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

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

The science and technology of ultracapacitors are reviewed for a number of electrode materials, including carbon, mixed metal oxides, and conducting polymers. More work has been done using microporous carbons than with the other materials and most of the commercially available devices use carbon electrodes and an organic electrolytes. The energy density of these devices is 3¯5 Wh/kg with a power density of 300¯500 W/kg for high efficiency (90¯95%) charge/discharges. Projections of future developments using carbon indicate that energy densities of 10 Wh/kg or higher are likely with power densities of 1¯2 kW/kg. A key problem in the fabrication of these advanced devices is the bonding of the thin electrodes to a current collector such the contact resistance is less than 0.1 cm2. Special attention is given in the paper to comparing the power density characteristics of ultracapacitors and batteries. The comparisons should be made at the same charge/discharge efficiency.

Ultracapacitors: Why, How, and Where is the Technology

In this paper we propose various types of two-dimensional (2D) square zigzag lattice structures, and we study their bandgaps and directional propagation of elastic waves. The band structures and the transmission spectra of the systems are calculated by using the finite element method. The effects of the geometry parameters of the 2D-zigzag lattices on the bandgaps are investigated and discussed. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. Multiple wide complete bandgaps are found in a wide porosity range owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the systems. The deformed displacement fields of the transient response of finite structures subjected to time-harmonic loads are presented to show the directional wave propagation. The research in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

https://iopscience.iop.org/article/10.1088/0022-3727/47/48/485102/pdf

Bandgaps and directional propagation of elastic waves in 2D square zigzag lattice structures

In this paper, we present a combined theoretical, numerical and experimental study of acoustic wave propagation in 1D locally resonant phononic crystals made of acoustic resonators grafted onto a waveguide. The case of one single resonator grafted onto the waveguide is first investigated and a model of transmission cancellation at resonant frequencies is obtained. The model includes the excitation of evanescent guided waves attached to the grafting points. When extended to periodical arrays of grafted resonators, the model provides us with a definite theoretical expression for the complex band structure. Comparison with experimental results and complex band structures obtained by numerical simulation suggests a strong dependence of transmission through the crystal on the lattice constant of the grafted resonators. It is found that evanescent waves in the waveguide play a key role when the lattice constant is in the sub-wavelength range.

https://iopscience.iop.org/article/10.1088/0022-3727/47/47/475502/pdf

Coupling of evanescent and propagating guided modes in locally resonant phononic crystals

Two-dimensional fretting contact analysis of piezoelectric materials

Fretting contact of a functionally graded piezoelectric layered half-plane under a conducting punch

In the present paper, the band structures of in-plane waves propagating in two-dimensional nanoscale phononic crystals composed of voids/inclusions in an elastic solid in square and triangular lattices are calculated by the method based on the Dirichlet-to-Neumann map. The surface/interface effects are taken into account due to the high surface-to-volume ratio by applying the Young–Laplace equilibrium equation at the surface/interface. Three systems at nanoscale are calculated in details: vacuum holes in an aluminum matrix in square and triangular lattices, aluminum cylinders in tungsten matrix in a square lattice, and tungsten cylinders in aluminum in a square lattice. The results show that the surface/interface effects are significant when the dimensions of the phononic crystals approach the nanometer scale.

Yue-Sheng Wang

Papers

Bandgaps and directional propagation of elastic waves in 2D square zigzag lattice structures

Coupling of evanescent and propagating guided modes in locally resonant phononic crystals

Two-dimensional fretting contact analysis of piezoelectric materials

Fretting contact of a functionally graded piezoelectric layered half-plane under a conducting punch

Bandgap calculation of in-plane waves in nanoscale phononic crystals taking account of surface/interface effects