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

Frictional slip of an elastic layer on a half-space caused by an anti-plane wave of an arbitrary form

Phoxonic crystals, which exhibit simultaneous phononic and photonic bandgaps, are promising artificial materials for optomechanical and acousto-optical devices. In this paper, simultaneous guidance of surface acoustic and surface optical waves in truncated phoxonic crystal slabs with veins is investigated using the finite element method. The phoxonic crystal slabs with veins can show dual large bandgaps of phononic and photonic even/odd modes. Based on the phononic and photonic bandgaps, simultaneous surface acoustic and optical modes can be realized by changing the surface geometrical configurations. Both acoustic and optical energies can be highly confined in the surface region. The effect of the surface structures on the dispersion relations of surface modes is discussed; by adjusting the surface geometrical parameters, dual single guided modes and/or slow acoustic and optical waves with small group velocity dispersions can be achieved. The group velocities are about 40 and 10 times smaller than the transverse velocity of the elastic waves in silicon and the speed of light in vacuum, respectively.

https://www.mdpi.com/2073-4352/7/11/350/pdf

Simultaneous Guidance of Surface Acoustic and Surface Optical Waves in Phoxonic Crystal Slabs

The paper analyses the interaction of an elastic pulse of arbitrary form with a frictional contact interface between two anisotropic solids which are pressed together and at the same time loaded by the in-plane and anti-plane shearing tractions. The incident pulse is assumed strong enough to break friction so that localized separation and slip take place. Coulomb friction, which causes the non-linear coupling between the in-plane and anti-plane motions, is supposed along the contact interface. The sub-critical angle incidence is first considered. By using Fourier analysis, the problem is reduced to a set of algebraic equations. A method to get the solution of the equations with determination of the slip/ stick/separation zones is developed. As an example, the detailed computation for the case of an incident parabolic stress pulse is carried out. Numerical results of the interface tractions and the slip velocities are presented for two contacting half-spaces of the same materials in the same orientation. The super-critical angle incidence is discussed. In this case the problem is cast to a set of non-linear Cauchy singular integral equations whose solution is still an open question in mathematics.

Nonlinear Interaction of an Elastic Pulse With a Frictional Contact Interface Between Two Anisotropic Dissimilar Media

In this work, we numerically and experimentally investigate topological rainbow trapping and energy amplification of acoustic waves in a gradient phononic crystal (PC) structure. Thanks to the acoustic valley Hall effect, topological interface states (TISs) are generated along the interface between two PCs with different topological phases. To achieve rainbow trapping, we introduce the gradient into a 3D-printed PC structure by varying the geometrical parameter of scatterers along the interface. The incident acoustic waves at different frequencies split, stop, and, hence, are significantly amplified at different positions. Notably, the rainbow trapping of TISs is immune to random structural disorders. The topological rainbow trapping is promising for the design of broadband energy harvesters with excellent robustness.

https://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0138982/16785508/112201_1_online.pdf

Topological rainbow trapping and acoustic energy amplification in two-dimensional gradient phononic crystals

Abstract In this work, the three-dimensional (3D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated. The analytical solutions of the fundamental wave and second harmonic with the quasi-longitudinal (qP) and quasi-shear (qS 1 and qS 2 ) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem. The transmission coefficients are calculated to support the band gap property, and the tunability of the nonreciprocal transmission by the initial stress is discussed. This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics. 

/pdf/tunable-three-dimensional-nonreciprocal-transmission-in-a-3mb3v7wv.pdf

Yue-Sheng Wang

Papers

Frictional slip of an elastic layer on a half-space caused by an anti-plane wave of an arbitrary form

Simultaneous Guidance of Surface Acoustic and Surface Optical Waves in Phoxonic Crystal Slabs

Nonlinear Interaction of an Elastic Pulse With a Frictional Contact Interface Between Two Anisotropic Dissimilar Media

Topological rainbow trapping and acoustic energy amplification in two-dimensional gradient phononic crystals

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses