Second harmonic generation in composites of ellipsoidal particles with core–shell structure

We study the enhancement of the second-harmonic generation (SHG) coefficient in a random composite consisting of ellipsoidal particles with a core–shell structure in a linear dielectric host. The material making up the ellipsoidal core is assumed to be dielectric, but with a nonlinear susceptibility for SHG. The coating material is assumed to be metallic with a linear susceptibility. The effective SHG coefficient is derived and its expression is related to various local field factors. The numerical calculations of the effective SHG response per unit volume of nonlinear material can be greatly enhanced at certain frequencies. For coated ellipsoidal particles, the core–shell structure and the particle shape allow for tuning of the resonance through the choice of material parameters and/or the ratio of the core to shell volume fraction and the depolarization factor of the particles.     

Analogue of the Cole-Hopf transform for the incompressible Navier–Stokes equations and its application

We consider the Navier–Stokes equations written in the stream function in two dimensions and vector potentials in three dimensions, which are critical dependent variables. On this basis, we introduce an analogue of the Cole-Hopf transform, which exactly reduces the Navier–Stokes equations to the heat equations with a potential term (i.e. the nonlinear Schrödinger equation at imaginary times). The following results are obtained. (i) A regularity criterion immediately obtains as the boundedness of condition for the potential term when the equations are recast in a path-integral form by the Feynman-Kac formula. (ii) This in turn gives an additional characterisation of possible singularities for the Navier–Stokes equations. (iii) Some numerical results for the two-dimensional Navier–Stokes equations are presented to demonstrate how the potential term captures near-singular structures. Finally, we extend this formulation to higher dimensions, where the regularity issues are markedly open.     

Modeling the crystallization of a Ti–Al nanoparticle by the molecular dynamics method

Crystallization of the Ti–Al intermetallide in the process of cooling from a melt at a constant volume has been simulated numerically using the molecular dynamics method.     

Primary resonance of fractional-order Duffing–van der Pol oscillator by harmonic balance method

The dynamical properties of fractional-order Duffing–van der Pol oscillator are studied, and the amplitude–frequency response equation of primary resonance is obtained by the harmonic balance method. The stability condition for steady-state solution is obtained based on Lyapunov theory. The comparison of the approximate analytical results with the numerical results is fulfilled, and the approximations obtained are in good agreement with the numerical solutions. The bifurcations of primary resonance for system parameters are analyzed. The results show that the harmonic balance method is effective and convenient for solving this problem, and it provides a reference for the dynamical analysis of similar nonlinear systems.     

Sonocatalytic–Fenton reaction for enhanced OH radical generation and its application to lignin degradation

The present study demonstrated that the combined use of the sonocatalytic reaction (using ultrasound and titanium dioxide) and the Fenton reaction exhibited synergistically enhanced hydroxyl (OH) radical generation. Dihydroxybenzoic acid (DHBA) concentration as index of OH radical generation was 13 and 115 μM at 10 min in the sonocatalytic reaction and Fenton reaction, respectively. On the other hand, the DHBA concentration was 378 μM at 10 min in the sonocatalytic–Fenton reaction. The sonocatalytic–Fenton reaction was used for degradation of lignin. The lignin degradation ratio was 1.8%, 49.9%, and 60.0% at 180 min in the sonocatalytic reaction, Fenton reaction, and sonocatalytic–Fenton reaction, respectively. Moreover, the sonocatalytic–Fenton reaction was applied to pretreatment of lignocellulosic biomass to enhance subsequent enzymatic saccharification. The cellulose saccharification ratio was 11%, 14%, 16% and 25% at 360 min of pretreatment by control reaction, the sonocatalytic reaction, Fenton reaction, and sonocatalytic–Fenton reaction, respectively.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Determination of the Galaxy age by the method of uranium–thorium–plutonium isotopic ratios

The dependence of the Galaxy age (Т _G), as determined by the method of uranium–thorium isotopic ratios, on the parameters of the nucleosynthesis model is studied within the theory of galactic nucleosynthesis. It is shown that ТG depends strongly both on the scenario of the production of nuclei in the r-process and those features of neutron-rich nuclei that are used in the respective analysis and on galactic-nucleosynthesis parameters. The effect of a sudden nucleosynthesis spike before the formation of a solar system on the Galaxy age is evaluated. The region of admissible values of the parameters of galacticnucleosynthesis theory is discussed. The method of uranium–thorium isotopic ratios is supplemented with the ²⁴⁴Pu/²³⁸U ratio for yet another cosmochronometer pair, and the Galaxy age is estimated on the basis of the model modified in this way.     

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.     

Vibration of a rectangular plate with a central power-law profiled groove by the Rayleigh–Ritz method

The prediction of natural frequencies of rectangular plates where a profiled indentation is present is made using a Rayleigh–Ritz variational energy method. Panels with holes are often found for access cables and access gaps, and it is shown that the application of damping to the profile leads to a more efficient method of reducing vibration than covering a whole rectangular plate, which is advantageous where weight saving is necessary.     

Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis

Investigating long-range correlation by the Hurst exponent, H$H$, is crucial in the study of time series. Recently, empirical-mode-decomposition-based arbitrary-order Hilbert spectral analysis (EMD-HSA) has been proposed to numerically obtain without proof a scaling relationship, generated from the amplitude–frequency distribution, related to H$H$. We propose a formalism to empirically study EMD-HSA, to deduce its scaling exponent ξ(q)$\xi \left(q\right)$ from the perspective of EMD-based arbitrary-order Hilbert marginal spectrum (EMD-HMS), and to numerically compare the results with the expected H$H$. EMD-HSA and EMD-HMS experiments show that, by incompletely removing (quasi-)periodic trends, the sunspot series should have an H$H$ value around 0.12.     

A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)--(G'/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method.     

Preparation of CeO2 by a simple microwave–hydrothermal method

Cerium carbonate hydroxide (orthorhombic Ce(OH)CO₃) hexagonal-shaped microplates were synthesized by a simple and fast microwave–hydrothermal method at 150 °C for 30 min. Cerium nitrate, urea and cetyltrimethylammonium bromide were used as precursors. Ceria (cubic CeO₂) rhombus-shape was obtained by a thermal decomposition oxidation process at 500 °C for 1 h using as- synthesized Ce(OH)CO₃. The products were characterized by X-ray powder diffraction, field-emission scanning electron microscopy, thermogravimetric analysis and Fourier transformed infrared spectroscopy. The use of microwave–hydrothermal method allowed to obtain cerium compounds at low temperature and shorter time compared to other synthesis methods.     

A connection between the （G′/G）-expansion method and the truncated Painlev ＇e expansion method and its application to the mKdV equation

Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.     

Spatial distribution of the interacting Waves’ amplitudes under third harmonic generation in a negative-positive refractive medium

The process of third harmonic generation in a cubically nonlinear medium that is negatively refractive at the fundamental frequency and positively refractive at the third harmonic frequency is considered. For the stationary case, the amplitude distribution was obtained for waves interacting inside a sample for different values of phase mismatch. In the periodic regime of generation, it is shown that the amplitude of the fundamental wave inside the medium can exceed its value at the input, which is impossible in the standard case of harmonic generation in a medium positively refractive at both frequencies. The influence of energy losses in the sample on the spatial distribution of waves’ amplitudes of both frequencies has been studied.     

Dynamics of Bose–Einstein condensate in a harmonic potential and a Gaussian energy barrier

We have studied the dynamics of Bose–Einstein condensate by solving numerically the Gross-Pitaevskii (GP) equation. We examined the periodic behaviour of the condensate in a shifted harmonic potential, and further demonstrated the tunneling effect of a condensate through a Gaussian energy barrier, which is inserted after the condensate has been excited by shifting the harmonic trapping potential to a side. Moreover, it is shown that the initial condensate evolves dynamically into two separate moving condensates after the tunneling time under certain conditions.     

Synthesis and characterization of nanostructured strontium hexaferrite thin films by the sol–gel method

Nanostructured single phase strontium hexaferrite, SrFe₁₂O₁₉, thin films have been synthesized on the (100) silicon substrate using a spin coating sol–gel process. The thin films with various Fe/Sr molar ratios of 8–12 were calcined at different temperatures from 500 to 900 °C. The composition, microstructure and magnetic properties of the SrFe₁₂O₁₉ thin films were characterized using Fourier transform infrared spectroscopy, differential thermal analysis, thermogravimetry, X-ray diffraction, electron microscopy and vibrating sample magnetometer. The results showed that the optimum molar ratio for Fe/Sr was 10 at which the lowest calcination temperature to obtain the single phase strontium hexaferrite thin film was 800 °C. The magnetic measurements revealed that the sample with Fe/Sr molar ratio of 10, exhibited higher saturation magnetization (267.5 emu/cm³) and coercivity (4290 Oe) in comparison with those synthesized under other Fe/Sr molar ratios.