Reduction and New Explicit Solutions of (2+1)-Dimensional Breaking Soliton Equation

By applying the Lie group method, the (2+1)-dimensional breaking soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.     

Extended Riccati Equation Rational Expansion Method and Its Application to Nonlinear Stochastic Evolution Equations

In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.     

Applying the finite-thickness model to designs of cylindrical microlenses with small -numbers

The finite-thickness model (FTM) is applied to the design of cylindrical microlenses based on the wave-front interference principle, rather than the existing zero-thickness model (ZTM). This design method is very simple in physics and highly efficient in computations. For cylindrical lenses with different f-numbers (from f/1.5 to f/0.6), the detailed designs by using both the FTM and the ZTM are carried out. To show the superiority of the FTM to the ZTM, we investigate the focal performance of all the designed lenses based on rigorous electromagnetic theory and the boundary element method. Numerical results reveal that the constructed cylindrical lenses by the FTM are witnessed to exhibit much better focusing performance than those by the ZTM, especially for the small f-numbers.     

Total internal reflection–refraction beam expander

Beam expanders being used presently have complex structure and none is perfect. A novel beam expander is proposed first. The beam expander can magnify (or decrease) the diameter of incident laser beam according to the theory of total internal reflection–refraction (TIR-R) principle. The characteristic of the beam expander was studied by using ray-tracing method and computer simulation. The beam expander can propagate a parallel laser beam along the propagation axis and would not change the propagation direction of the beam. For a nonparallel beam the Lagrange invariant (the product of diameter and divergence angle) is not constant. This beam expander would be an effective device in some applications.     

Structure comparison between Th2Zn17-type and TbCu7-type Sm–Fe intermetallic compounds and their nitrides by means of 57Fe-Mössbauer spectroscopy

Samarium–iron intermetallic compounds were prepared by a melt spinning method with low and high wheel speeds, which resulted in a Th₂Zn₁₇-type and a TbCu₇-type structure, respectively. Structure comparison between these types was investigated for Sm–Fe intermetallic compounds and their nitrides by ⁵⁷Fe-Mössbauer spectroscopy.     

Using transient and steady-state SEA to assess potential errors in the measurement of structure-borne sound power input from machinery on coupled reception plates

Isolated reception plates provide an engineering approach to quantify the structure-borne sound power input from machinery through the measurement of the spatial-average velocity level and structural reverberation times. For applications in building acoustics there are practical and economic reasons to consider using coupled reception plates formed by solid heavyweight walls or floors that are structurally coupled to other building elements. This paper uses transient and steady-state statistical energy analysis to investigate how the errors depend upon the building structure to which the coupled reception plate is connected. It is shown that the problem is twofold. Firstly, in the low- and mid-frequency ranges, the steady-state velocity level on the coupled reception plate is increased by energy returning from other coupled plates. Secondly, the structural decays on the coupled reception plate have significant curvature due to returning energy; hence short evaluation ranges are needed to minimise the error when determining the total loss factor. This leads to a problematic situation where the coupled reception plate appears to give the correct answer due to the error in the energy cancelling out the error in the total loss factor. The latter error can be minimised using short evaluation ranges for the structural reverberation time.     

Measurements of the optical absorption coefficient of Ar8+ ion implanted silicon layers using the photothermal radiometry and the modulated free carrier absorption methods

This paper presents a method of the measurement of the optical absorption coefficient of the Ar⁸⁺ ions implanted layers in the p-type silicon substrate. The absorption coefficient is calculated using a value of the attenuation of amplitudes of a photothermal radiometry (PTR) and/or a modulation free carrier absorption (MFCA) signals and the implanted layer thickness calculated by means of the TRIM program. The proposed method can be used to indicate the amorphization of the ions implanted layers.     

Small amplitude ion-acoustic double layers with cold electron beam and q-nonextensive electrons

Small amplitude ion-acoustic double layers in an unmagnetized and collisionless plasma consisting of cold positive ions, q-nonextensive electrons, and a cold electron beam are investigated. Small amplitude double layer solution is obtained by expanding the Sagdeev potential truncated method. The effects of entropic index q, speed and density of cold electron beam on double layer structures are discussed.     

Propagation and collision of soliton rings in quantum semiconductor plasmas

The intrinsic localization of electrostatic wave energies in quantum semiconductor plasmas can be described by solitary pulses. The collision properties of these pulses are investigated. In the present study, the fundamental model includes the quantum term, degenerate pressure of the plasma species, and the electron/hole exchange–correlation effects. In cylindrical geometry, using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations and the analytical phase shifts after the collision of two soliton rings are derived. Typical values for GaSb and GaN semiconductors are used to estimate the basic features of soliton rings. It is found that the pulses of GaSb semiconductor carry more energies than the pulses of GaN semiconductor. In addition, the degenerate pressure terms of electrons and holes have strong impact on the phase shift. The present theory may be useful to analyze the collision of localized coherent electrostatic waves in quantum semiconductor plasmas.     

Intrinsic anisotropy of the effective acoustic properties in metafluids made of two-dimensional cylinder arrays

Within a unified theoretical framework, we extract the omnidirectional effective acoustic parameters for the metafluid consisting of isotropic fluid cylinders embedded in an isotropic fluid background. Besides the analytical formulas for the effective parameters reported previously, i.e., the bulk modulus and the mass density perpendicular to the cylinders, we also derive a simple expression for the effective mass density parallel to the cylinders. As expected, these two effective mass densities are not identical and constitute an anisotropic density tensor. Such intrinsic anisotropy can be engineered much stronger than the pure in-plane anisotropy induced by either anisotropic lattices or anisotropic scatterers.