I-Ling Chang

A new algorithm for calculating two-dimensional differential transform of nonlinear functions

A new algorithm for calculating the two-dimensional differential transform of nonlinear functions is developed in this paper. This new technique is illustrated by studying suitable forms of nonlinearity. Three strongly nonlinear partial differential equations are then solved by differential transform method to demonstrate the validity and applicability of the proposed algorithm. The present framework offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability.

Mechanical buckling of single-walled carbon nanotubes: Atomistic simulations

Various geometric sizes and helical types (i.e., armchair, zigzag, and chiral) of single-walled carbon nanotubes (CNTs) are considered in molecular dynamics simulations in order to systematically examine the length-to-radius ratio and chirality effects on the buckling mechanism. The buckling strain is getting smaller as the CNT becomes slender for most nanotubes, which implies that the slender nanotubes have lower buckling resistance regardless of the radius of the CNTs. The applicability of the continuum buckling theory, which has been well developed for thin tubes, on predicting the buckling strain of the CNT is also examined. In general, the corresponding buckling strain and buckling type predicted by the continuum buckling theory could agree reasonably well with simulation results except at the transition region due to the competition of two buckling mechanisms.

Is the molecular statics method suitable for the study of nanomaterials? A study case of nanowires

Both molecular statics and molecular dynamics methods were employed to study the mechanical properties of copper nanowires. The size effect on both elastic and plastic properties of square cross-sectional nanowire was examined and compared systematically using two molecular approaches. It was found consistently from both molecular methods that the elastic and plastic properties of nanowires depend on the lateral size of nanowires. As the lateral size of nanowires decreases, the values of Youngs modulus decrease and dislocation nucleation stresses increase. However, it was shown that the dislocation nucleation stress would be significantly influenced by the axial periodic length of the nanowire model using the molecular statics method while molecular dynamics simulations at two distinct temperatures (0.01 and 300 K) did not show the same dependence. It was concluded that molecular statics as an energy minimization numerical scheme is quite insensitive to the instability of atomic structure especially without thermal fluctuation and might not be a suitable tool for studying the behaviour of nanomaterials beyond the elastic limit.

Molecular dynamics investigation of carbon nanotube resonance

In this work, a methodology to directly extract resonant information from an equilibrium molecular dynamics simulation is proposed and demonstrated by analyzing the vibrational behavior of carbon nanotubes (CNTs). Different vibrational motions, i.e. longitudinal, transverse, rotational and radial, could be easily distinguished and computed through the time sequence of the velocity components of atoms at the equilibrating process. Fast Fourier transform is adopted to perform the transformation of vibration information from time to frequency domain. The effects of CNT length, radius and boundary condition on the resonant behaviors of CNTs are systematically investigated. Moreover, the simulation results are compared with those predicted based on the Euler–Bernoulli beam theory. Note that the simulated longitudinal and rotational resonant behaviors agree quite well with the theoretical prediction and a slight deviation is observed in the transverse prediction.

An atomistic study of nanosprings

Molecular statics method incorporating minimum energy concept was employed to study the one-dimensional copper nanospring with faced-center-cubic crystal structure. Various geometric sizes (wire diameter, radius, pitch), numbers of turns and crystal orientations of nanosprings were systematically modeled to investigate the size dependence of elastic properties. It was observed that as the wire diameter increases and the radius and number of turns decrease, the nanospring stiffness would increase irrespective of the crystal orientations. Moreover, the elastic constants of nanosprings would become larger while the pitches become smaller for almost all the crystal orientations. Also the simulation results were compared to the predictions based on continuum theory in order to clarify whether the classical theory could apply to nanosprings.

A molecular analysis of carbon nanotori formation

This study uses molecular dynamics simulation to examine the geometric criteria and stability of forming a perfect carbon nanotorus without pentagon-heptagon defects or surface buckles. Various nanotube diameters and nanoring diameters of both armchair and zigzag nanotori were relaxed at room temperature, and the equilibrated atomic configurations were inspected. This study uses the coordinate parameter, which illustrates the atomic arrangement around each atom, as an indicator of buckles to avoid misjudgment caused by transient or thermal disturbance. For each nanotube diameter, there exists a critical nanoring diameter beyond which the perfect carbon nanotori can form. This study examines the binding potential energy and deformation energy of the relaxed nanotorus model, showing that the critical nanoring diameter cannot be easily predicted through critical energy consideration because buckling is a form of structural instability. Results show that the structural stability of a perfect nanoring primarily depends on the nanotube diameter and nanoring diameter, whereas its chirality has little effect, and one empirical relation is fitted to determine the critical nanoring diameters.

An acoustic absorber implemented by graded index phononic crystals

In this paper, we proposed the implementation of a two-dimensional omnidirectional and broadband acoustic absorber using graded index phononic crystals as the shell with an inner absorbing core. The phononic crystal was consisted of circular steel rod arranged as square lattice in air background. The plane wave expansion method was used to obtain the band diagram of the phononic crystal from which the effective refractive index could be computed. The radially distributed refractive index of the acoustic absorber was achieved by placing steel rods with spatially varying radii. The finite element method was employed in order to confirm the acoustic properties of the designed device. Numerical simulations illustrated that the acoustic waves were bent toward the central area by the outer shell and absorbed by the inner core of the implemented acoustic absorber. Furthermore, it was demonstrated that the implemented acoustic absorber could operate independent of the incident wave directions for a relative wide range of frequencies.

Vibrational Behavior of Single-Walled Carbon Nanotubes: Atomistic Simulations

This study examines the vibrational behaviors of both armchair and zigzag carbon nanotubes (CNTs). The natural longitudinal/flexural/torsional/radial frequencies of CNTs were extracted and analyzed simultaneously from an equilibrium molecular dynamics (MD) simulation without imposing any initial modal displacement or force. Initial random atomic velocities, which were assigned to fit the simulated temperature, could be considered as an excitation on CNTs composing of wide range of spatial frequencies. The position and velocity of each atom at every time step was calculated using finite difference algorithm, and fast Fourier transform (FFT) was used to perform time-to-frequency domain transform. The effects of CNT length, radius, chirality, and boundary condition on the vibrational behaviors of CNTs were systematically examined. Moreover, the simulated natural frequencies and mode shapes were compared with the predictions based on continuum theories, i.e., rod, Euler–Bernoulli beam and nonlocal Timoshenko beam, to examine their applicability in nanostructures.

Asymmetric transmission of acoustic waves in a layer thickness distribution gradient structure using metamaterials

This research presents an innovative asymmetric transmission design using alternate layers of water and metamaterial with complex mass density. The directional transmission behavior of acoustic waves is observed numerically inside the composite structure with gradient layer thickness distribution and the rectifying performance of the present design is evaluated. The layer thickness distributions with arithmetic and geometric gradients are considered and the effect of gradient thickness on asymmetric wave propagation is systematically investigated using finite element simulation. The numerical results indicate that the maximum pressure density and transmission through the proposed structure are significantly influenced by the wave propagation direction over a wide range of audible frequencies. Tailoring the thickness of the layered structure enables the manipulation of asymmetric wave propagation within the desired frequency range. In conclusion, the proposed design offers a new possibility for developing directional-dependent acoustic devices.

Spiral hyperlens with enhancements of image resolution and magnification

Abstract A subwavelength spiral hyperlens that is able to image beyond the diffraction limit is studied. The spiral hyperlens is made from an anisotropic metamaterial with a hyperbolic dispersion relation in which the evanescent wave is converted into a propagating wave. Therefore, the propagating wave can be processed by conventional optical systems outside of the spiral hyperlens. The possibility of using a cylindrical hyperlens for overcoming the diffraction limit has been proven analytically and experimentally. In this study, we designed two types of spiral hyperlenses composed of a spiral periodic stack of silver and alumina multilayers. A spiral hyperlens utilizes the spiral geometry to magnify the objects. In comparison with a cylindrical hyperlens, a spiral hyperlens has improved performance in terms of higher image resolution and better image magnifications. Numerical simulations illustrate that the far-field imaging resolution of cylindrical spiral hyperlens is no greater than 110 nm at 365 nm working wavelength.