There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Statistics for Spatial Data.

▶ Addresses a wide range of timely environment, economic and energy topics ▶ A forum to review, analyze and stimulate the development, testing and implementation of mitigation and adaptation strategies at regional, national and global scales ▶ Contributes to real-time policy analysis and development as national and international policies and agreements are discussed and promulgated ▶ 94% of authors who answered a survey reported that they would definitely publish or probably publish in the journal again

Mitigation and Adaptation Strategies for Global Change

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters

Process mineralogy and applications in mineral processing

This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.

A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

A novel meshfree weak-strong (MWS) form method is proposed based on a combined formulation of both the local weak form and the strong form. In the MWS method, the problem domain and its boundary is represented by a set of distributed nodes. The strong form or the collocation method is used for all internal nodes and the nodes on the essential boundaries. The local weak form (Petrov-Galerkin weak form) is used for nodes on or near the natural boundaries. The natural boundary conditions can then be easily imposed to produce stable and accurate solutions. The MWS method has advantages of both meshfree methods based on strong forms and weak forms. In the entire problem, only local integration meshes for nodes on or near the natural boundary are required.

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YuanTong Gu

Papers

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters

Process mineralogy and applications in mineral processing

A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

A Meshfree Weak-strong Form Method

Estimation of load conditions and strain distribution for in vivo murine tibia compression loading using experimentally informed finite element models