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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

Cracks, microcracks and fracture in polymer structures: Formation, detection, autonomic repair

石墨烯（graphene）是一种由碳原子以sp2杂化轨道构成的六角型呈蜂巢晶格的单层片状结构的新材料。英国曼彻斯特大学物理学家安德烈·海姆和康斯坦丁·诺沃肖洛夫，因成功地在实验室中从石墨中分离出石墨烯，而共同获得2010年诺贝尔物理学奖。目前，它是世界上最薄却也是最坚硬的纳米材料。它几乎完全透明，导热系数高于碳纳米管和金刚石，而电阻率只有约10-6Ω·cm，比铜或银更低，为目前世上电阻率最小的材料。因其电阻率极低，电子迁移速度极快，因此被期待可用于发展出更薄、导电速度更快的新一代电子元件或晶体管。

石墨烯（graphene）

This paper presents a comprehensive molecular dynamics study on the effects of nanocracks (a row of vacancies) on the fracture strength of graphene sheets at various temperatures. Comparison of the strength given by molecular dynamics simulations with Griffith’s criterion and quantized fracture mechanics theory demonstrates that quantized fracture mechanics is more accurate compared to Griffith’s criterion. A numerical model based on kinetic analysis and quantized fracture mechanics theory is proposed. The model is computationally very efficient and it quite accurately predicts the fracture strength of graphene with defects at various temperatures. Critical stress intensity factors in mode I fracture reduce as temperature increases. Molecular dynamics simulations are used to calculate the critical values of $$J$$
 integral (
 $$J_\mathrm{IC}$$
 ) of armchair graphene at various crack lengths. Results show that $$J_\mathrm{IC}$$
 depends on the crack length. This length dependency of $$J_\mathrm{IC}$$
 can be used to explain the deviation of the strength from Griffith’s criterion. The paper provides an in-depth understanding of fracture of graphene, and the findings are important in the design of graphene based nanomechanical systems and composite materials

Atomistic and continuum modelling of temperature-dependent fracture of graphene

A systematic molecular dynamics simulation study is performed to assess the effects of temperature and free edges on the ultimate tensile strength and Young's modulus of a single-layer graphene sheet It is observed that graphene sheets at higher temperatures fail at lower strains, due to the high kinetic energy of atoms A numerical model, based on kinetic analysis, is used to predict the ultimate strength of the graphene under various temperatures and strain rates As the width of a graphene reduces, the excess edge energy associated with free edge atoms induces an initial strain on the relaxed configuration of the sheets This initial strain has a greater influence on the Young's modulus of the zigzag sheet compared with that of the armchair sheets The simulations reveal that the carbon–carbon bond length and amplitude of intrinsic ripples of the graphene increases with temperature The initial out-of-plane displacement of carbon atoms is necessary to simulate the physical behaviour of a graphene when the Nose–Hoover or Berendsen thermostat is used

https://iopscience.iop.org/article/10.1088/0965-0393/21/6/065017/pdf

M.A.N. Dewapriya

Papers

Atomistic and continuum modelling of temperature-dependent fracture of graphene

Influence of temperature and free edges on the mechanical properties of graphene

Molecular dynamics study of the reinforcement effect of graphene in multilayered polymer nanocomposites

Molecular Dynamics Simulations and Continuum Modeling of Temperature and Strain Rate Dependent Fracture Strength of Graphene With Vacancy Defects

Size dependency and potential field influence on deriving mechanical properties of carbon nanotubes using molecular dynamics