Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Seismic tomography models of the three-dimensional upper mantle velocity structure of the Mediterranean-Carpathian region provide a better understanding of the lithospheric processes governing its geodynamical evolution. Slab detachment, in particular lateral migration of this process along the plate boundary, is a key element in the lithospheric dynamics of the region during the last 20 to 30 million years. It strongly affects arc and trench migration, and causes along-strike variations in vertical motions, stress fields, and magmatism. In a terminal-stage subduction zone, involving collision and suturing, slab detachment is the natural last stage in the gravitational settling of subducted lithosphere.

http://www.mantleplumes.org/WebDocuments/Wortel2000.pdf

Subduction and Slab Detachment in the Mediterranean-Carpathian Region

The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

/pdf/heat-transfer-and-large-scale-dynamics-in-turbulent-rayleigh-39oz2czpiy.pdf

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

Recent global travel time tomography studies by Zhou [1996] and van der Hilst et al. [1997] have been performed with cell parameterizations of the order of those frequently used in regional tomography studies (i.e., with cell sizes of 1°–2°). These new global models constitute a considerable improvement over previous results that were obtained with rather coarse parameterizations (5° cells). The inferred structures are, however, of larger scale than is usually obtained in regional models, and it is not clear where and if individual cells are actually resolved. This study aims at resolving lateral heterogeneity on scales as small as 0.6° in the upper mantle and 1.2°–3° in the lower mantle. This allows for the adequate mapping of expected small-scale structures induced by, for example, lithosphere subduction, deep mantle upwellings, and mid-ocean ridges. There are three major contributions that allow for this advancement. First, we employ an irregular grid of nonoverlapping cells adapted to the heterogeneous sampling of the Earth's mantle by seismic waves [Spakman and Bijwaard, 1998]. Second, we exploit the global data set of Engdahl et al. [1998], which is a reprocessed version of the global data set of the International Seismological Centre. Their reprocessing included hypocenter redetermination and phase reidentification. Finally, we combine all data used (P, pP, and pwP phases) into nearly 5 million ray bundles with a limited spatial extent such that averaging over large mantle volumes is prevented while the signal-to-noise ratio is improved. In the approximate solution of the huge inverse problem we obtain a variance reduction of 57.1%. Synthetic sensitivity tests indicate horizontal resolution on the scale of the smallest cells (0.6° or 1.2°) in the shallow parts of subduction zones decreasing to approximately 2°–3° resolution in well-sampled regions in the lower mantle. Vertical resolution can be worse (up to several hundreds of kilometers) in subduction zones with rays predominantly pointing along dip. Important features of the solution are as follows: 100–200 km thick high-velocity slabs beneath all major subduction zones, sometimes flattening in the transition zone and sometimes directly penetrating into the lower mantle; large high-velocity anomalies in the lower mantle that have been attributed to subduction of the Tethys ocean and the Farallon plate; and low-velocity anomalies continuing across the 660 km discontinuity to hotspots at the surface under Iceland, east Africa, the Canary Islands, Yellowstone, and the Society Islands. Our findings corroborate that the 660 km boundary may resist but not prevent (present day) large-scale mass transfer from upper to lower mantle or vice versa. This observation confirms the results of previous, global mantle studies that employed coarser parameterizations.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB02467

Closing the gap between regional and global travel time tomography

A boundary between compositionally distinct regions at a depth of about 1600 kilometers may explain the seismological observations pertaining to Earth's lower mantle, produce the isotopic signatures of mid-ocean ridge basalts and oceanic island basalts, and reconcile the discrepancy between the observed heat flux and the heat production of the mid-ocean ridge basalt source region. Numerical models of thermochemical convection imply that a layer of material that is intrinsically about 4 percent more dense than the overlying mantle is dynamically stable. Because the deep layer is hot, its net density is only slightly greater than adiabatic and its surface develops substantial topography.

/pdf/compositional-stratification-in-the-deep-mantle-so21hlts35.pdf

Compositional stratification in the deep mantle

A long-standing problem in geodynamics is how to incorporate surface plates in numerical models of mantle convection. Plates have usually been inserted explicitly in convection models as rigidrafts1,2,3, as a separate rheological layer4,5 or as a high-viscosity region within weak zones6,7,8,9,10,11. Plates have also been generated intrinsically through the use of a more complex (non-newtonian) rheology for the entire model12,13 but with a prescribed mantle flow. However, previous attempts to generate plates intrinsically and in a self-consistent manner (without prescribed flow) have not produced surface motions that appear plate-like14,15,16. Here we present a three-dimensional convection model that generates plates in a self-consistent manner through the use of a rheology that is temperature and strain-rate dependent, and which incorporates the concept of a yield stress. This rheology induces a stiff layer on top of a convecting fluid, and we find that this layer breaks at sufficiently high stresses. The model produces a style of convection that contains some of the important features of plate tectonics, such as the subduction of the stiff layer and plate-like motion on the surface of the fluid mantle. However, the model also produces some non-Earth-like features, such as episodic subduction followed by the slow growth of a new stiff layer, which may be more consistent with the style of convection found on Venus.

Mantle convection simulations with rheologies that generate plate-like behaviour

Turbulent rotating convection is an important dynamical process occurring on nearly all planetary and stellar bodies, influencing many observed features such as magnetic fields, atmospheric jets and emitted heat flux patterns. For decades, it has been thought that the importance of rotation's influence on convection depends on the competition between the two relevant forces in the system: buoyancy (non-rotating) and Coriolis (rotating). The force balance argument does not, however, accurately predict the transition from rotationally controlled to non-rotating heat transfer behaviour. New results from laboratory and numerical experiments suggest that the transition is in fact controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. Turbulent rotating convection controls many observed features in stars and planets, such as magnetic fields. It has been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force. This paper presents results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns1,2,3,4,5,6. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force7,8,9,10,11,12. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments8,9,10,11,12,13,14,15, and is broadly applicable to natural convection systems.

/pdf/boundary-layer-control-of-rotating-convection-systems-2nwe0cq4yc.pdf

Boundary layer control of rotating convection systems

The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection

Bends in volcanic hotspot lineaments, best represented by the large elbow in the Hawaiian-Emperor chain, were thought to directly record changes in plate motion. Several lines of geophysical inquiry now suggest that a change in the locus of upwelling in the mantle induced by mantle dynamics causes bends in hotspot tracks. Inverse modeling suggests that although deep flow near the core-mantle boundary may have played a role in the Hawaiian-Emperor bend, capture of a plume by a ridge, followed by changes in sub-Pacific mantle flow, can better explain the observations. Thus, hotspot tracks can reveal patterns of past mantle circulation.

http://www.mantleplumes.org/WebDocuments/Tarduno2009.pdf

Ulrich Hansen

Papers

Mantle convection simulations with rheologies that generate plate-like behaviour

Boundary layer control of rotating convection systems

The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection

The Bent Hawaiian-Emperor Hotspot Track: Inheriting the Mantle Wind

Boundary Layer Control of Rotating Convection Systems