Loss of classicality in the alternating spin-½/spin-1 chain, in the presence of next-neighbor couplings and Dzyaloshinskii-Moriya interactions

We have considered and alternating spin-½/spin-1 chain with nearest-neighbor (J1), next-nearest neighbor (J2) antiferromagnetic Heisenberg interactions along with z-component of the Dzyaloshinskii-Moriya(DM) (Dz) interaction. The Hamiltonian has been studied using (a) Linear Spin-Wave Theory(LSWT) and (b) Density Matrix Renormalization Group (DMRG). The system had been reported earlier as a classical ferrimagnet only when nearest neighbor exchange interactions are present. Both the antiferromagnetic next-nearest neighbor interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzero J2 introduces strong quantum fluctuations in each of the spin sites due to which the z-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence of J1 along with Dzintroduces a short range order but develops long range order along the XY plane. J1 along with J2induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that the Dz term removes the local spin spiral structure in z-direction, while developing a spiral order in the XY plane.

An Efficient Method for Analytically Solving (1+2)-dimensional Chiral Non-linear Schrödinger Equation

In this paper, we have successfully extracted novel analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger (NLS) equation by modified extended tanh expansion method combined with new Riccati solutions (METEM-cNRCS) as far as we know. When a wave transformation is applied to the considered Chiral NLS equation, a nonlinear ODE is obtained. Assuming the solutions of ODE have a form as the method suggests, and substituting the trial solutions to the ODE, we get a polynomial. Gathering the coefficients with the same power in the polynomial, we acquire an algebraic equation system. So, we may obtain the abundant solutions of the (1+2)-dimensional Chiral NLS equation by solving the system via Maple. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper are a guide for future works in traveling wave theory.

Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction

In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.

Wave theory of the laminated plates with approximate consideration of the transverse shear

Composite materials are widely used in the production of aircraft for various purposes. Having several unique properties, composites, due to their heterogeneous structure, are poorly resistant to shock loads. Impulse action spreads inside the material in the form of stress waves, which are reflected on internal inhomogeneities, can overlap, and create very significant bursts of stress. This often leads to the well-known types of failure – spalling and delamination. Practice shows that these fractures occur almost immediately after the loading impulse. To verify the spalling strength, it is necessary to consider the initial unsteady phase of the response to the external impulse. There are sufficiently reliable theories to verify this strength; usually, they do not take transverse shear into account, otherwise the solution becomes unnecessarily cumbersome and poorly observable. Nevertheless, attempts are often made to refine the calculations by approximate consideration of transverse shear. This article presents the wave theory of laminated plates with approximate consideration of transverse shear. The possibility of specifying the calculation of impulse-loaded plates is considered. The inconsistency of the resulting model is proved.

A Semi-Analytical Model for Studying Hydroelastic Behaviour of a Cylindrical Net Cage under Wave Action

In the present study, a semi-analytical model based on the small-amplitude wave theory is developed to describe the wave fields around a single gravity-type cylindrical open fish net cage. The cage may be submerged to different depths below the free-water surface. The fish cage net is modelled as a flexible porous membrane, and the deflection of the net chamber is expressed by the transverse vibration equation of strings. The velocity potential is expanded in the form of the Fourier–Bessel series and the unknown coefficients in these series are determined from matching the boundary conditions and the least squares method. The number of terms for the series solution to be used is determined from convergence studies. The model results exhibit significant hydroelastic characteristics of the net cages, including the distribution properties of wave surface, pressure drop at the net interface, structural deflection, and wave loading along the cage height. In addition, the relationships between wave forces on the net cage with hydrodynamic and structural parameters are also revealed. The findings presented herein should be useful to engineers who are designing fish cage systems.

Mechanism analysis and prediction of explosive formed projectile’s axial fracture

To explain the axial fracture phenomenon of Explosively Formed Projectile (EFP), the fracture mechanism of long rod EFP during the forming phase is analyzed by the stress wave theory. When the velocity gradient [Formula: see text] between the head and tail parts exceeds the critical value [Formula: see text], the EFP would fracture in the axial direction. Based on the Johnson–Cook constitutive model parameters and the special conditions in the forming phase of EFP, the critical velocity gradient [Formula: see text] can be determined by theoretical calculation and then validated by experimental results for both copper and tantalum EFPs. The experimental results for EFP’s fracture agree well with the prediction of the theoretical analysis. The theoretical analysis method can be applied as an important measure to determine the critical velocity gradient and predict the fracture of long rod EFP, providing reference for the application of new kinds of high density materials in the EFP research area.

Research on Wave Attenuation Performance of Floating Breakwater

In this study, a new type of double-pontoon floating breakwater was designed to improve the wave attenuation performance through the addition of suspended Savonius propeller-blade. Its hydrodynamic characteristics were studied through numerical simulations and performance-testing experiment. The following investigations were performed in this study: Firstly, wave theory and hydrodynamic theory were combined to calculate the wave attenuation performance and motion response of double-pontoon floating breakwater under linear wave conditions. The numerical results showed that the wave attenuation performance was better under a specific wave period and height, the transmission coefficient reached a relatively small value, and the mooring line tension responded periodically and satisfied the condition of maximum breaking force. Secondly, three key geometric parameters of breakwater were researched, including the relative spacing of pontoons, the relative spacing between pontoons and blades, and the height–diameter ratio of Savonius blades. The calculation results showed that the pontoon spacing was closer to the wavelength and the breakwater wave attenuation performance was better. Lastly, experimental tests were also performed on the new double-pontoon floating breakwater and the results showed that the wave attenuation performance and numerical projections were basically the same, which verified the validity and effectiveness of the design method.