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

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

The American Society for Testing and Materials (ASTM) is an independent organization devoted to the development of standards.

American Society for Testing and Materials

SUMMARY We develop a three-dimensional nite-deformation cohesive element and a class of irreversible cohesive laws which enable the accurate and ecient tracking of dynamically growing cracks. The cohesive element governs the separation of the crack anks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional nite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of a drop-weight dynamic fracture test similar to those reported by Zehnder and Rosakis. 1 The ability of the method to approximate the experimentally observed crack-tip trajectory is particularly noteworthy. Copyright ? 1999 John Wiley & Sons, Ltd.

Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis

T he heat generated due to plastic deformation at the tip of a dynamically propagating crack in a metal causes a large local temperature increase at the crack tip which is expected to affect the selection of failure modes during dynamic fracture and to thus influence the fracture toughness of the material. The distribution of temperature at the tips of dynamically propagating cracks in two heat treatments of AISI 4340 carbon steel was investigated experimentally using an array of eight high speed indium antimonide, infrared detectors. Experiments were performed on wedge loaded, compact tension specimens with initially blunted cracks, producing crack speeds ranging from 1900 to 730 m/s. The measurements provide the spatial distribution of temperature increase near the crack tip on the specimen surface. Temperature increases were as high as 465° C over ambient and the region of intense heating (greater than 100° C temperature rise) covered approximately one third of the active plastic zone on the specimen surface. The observed temperature increase profiles clearly show the three-dimensional nature of the fracture process near the specimen surface and provide valuable information regarding the dynamic formation of shear lips and their role in the dissipation of energy during dynamic crack growth. Preliminary temperature measurements performed on side-grooved specimens are also reported.

On the temperature distribution at the vicinity of dynamically propagating cracks in 4340 steel

Velocity field for the trishear model

Micromechanical oscillators in the rf range were fabricated in the form of silicon discs supported by a SiO2 pillar at the disk center. A low-power laser beam, (Plaser∼100 μW), focused at the periphery of the disk, causes a significant change of the effective spring constant producing a frequency shift, Δf(Δf/f∼10−4). The high quality factor, Q, of the disk oscillator (Q∼104) allows us to realize parametric amplification of the disk’s vibrations through a double frequency modulation of the laser power. An amplitude gain of up to 30 was demonstrated, with further increase limited by nonlinear behavior and self-generation. Phase dependence, inherent in degenerate parametric amplification, was also observed. Using this technique, the sensitivity of detection of a small force is greatly enhanced.

Optically pumped parametric amplification for micromechanical oscillators

Limit cycle, or self-oscillations, can occur in a variety of NEMS devices illuminated within an interference field. As the device moves within the field, the quantity of light absorbed and hence the resulting thermal stresses changes, resulting in a feedback loop that can lead to limit cycle oscillations. Examples of devices that exhibit such behavior are discussed as are experimental results demonstrating the onset of limit cycle oscillations as continuous wave (CW) laser power is increased. A model describing the motion and heating of the devices is derived and analyzed. Conditions for the onset of limit cycle oscillations are computed as are conditions for these oscillations to be either hysteretic or nonhysteretic. An example simulation of a particular device is discussed and compared with experimental results.

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Limit cycle oscillations in CW laser-driven NEMS

Dynamic fracture initiation and propagation in 4340 steel was investigated experimentally using the optical method of reflected caustics combined with high speed photography. A new crack propagation testing configuration consisting of a three point bend specimen loaded in a drop weight tower was used. It was found that prior to crack initiation the stress intensity factor time record calculated using the dynamic tup load and a static formula disagrees with the actual stress intensity factor measured by caustics. During crack propagation, the crack tip velocity and stress intensity factor time records varied smoothly and repeatably allowing for a straightforward interpretation of the data. The experiments show that for the particular heat treatment of 4340 steel used, the dynamic fracture propagation toughness depends on crack tip velocity through a relation that is a material property.

Alan T. Zehnder

Papers

On the temperature distribution at the vicinity of dynamically propagating cracks in 4340 steel

Velocity field for the trishear model

Optically pumped parametric amplification for micromechanical oscillators

Limit cycle oscillations in CW laser-driven NEMS

Dynamic fracture initiation and propagation in 4340 steel under impact loading