Exact solutions of the nonlinear differential-difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete（G＇/G）-expansion method

We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve the nonlinear differential–difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.     

Constrains on f(T) gravity with the strong gravitational lensing data

Strong lensing is an effective way to probing the properties of dark energy.In this paper,we use the strong lensing data to constrain the f(T)theory,which is a new modified gravity to explain the present accelerating cosmic expansion without the need of dark energy.In our discussion,the CMB and BAO data are also added to constrain model parameters tightly and three different f(T)models are studied.We find that strong lensing has an important role on constraining f(T)models,and once the CMB+BAO data is added,a tighter constraint is obtained.However,the consistency of our result with what is obtained from SNIa+CMB+BAO is actually model-dependent.     

Constraining fast radio burst progenitors with gravitational lensing

Fast Radio Bursts(FRBs)are new transient radio sources discovered recently.Because of the angular resolution restriction in radio surveys,no optical counter part has been identified yet so it is hard to determine the progenitor of FRBs.In this paper we propose to use radio lensing survey to constrain FRB progenitors.We show that,different types of progenitors lead to different probabilities for a FRB to be gravitationally lensed by dark matter halos in foreground galaxies,since different type progenitors result in different redshift distributions of FRBs.For example,the redshift distribution of FRBs arising from double stars shifts toward lower redshift than of the FRBs arising from single stars,because double stars and single stars have different evolution timescales.With detailed calculations,we predict that the FRB sample size for producing one lensing event varies significantly for different FRB progenitor models.We argue that this fact can be used to distinguish different FRB models and also discuss the practical possibility of using lensing observation in radio surveys to constrain FRB progenitors.     

Double-Wronskian solitons and rogue waves for the inhomogeneous nonlinear Schrödinger equation in an inhomogeneous plasma

Plasmas are the main constituent of the Universe and the cause of a vast variety of astrophysical, space and terrestrial phenomena. The inhomogeneous nonlinear Schrödinger equation is hereby investigated, which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping. By virtue of the double Wronskian identities, the equation is proved to possess the double-Wronskian soliton solutions. Analytic one- and two-soliton solutions are discussed. Amplitude and velocity of the soliton are related to the damping coefficient. Asymptotic analysis is applied for us to investigate the interaction between the two solitons. Overtaking interaction, head-on interaction and bound state of the two solitons are given. From the non-zero potential Lax pair, the first- and second-order rogue-wave solutions are constructed via a generalized Darboux transformation, and influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave is discussed.     

Anticrossing spectroscopy in multi-nanolayer structures

Presently we explored nanosandwich structures with graphite (Gt) and graphene (Gn) nanolayers. We found that in Pt–SiO₂–Gt, Pt–BN–Gt and Pt–SiO₂–Ni–Gn structures the spectra may be decomposed into several components, each corresponding to a different value of the total spin angular momentum S. Only one component was required to describe the Pt–SiO₂–Ni–Gn spectra at 5.3 K, with additional components appearing at higher temperatures. On the other hand, a single component described the Pt–BN–Ni–Gn spectra at all temperatures. Temperature dependence of the spectra of the Pt–SiO₂–Ni–Gn system was studied in the 5.3–75.3 K range. Presently we obtained experimental results for novel sandwich systems, with the Gn layer only two monoatomic layers thick. Thus, we compared experimental spectra of a three-nanolayer sandwich system containing a Gt nanolayer with those of a four-nanolayer system containing a diatomic Gn layer. The experimental results were discussed using a theoretical model of the respective physical mechanisms. We propose an exchange anticrossing mechanism, whereby the spin-state polarization of the given Zeeman?s substate in the Pt nanolayer is transported to Gt or Ni–Gn nanolayer by the exchange interaction between the two layers. As long as exchange interaction coupling spin states in different nanolayers is involved, we term the respective spectra the “spin anticrossing exchange-resonance spectra”. This clarifies the physical origins of some of the model parameters, i.e. the growing external magnetic field shifts the Zeeman?s substates in the different layers differently, producing the anticrossing spectrum. In the frameworks of the developed model, we propose spin–orbit (SO) interaction as the main factor inducing the spin–lattice relaxation, which is one of the important factors determining the line shape. We performed ab initio calculations of the SO interaction in carbon and metal nanolayers, finding that the SO interactions monotonously increase with the atomic number.     

Experimental study of ultrasonic beam sectors for energy conversion into Lamb waves and Rayleigh waves

When a bounded beam is incident on an immersed plate Lamb waves or Rayleigh waves can be generated. Because the amplitude of a bounded beam is not constant along its wave front, a specific beam profile is formed that influences the local efficiency of energy conversion of incident sound into Lamb waves or Rayleigh waves. Understanding this phenomenon is important for ultrasonic immersion experiments of objects because the quality of such experiments highly depends on the amount of energy transmitted into the object. This paper shows by means of experiments based on monochromatic Schlieren photography that the area within the bounded beam responsible for Lamb wave generation differs from that responsible for Rayleigh wave generation. Furthermore it provides experimental verification of an earlier numerical study concerning Rayleigh wave generation.     

High order shear horizontal modes for minimum remnant thickness

Thickness mapping in aging structures suffering from corrosion is challenging especially when the structure is only partially accessible. In plates the high order shear horizontal guided wave modes all have a cutoff frequency thickness product below which they cannot propagate. This property is potentially attractive to estimate the minimum remnant thickness between two transducers. When using a source and a sensor array it is possible to control the number of modes being excited and the size of the region interrogated by the technique. Finite element simulations were used to show that by exciting multiple guided wave modes simultaneously and identifying which modes are received by a sensor array it is possible to estimate the minimum remaining thickness along the propagation path. Initial experimental results showed excellent agreement with the finite element simulations when the plate is uniform and with a thickness reduction between the source and the sensor arrays the minimum remnant thickness was underestimated by approximately 20%.     

The computation of dispersion relations for axisymmetric waveguides using the Scaled Boundary Finite Element Method

This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior.     

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.     

A new multichannel time reversal focusing method for circumferential Lamb waves and its applications for defect detection in thick-walled pipe with large-diameter

This paper proposes a new multichannel time reversal focusing (MTRF) method for circumferential Lamb waves which is based on modified time reversal algorithm and applies this method for detecting different kinds of defects in thick-walled pipe with large-diameter. The principle of time reversal of circumferential Lamb waves in pipe is presented along with the influence from multiple guided wave modes and propagation paths. Experimental study is carried out in a thick-walled and large-diameter pipe with three artificial defects, namely two axial notches on its inner and outer surface respectively, and a corrosion-like defect on its outer surface. By using the proposed MTRF method, the multichannel signals focus at the defects, leading to the amplitude improvement of the defect scattered signal. Besides, another energy focus arises in the direct signal due to the partial compensation of dispersion and multimode of circumferential Lamb waves, alongside the multichannel focusing, during MTRF process. By taking the direct focus as a time base, accurate defect localization is implemented. Secondly, a new phenomenon is exhibited in this paper that defect scattered wave packet appears just before the right boundary of truncation window after time reversal, and to which two feasible explanations are given. Moreover, this phenomenon can be used as the theoretical basis in the determination of defect scattered waves in time reversal response signal. At last, in order to detect defects without prior knowing their exact position, a large-range truncation window is used in the proposed method. As a result, the experimental operation of MTRF method is simplified and defect detection and localization are well accomplished.