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

The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

Differential Quadrature Method in Computational Mechanics: A Review

Experiments in hearing

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Topological Phononic Crystals with One-Way Elastic Edge Waves

A 3-D finite element (FE) model of the human ear consisting of the external ear canal, middle ear, and cochlea is reported in this paper. The acoustic-structure-fluid coupled FE analysis was conducted on the model which included the air in the ear canal and middle ear cavity, the fluid in the cochlea, and the middle ear and cochlea structures (i.e., bones and soft tissues). The middle ear transfer function such as the movements of tympanic membrane, stapes footplate, and round window, the sound pressure gain across the middle ear, and the cochlear input impedance in response to sound stimulus applied in the ear canal were derived and compared with the published experimental measurements in human temporal bones. The frequency sensitivity of the basilar membrane motion and intracochlear pressure induced by sound pressure in the ear canal was predicted along the length of the basilar membrane from the basal turn to the apex. The satisfactory agreements between the model and experimental data in the literature indicate that the middle ear function was well simulated by the model and the simplified cochlea was able to correlate sound stimulus in the ear canal with vibration of the basilar membrane and pressure variation of the cochlear fluid. This study is the first step toward the development of a comprehensive FE model of the entire human ear for acoustic-mechanical analysis.

Modeling of Sound Transmission from Ear Canal to Cochlea

Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates

Effect of machining-induced surface residual stress on initiation of stress corrosion cracking in 316 austenitic stainless steel

This paper presents an analytical method based on the unequal division shear-zone model to study the machining predictive theory. The proposed model only requires workpiece material properties and cutting conditions to predict the cutting forces during the orthogonal cutting process. In the shear zone, the material constitutive relationship is described by Johnson–Cook model, and the material characteristics such as strain rate sensitivity, strain hardening, and thermal softening are considered. The chip formation is supposed to occur mainly by shearing within the primary shear zone. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of the shear strain rate. The cutting forces are calculated for different machining conditions and flow stress data. Prediction results were compared with the orthogonal cutting test data from the available literature and found in reasonable agreement. In addition, an analysis of the deviation from experimental data for the proposed model is performed, the effects of cutting parameters and tool geometry were investigated.

Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model

The new approach for application of boundary conditions in the differential quadrature (DQ) method, proposed earlier by the present authors, is extended to generalized force boundary conditions in two dimensions A variety of problems is then analyzed by theDQ method with the new approach for application of boundary conditions, such as deflections of beams and circular and rectangular plates under nonuniformly distributed loadings, deflection of a rectangular plate on a Winkler foundation, and buckling and free vibrational analyses of circular plates It is found that the present method gives good accuracy and is computationally efficient Exact solutions can be obtained by theDQ method if analytical solutions are polynomials and the method is insensitive to the spacing of grid points for the cases considered

Xuelin Wang

Papers

Modeling of Sound Transmission from Ear Canal to Cochlea

Differential quadrature analysis of deflection, buckling, and free vibration of beams and rectangular plates

Effect of machining-induced surface residual stress on initiation of stress corrosion cracking in 316 austenitic stainless steel

Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model

Static and free vibrational analysis of beams and plates by differential quadrature method