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

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

http://web.stanford.edu/group/cui_group/papers/Hui_Today_2012.pdf

Designing nanostructured Si anodes for high energy lithium ion batteries

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

http://dprl2.me.gatech.edu/sites/default/files/PDFpub/ijie-part1.pdf

Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization

The virial stress is the most commonly used definition of stress in discrete particle systems. This quantity includes two parts. The first part depends on the mass and velocity (or, in some versions, the fluctuation part of the velocity) of atomic particles, reflecting an assertion that mass transfer causes mechanical stress to be applied on stationary spatial surfaces external to an atomic‐particle system. The second part depends on interatomic forces and atomic positions, providing a continuum measure for the internal mechanical interactions between particles. Historic derivations of the virial stress include generalization from the virial theorem of Clausius (1870) for gas pressure and solution of the spatial equation of balance of momentum. The virial stress is stress‐like a measure for momentum change in space. This paper shows that, contrary to the generally accepted view, the virial stress is not a measure for mechanical force between material points and cannot be regarded as a measure for mechanical stress in any sense. The lack of physical significance is both at the individual atom level in a time‐resolved sense and at the system level in a statistical sense. It is demonstrated that the interatomic force term alone is a valid stress measure and can be identified with the Cauchy stress. The proof in this paper consists of two parts. First, for the simple conditions of rigid translation, uniform tension and tension with thermal oscillations, the virial stress yields clearly erroneous interpretations of stress. Second, the conceptual flaw in the generalization from the virial theorem for gas pressure to stress and the confusion over spatial and material equations of balance of momentum in theoretical derivations of the virial stress that led to its erroneous acceptance as the Cauchy stress are pointed out. Interpretation of the virial stress as a measure for mechanical force violates balance of momentum and is inconsistent with the basic definition of stress. The versions of the virial‐stress formula that involve total particle velocity and the thermal fluctuation part of the velocity are demonstrated to be measures of spatial momentum flow relative to, respectively, a fixed reference frame and a moving frame with a velocity equal to the part of particle velocity not included in the virial formula. To further illustrate the irrelevance of mass transfer to the evaluation of stress, an equivalent continuum (EC) for dynamically deforming atomistic particle systems is defined. The equivalence of the continuum to discrete atomic systems includes (i) preservation of linear and angular momenta, (ii) conservation of internal, external and inertial work rates, and (iii) conservation of mass. This equivalence allows fields of work‐ and momentum‐preserving Cauchy stress, surface traction, body force and deformation to be determined. The resulting stress field depends only on interatomic forces, providing an independent proof that as a measure for internal material interaction stress is independent of kinetic energy or mass transfer.

A new look at the atomic level virial stress: on continuum-molecular system equivalence

The initiation and propagation of shear bands are investigated by subjecting prenotched plates to asymmetric impact loading (dynamic mode-II). The materials studied are C-300 (a maraging steel) and Ti-6Al-4V. A shear band emanates from the notch tip and propagates rapidly in a direction nearly parallel to the direction of impact. When the impact velocity is higher than a critical value, the shear band propagates throughout the specimen. The shear band arrests inside the specimen when the impact velocity is below this critical value. In the latter case and for the C-300 steel, a crack initiates and propagates from the tip of the arrested shear band at an angle to the direction of shear band propagation. Microscopic examinations of the shear band and crack surfaces reveal a ductile mode of shear failure inside the shear band and an opening mode of failure for the crack. The coexistence of shear banding and fracture events in the same specimen signifies a transition in the modes of failure for this material under the conditions described. For Ti-6Al-4V, the only mode of failure observed is shear banding. While the transition is induced by changes in loading conditions, the different behaviors of these two materials suggest it is also related to material properties. The experimental investigation focuses on both the thermal and the mechanical aspects of the propagation of shear bands. Real time temperature histories along lines intersecting and perpendicular to and along the shear band path are recorded by means of a high speed infrared detector system. Experiments show that the peak temperatures inside the propagating shear bands increase with impact velocity. The highest temperature measured is in excess of 1400 °C or approximately 90% of the melting point of the C-300 steel. For Ti-6Al-4V, the peak temperatures are approximately 450 °C. In the mechanical part of the study, high speed photography is used to record the initiation and propagation of shear bands. Recorded images of propagating shear bands at different impact velocities provide histories of the speed of shear band propagation for the C-300 steel. A strong dependence of shear band speed on the impact velocity is found. The highest speed observed for the C-300 steel is approximately 1200 ms−1 or 40% of its shear wave speed.

Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed

Molecular dynamics simulations are performed to characterize the response of zinc oxide (ZnO) nanobelts to tensile loading. The ultimate tensile strength (UTS) and Young's modulus are obtained as functions of size and growth orientation. Nanobelts in three growth orientations are generated by assembling the unit wurtzite cell along the [0001], , and crystalline axes. Following the geometric construction, dynamic relaxation is carried out to yield free-standing nanobelts at 300 K. Two distinct configurations are observed in the [0001] and orientations. When the lateral dimensions are above 10 A, nanobelts with rectangular cross-sections are seen. Below this critical size, tubular structures involving two concentric shells similar to double-walled carbon nanotubes are obtained. Quasi-static deformations of belts with and orientations consist of three stages, including initial elastic stretching, wurtzite-ZnO to graphitic-ZnO structural transformation, and cleavage fracture. On the other hand, [0001] belts do not undergo any structural transformation and fail through cleavage along (0001) planes. Calculations show that the UTS and Young's modulus of the belts are size dependent and are higher than the corresponding values for bulk ZnO. Specifically, as the lateral dimensions increase from 10 to 40 A, decreases between 38–76% and 24–63% are observed for the UTS and Young's modulus, respectively. This effect is attributed to the size-dependent compressive stress induced by tensile surface stress in the nanobelts. and nanobelts with multi-walled tubular structures are seen to have higher values of elastic moduli (~340 GPa) and UTS (~36 GPa) compared to their wurtzite counterparts, echoing a similar trend in multi-walled carbon nanotubes.

https://iopscience.iop.org/article/10.1088/0957-4484/16/12/001/pdf

Orientation and size dependence of the elastic properties of zinc oxide nanobelts

A rubber-like pseudoelastic behavior is discovered in single-crystalline face-centered-cubic (FCC) Cu nanowires in atomistic simulations. Nonexistent in bulk Cu, this phenomenon is associated primarily with a reversible crystallographic lattice reorientation driven by the high surface-stress-induced internal stresses due to high surface-to-volume ratios at the nanoscale level. The temperature-dependence of this behavior leads to a shape memory effect (SME). Under tensile loading and unloading, the nanowires exhibit recoverable strains up to over 50%, well beyond the typical recoverable strains of 5−8% for most bulk shape memory alloys (SMAs). This behavior is well-defined for wires between 1.76 and 3.39 nm in size over the temperature range of 100−900 K.

Min Zhou

Papers

Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization

A new look at the atomic level virial stress: on continuum-molecular system equivalence

Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed

Orientation and size dependence of the elastic properties of zinc oxide nanobelts

Shape memory effect in Cu nanowires.