Solitons and conservation laws in magneto–optic waveguides having parabolic–nonlocal law of refractive index

This paper reveals soliton solutions to magneto–optic waveguides that maintain parabolic–nonlocal law of refractive index. The unified Riccati equation expansion together with extended auxiliary equation approach together reveal bright, dark, singular as well as straddled optical solitons. These soliton solutions are obtained through a limiting process when the modulus of ellipticity approaches unity. Finally, the conservation laws are also listed.     

Sonication enhances the stability of MnO2 nanoparticles on silk film template for enzyme mimic application

We have developed an in-situ method using sonication (3 mm probe sonicator, 30 W, 20 kHz) and auto-reduction (control) to study the mechanism of the formation of manganese dioxide (MnO₂) on a solid template (silk film), and its resulting enzymatic activity on tetramethylbenzidine (TMB) substrate. The fabrication of the silk film was first optimized for stability (no degradation) and optical transparency. A factorial approach was used to assess the effect of sonication time and the initial concentration of potassium permanganate (KMnO₄). The result indicated a significant correlation with a fraction of KMnO₄ consumed and MnO₂ formation. Further, we found that the optimal process conditions to obtain a stable silk film with highly catalytic MnO₂ nanoparticles (NPs) was 30 min of sonication in the presence of 0.5 mM of KMnO₄ at a temperature of 20–24 °C. Under the optimal condition, we monitored in-situ the formation of MnO₂ on the silk film, and after thorough rinsing, the in-situ catalysis of 0.8 mM of TMB substrate. For control, we used the auto-reduction of KMnO₄ onto the silk film after about 16 h. The result from single-wavelength analysis confirmed the different kinetics rates for the formation of MnO₂ via sonication and auto-reduction. The result from the multivariate component analysis indicated a three components route for sonication and auto-reduction to form MnO₂-Silk. Overall, we found that the smaller size, more mono-dispersed, and deeper buried MnO₂ NPs in silk film prepared by sonication, conferred a higher catalytic activity and stability to the hybrid material.     

First-principles investigation on ideal strength of B2 NiAl and NiTi alloys

For B2 NiAl and NiTi intermetallic compounds, the ideal stress–strain image is lack from the perspective of elastic constants. We use first-principles calculation to investigate the ideal strength and elastic behavior under the tensile and shear loads. The relation between the ideal strength and elastic constants is found. The uniaxial tension of NiAl and NiTi along <001> crystal direction leads to the change from tetragonal path to orthogonal path, which is driven by the vanishing of the shear constant C(66). The shear failure under {110}{111} shear deformation occurring in process of tension may result in a small ideal tensile strength(~ 2 GPa) for NiTi. The unlikeness in the ideal strength of Ni Al and Ni Ti alloys is discussed based on the charge density difference.     

The structural and catalytic properties of nanoparticles@MOF composites: A case study of Au@ZIF-8 hybrid crystals

Strain analysis of the MOF and its composites using high-resolution X-ray diffractionmeter (XRD) was carried out and the presence of non-uniform, depth-related strain in the MOF crystals was confirmed. Further analysis showed that the magnitude and distribution of strain in MOF crystals can be tuned with the incorporation of nanoparticles (NPs). Moreover, the spatial controlled structures can also optimize functionalities of the NPs@MOF, which was exemplified by their applications on the catalytic reduction of nitroarenes. It is anticipated that the investigation of MOF structure evolution through controlling the architectures of the MOF/NPs hybrid materials will shed a light on the study of optimizing the mechanical and chemical properties of MOF composites.     

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.     

An analysis of the simulated acoustic emission sources with different propagation distances,types and depths for rail defect detection

Acoustic Emission (AE) technique is an effective nondestructive detecting method, and has a promising application for rail defect detection. So far, little attention has been paid to propagation distances, types, and depths of AE sources, which are important for rail defect detection accurately. This paper presents an experimental study on the simulated AE sources with different propagation distances, types and depths for rail defect detection. Three simulated AE sources with different frequencies are seeded on the cross section of rail, and the depths of AE sources are changed in the vertical direction. After receiving AE signals, wavelet transform and Rayleigh–Lamb equations are utilized to extract time–frequency features and modes. Based on the wavelet transform with corresponding group-velocity curves, the influences of different propagation distances, the features of different source types and the rules of different source depths are examined. It is concluded that the features of AE sources with different propagation distances, types and depths can be obtained by AE technique for rail defect detection. It is very useful to analyze and detect defects in rail defect detection.     

Miura transformation for the “good” Boussinesq equation

It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura-type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann–Hilbert problems and this is in fact how we construct the new transformation.     

Oscillations in three-reaction quadratic mass-action systems

It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation. However, some of our intermediate results are valid in greater generality. One key finding is that an isolated periodic orbit cannot occur in a three-reaction, trimolecular, mass-action system with bimolecular sources. In fact, we characterize all networks in this class that admit a periodic orbit; in every case, all nearby orbits are periodic too. Apart from the well-known Lotka and Ivanova reactions, we identify another network in this class that admits a center. This new network exhibits a vertical Andronov–Hopf bifurcation. Furthermore, we characterize all two-species, three-reaction, bimolecular-sourced networks that admit an Andronov–Hopf bifurcation with mass-action kinetics. These include two families of networks that admit a supercritical Andronov–Hopf bifurcation and hence a stable limit cycle. These networks necessarily have a target complex with a molecularity of at least four, and it turns out that there are exactly four such networks that are tetramolecular.