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

where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Journal of Statistical Mechanics: theory and experiment

The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

A review of statistically-based landslide susceptibility models

The acoustic emission (AE) and the mechanical behavior of granite samples during triaxial compression tests have been analyzed. The size of AE events displays power law distributions, conforming to the Gutenberg-Richter law observed for earthquakes, which is characterized by the b value. As the confining pressure increases, the macroscopic behavior becomes more ductile. For all different stages of the rock mechanical behavior (linear, nonlinear prepeak, nonlinear postpeak, shearing), there is a systematic decrease of the b value with increasing confining pressure. A numerical model based on progressive elastic damage and the finite element method allows simulations of the main experimental observations on AE and of a wide range of macroscopic behaviors from brittleness to ductility. The model reproduces a decrease in the b value that appears to be related to the type of macroscopic behavior (brittle-ductile) rather than to the confining pressure. Both experimental and numerical results suggest a relationship between the b value and the brittle-ductile transition. Moreover, these results are consistent with recent earthquake observations and give new insight into the behavior of the Earth's crust.

https://hal.archives-ouvertes.fr/hal-00173129/document

Brittle‐ductile transition and associated seismicity: Experimental and numerical studies and relationship with the b value

[1] We analyse the statistical pattern of seismicity before a 1–2 103 m3 chalk cliff collapse on the Normandie ocean shore, Western France. We show that a power law acceleration of seismicity rate and energy in both 40 Hz–1.5 kHz and 2 Hz–10kHz frequency range, is defined on 3 orders of magnitude, within 2 hours from the collapse time. Simultaneously, the average size of the seismic events increases toward the time to failure. These in situ results are derived from the only station located within one rupture length distance from the rock fall rupture plane. They mimic the “critical point” like behavior recovered from physical and numerical experiments before brittle failures and tertiary creep failures. Our analysis of this first seismic monitoring data of a cliff collapse suggests that the thermodynamic phase transition models for failure may apply for cliff collapse.

https://hal.archives-ouvertes.fr/hal-00172676/document

Seismic precursory patterns before a cliff collapse and critical point phenomena

We propose a numerical model based on static fatigue laws in order to model the time-dependent damage and deformation of rocks under creep. An empirical relation between time to failure and applied stress is used to simulate the behavior of each element of our finite element model. We review available data on creep experiments in order to study how the material properties and the loading conditions control the failure time. The main parameter that controls the failure time is the applied stress. Two commonly used models, an exponential tfexp (bs/s0) and a power law function tfsb0 fit the data as well. These time-to-failure laws are used at the scale of each element to simulate its damage as a function of its stress history. An element is damaged by decreasing its Young's modulus to simulate the effect of increasing crack density at smaller scales. Elastic interactions between elements and heterogeneity of the mechanical properties lead to the emergence of a complex macroscopic behavior, which is richer than the elementary one. In particular, we observe primary and tertiary creep regimes associated respectively with a power law decay and increase of the rate of strain, damage event and energy release. Our model produces a power law distribution of damage event sizes, with an average size that increases with time as a power law until macroscopic failure. Damage localization emerges at the transition between primary and tertiary creep, when damage rate starts accelerating. The final state of the simulation shows highly damaged bands, similar to shear bands observed in laboratory experiments. The thickness and the orientation of these bands depend on the applied stress. This model thus reproduces many properties of rock creep, which were previously not modeled simultaneously.

/pdf/brittle-creep-damage-and-time-to-failure-in-rocks-2qr2zn7zow.pdf

Brittle creep, damage and time to failure in rocks

We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. The EB framework considers sea ice as a continuous elastic plate encountering progressive damage, simulating the opening of cracks and leads. As a result of long-range elastic interactions, the stress relaxation following a damage event can induce an avalanche of damage. Damage propagates in narrow linear features, resulting in a very heterogeneous strain field. Idealized simulations of the Arctic sea-ice cover are analyzed in terms of ice strain rates and contrasted to observations and simulations performed with the classical viscous-plastic (VP) rheology. The statistical and scaling properties of ice strain rates are used as the evaluation metric. We show that EB simulations give a good representation of the shear faulting mechanism that accommodates most sea-ice deformation. The distributions of strain rates and the scaling laws of ice deformation are well captured by the EB framework, which is not the case for VP simulations. These results suggest that the properties of ice deformation emerge from elasto-brittle ice-mechanical behavior and motivate the implementation of the EB framework in a global sea-ice model.

/pdf/a-new-modeling-framework-for-sea-ice-mechanics-based-on-4gxj6gi0on.pdf

David Amitrano

Papers

Brittle‐ductile transition and associated seismicity: Experimental and numerical studies and relationship with the b value

Seismic precursory patterns before a cliff collapse and critical point phenomena

Brittle creep, damage and time to failure in rocks

A new modeling framework for sea-ice mechanics based on elasto-brittle rheology

Brittle Creep, Damage and Time to Failure in Rocks