Scattering coefficients for a sphere in a visco-acoustic medium for arbitrary partial wave order

Analytical solutions are reported for the scattering coefficients of a solid elastic sphere suspended in a viscous fluid for arbitrary partial wave order. Expressions are derived for incident compressional and shear wave modes, taking into account the viscosity of the surrounding fluid and resultant wave mode conversion. The long compressional wavelength limit is employed to simplify the derivation, whereas no restriction is placed on the shear wavelength in the fluid compared to the particle dimension. The analytical approximations are compared with numerical results obtained from matrix inversion of the boundary equations and agree within the validity domain of the solutions.     

Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.     

Physical,Thermal and Biological Properties of Yellow Dyes with Two Azodiphenylether Groups of Anthracene

Two yellow bis-azo dyes containing anthracene and two azodiphenylether groups (BPA and BTA) were prepared, and an extensive investigation of their physical, thermal and biological properties was carried out. The chemical structure was confirmed by the FTIR spectra, while from the UV–Vis spectra, the quantum efficiency of the laser fluorescence at the 476.5 nm was determined to be 0.33 (BPA) and 0.50 (BTA). The possible transitions between the energy levels of the electrons of the chemical elements were established, identifying the energies and the electronic configurations of the levels of transition. Both crystals are anisotropic, the optical phenomenon of double refraction of polarized light (birefringence) taking place. Images of maximum illumination and extinction were recorded when the crystals of the bis-azo compounds rotated by 90° each, which confirms their birefringence. A morphologic study of the thin films deposited onto glass surfaces was performed, proving the good adhesion of both dyes. By thermal analysis and calorimetry, the melting temperatures were determined (~224–225 °C for both of them), as well as their decomposition pathways and thermal effects (enthalpy variations during undergoing processes); thus, good thermal stability was exhibited. The interaction of the two compounds with collagen in the suede was studied, as well as their antioxidant activity, advocating for good chemical stability and potential to be safely used as coloring agents in the food industry.     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Capturing the experimental behaviour of a point-absorber WEC by simplified numerical models

The paper presents a wave basin experiment of a direct-driven point-absorber wave energy converter moving in six degrees of freedom. The goal of the work is to study the dynamics and energy absorption of the wave energy converter, and to verify under which conditions numerical models restricted to heave can capture the behaviour of a point-absorber moving in six degrees of freedom. Several regular and irregular long-crested waves and different damping values of the power take-off system have been tested. We collected data in terms of power output, device motion in six degrees of freedom and wave elevation at different points of the wave basin. A single-body numerical model in the frequency domain and a two-body model in the time domain are used in the study. Motion instabilities due to parametric resonance observed during the experiments are discussed and analysis of the buoy motion in terms of the Mathieu instability is also presented. Our results show that the simplified models can reproduce the body dynamics of the studied converter as long as the transverse non-linear instabilities are not excited, which typically is the case in irregular waves. The performance of the more complex time domain model is able to reproduce both the buoy and PTO dynamics, while the simpler frequency domain model can only reproduce the PTO dynamics for specific cases. Finally, we show that the two-body dynamics of the studied wave energy converter affects the power absorption significantly, and that common assumptions in the numerical models, such as stiff mooring line or that the float moves only in heave, may lead to incorrect predictions for certain sea states.     

Pattern formation in a variable diffusion predator–prey model with additive Allee effect

This paper deals with a variable diffusion predator–prey model with additive Allee effect. A good understanding of the existence of steady states is gained for the case  $\sigma =0$. The result shows that the reduce problem has multiple solutions. Moreover, by applying the singular perturbation method, we give a proof of existence of large amplitude solutions when  $\sigma$ is sufficiently small.