plastic lithospheric deformation in which we addressed the effects of various
parameters and we found that a sharp transition exists between localising and non-localising
regimes. In a next step we develop a semi-analytical model that combines scaling laws with a
1-D lithospheric deformation model. We show that the 1-D model successfully predicts the
occurrence of shear localisation in 2-D models, if the thickness of the plastically deforming
part of the (lower) lithosphere is employed as characteristic length-scale. An application of
the 1-D model to the terrestrial planets shows that this type of shear localisation is expected
to occur most readily on Earth (Crameri and Kaus 2010).

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Mantle Plumes

Hot mantle plumes
can crucially weaken the lithosphere regionally.
Thermal erosion at the plate bottom produces critical variation in plate thickness.
Laterally mobile mantle plumes further excite horizontal mantle flow below the plate that leads to drips in thickned plate portions.
All these mechanisms combined can lead to plate failure and subsequent subduction initiation.

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Self-Consistent Single-Sided Subduction

We have, for the first time, produced a mantle convection model that
self-consistently reproduces the realistic single-sided sinking of the surface plates.
Numerical results show that a free surface upper boundary condition
(i.e., the free development of surface topography) and a weak crustal
layer (decoupling the two colliding plates) lead to nature-like single-sided subduction. The first allows the
lithosphere to bend in a natural manner and thus promotes the asymmetry
of the subduction zone. The latter provides a weak zone, which allows the
surrounding part of the lithosphere to be sufficiently strong and, therefore,
also prevents the subduction zone to become two-sided.

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Arcuate Subduction Trenches

We present temporally evolving 3-D global mantle convection models with single-sided
subduction and a free surface in both 3-D Cartesian and fully spherical geometry.
Special focus is given to the spontaneous development of three-dimensional structures
at the surface and in the upper mantle. We find that an arcuate shape is the natural
form for trenches and slabs. Cartesian models are used first to study the dynamic
evolution of subduction zones, spreading ridges, and interconnected transform features.
These experiments highlight the strong variation of spontaneously developing, arcuate
slab curvature and subduction polarity along the trench strike. The spontaneous
development of spreading ridges leads to lateral offsets between separated segments
that are characterized by normal transform motion. Spherical models then allow insights
into the evolution of plate tectonics on a sphere. Investigated are the spontaneous
evolution of slab geometry, trench motion, and subduction-induced mantle flow. Two
new dynamical features are discovered: 'back-slab spiral flow' and 'slab tunneling'.

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Subduction Shut-Off in 2-D

Recent advances in numerical modelling allow global models of mantle convection to more
realistically reproduce the behaviour at convergent plate boundaries; in particular, the
inclusion of a free surface at the outer boundary has been shown to facilitate self-consistent
development of single-sided subduction. This allows for a more extensive study of subduction
in the context of global mantle convection, as opposed to commonly-used regional models.
Here, we further investigate the
effect of various physical parameters and complexities on inducing Earth-like plate tectonics
and its evolution in time. The time-evolution displays interesting events including subduction polarity reversals,
subduction shut-off and slab break-off.

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Subduction Shut-Off in 3-D

We present temporally evolving 3-D global mantle convection models with single-sided
subduction and a free surface in both 3-D Cartesian and fully spherical geometry.
Special focus is given to the spontaneous development of three-dimensional structures
at the surface and in the upper mantle. We find that an arcuate shape is the natural
form for trenches and slabs. Cartesian models are used first to study the dynamic
evolution of subduction zones, spreading ridges, and interconnected transform features.
These experiments highlight the strong variation of spontaneously developing, arcuate
slab curvature and subduction polarity along the trench strike. The spontaneous
development of spreading ridges leads to lateral offsets between separated segments
that are characterized by normal transform motion. Spherical models then allow insights
into the evolution of plate tectonics on a sphere. Investigated are the spontaneous
evolution of slab geometry, trench motion, and subduction-induced mantle flow.

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Mantle Convection and Resurfacing on Io

Across Io's lithosphere, like previous work showed, magmatic resurfacing is thought
to be the dominant process transporting the heat. Because of that and the relatively
high fraction of partial melt in the mantle, melting may also play an important role
in the heat transport of Ioâs interior. The key objective of this work was to know
about the effects of magmatism on convection and on the resurfacing. Therefore, highly
viscous 2-D simulations of the mantle including melt segregation have been run to
determine scaling laws. These scaling laws are for velocity, lateral temperature
variations, lateral variations in heat flux and magmatism.
In contrast to previous studies, the simulations show a thick rigid top layer, which is
strong enough to support the observed topography on Io and a less hot bottom layer,
which allows the model to be self consistent. Further, magmatism rather than conduction
compensates higher heat inputs by an increased magmatic heat transport and thus leads
to a faster resurfacing of the crust/lithosphere.

The Sticky-Air Approach

Topography is a direct observable of the interaction between the Earth's internal and external dynamics.
Therefore, it is important for numerical models of lithospheric deformation to compute topography accurately.
Earth's surface is a so-called free surface, which means that both normal and shear stress should vanish
at this interface. It has been shown that correct treatment of the EarthÃ¢ÂÂs surface as a free surface can
have a significant effect in models of lithospheric and mantle dynamics
(Zhong et al., 1996, Kaus et al., 2008; Kaus et al., 2010). However, a true free surface is computationally
expensive which is why most mantle convection simulations until now treat the surface as a free-slip boundary.
For these models, topography is computed directly from normal stresses.

A free surface approximation, the so-called 'sticky air', requires the addition of a fluid layer in the model domain while retaining the computational
advantage of a free-slip top boundary. The fluid layer is a proxy for air (or water) and should, therefore,
have a near-zero density and a viscosity, which is several orders of magnitude lower than the lithosphere viscosity.

We present a theoretical background that provides the physical conditions under which the sticky-air approach
is a valid approximation of a true free surface. We evaluate two cases that characterise the evolution of
topography on different timescales. We quantitatively compare topographies for five different numerical codes
(using finite difference and finite element techniques) and for several different topography calculation
methods. It is found that the sticky-air approach works fine as long as the term (η_{st}/η_{ch})/(h_{st}/h_{ch})^{3} is sufficiently small, where η_{st} and h_{st}
are the viscosity and thickness of the sticky-air layer, and η_{ch} and h_{ch} are the characteristic viscosity
and length scale of the model, respectively.

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Crowd Dynamics

In the last decade, advances in numerical modelling of pedestrian dynamics
have made it possible to model realistic crowd dynamics and to test the
influence of several parameters on evacuation dynamics. In this study, we
developed a code that attempts to model pedestrian dynamics. This code was
written entirely in MatLab (except some external packages, which were included
as mex files) and initiated in the frame of the lecture 'Modelling and Simulating
Social Systems with MatLab'. We describe the behaviour of the code using
different approaches the path finding process of a pedestrian and then apply
our code to an artificial model of the evacuation of a beach in the case of a
rapid flooding event.