Stability of Viscoelastic Wave Equation with Structural $\delta$-Evolution in $\mathbb{R}^{n}$

The aim of this paper is to study the Cauchy problem for the viscoelastic wave equation for structural $\delta$-evolution models. By using the energy method in the Fourier spaces, we obtain the decay estimates of the solution to considered problem.     

Tensile properties of microtubules: A study by nonlinear molecular structural mechanics modelling

A nonlinear molecular structural mechanics (MSM) model is proposed in this paper for studying the tensile properties of microtubules (MTs). In the nonlinear MSM models, the interactions between tubulin monomers in MTs are treated as nonlinear axial and torsional springs, whose stiffness coefficients are extracted from all-atom molecular dynamics simulations. The Young's modulus and fracture properties of MTs under tension extracted from the present nonlinear MSM models are found to agree well with the existing simulation and experiment results, which shows the efficiency and accuracy of the proposed nonlinear MSM models. In addition, the nonlinear MSM models are also extended to investigate the tensile properties including Young's modulus and fracture strain of MTs possessing lattice defects. The results obtained from nonlinear MSM models are utilized to develop a predictive equation for quickly predicting the tensile properties of MTs with different lattice defect levels.     

Instantaneous work hardening behaviour of two-phase tungsten heavy alloys: a phenomenological approach

ABSTRACT

The present work describes a phenomenological approach to explain the instantaneous behaviour of tungsten heavy alloys (WHAs) in heat-treated and swaged conditions. The strengths and elongation values of heat-treated materials are lower and higher than those of the swaged samples respectively. The heat-treated materials exhibit two slopes in true stress–true plastic strain curves and follow the Ludwigson constitutive equation. On the other hand, swaged materials display a single slope and adhere to typical Swift constitutive equation. The latter reflect the presence of pre-strain in the materials due to swaging deformation. The fracture surfaces in heat-treated materials consist of W-W decohesion along with matrix rupture and W-cleavage, while swaged samples consist of mainly W-cleavage. Both the materials display three typical stages (I, II and III) of work hardening. The second derivatives of true stress–true plastic strain curves of these alloys exhibit a perfect parabola although the nature of true stress–true strain as well as true stress–true plastic strain curves is quite different in heat-treated and swaged materials. This has been observed for the first time in WHAs consisting of matrix and W-grains. The shape of the parabola is simple and easy to fit. The fitting parameters of parabolas have been successfully employed to explain the flow behaviour of a large number of tungsten heavy alloys having two-phase microstructure in different processing conditions.     

A note on the spheroidal modes vibration of an elastic sphere in linear viscoelastic fluid

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing, and also to investigate materials mechanical properties. An analytical approach based on the exact theory has been developed in this paper, to establish a new accurate and simple generalized frequency equation to predict spheroidal vibration of an elastic nanosphere, in a compressible viscoelastic fluid using linear Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. Thus, the obtained frequency equation can be very useful to interpret the experimental measurements of vibrational dynamics of nanospheres and can serve as benchmark solution in design of liquid sensors.     

Composition-dependent melting behaviour of NaxK55–x core–shell nanoalloys

Molecular dynamics simulations at constant temperature are performed to investigate melting-like transition in Na₁₃K₄₂, Na₁₉K₃₆ and Na₂₆K₂₉ nanoalloys using a second-moment-approximation tight-binding analytic potential to calculate the forces on the constituent atoms. A weighted histogram analysis method is employed to remove non-ergodicity issues due to the complex potential energy surface of these nanoalloys. The heat capacity shows three distinctive steps in melting for Na₁₃K₄₂, while Na₂₆K₂₉ and Na₁₉K₃₆ have two-step and one-step melting transition, respectively. The steepest descent method is used to quench the configurations in a given interval during the simulation and also study the isomerisation processes occurring at different temperatures. Analysing the configuration energies of quenched structures for the entire nanoalloy and the core atoms separately gives more details about the melting mechanism. The Lindemann parameter is also calculated at several temperatures during the simulation which shows a gradual increase for Na₁₃K₄₂ and Na₂₆K₂₉ while a sharp change is observed for Na₁₉K₃₆. These findings are in agreement with the multi-step nature of the phase transition in Na₁₃K₄₂ and Na₂₆K₂₉ and one-step melting of the Na₁₉K₃₆ magic composition.     

A two‐dimensional layered CdII coordination polymer with a three‐dimensional supramolecular architecture incorporating mixed multidentate N‐ and O‐donor ligands

The combination of N‐heterocyclic and multicarboxylate ligands is a good choice for the construction of metal–organic frameworks. In the title coordination polymer, poly[bis{μ₂‐1‐[(1H‐benzimidazol‐2‐yl)methyl]‐1H‐tetrazole‐κ²N³:N⁴}(μ₄‐butanedioato‐κ⁴O¹:O^1′:O⁴:O^4′)(μ₂‐butanedioato‐κ²O¹:O⁴)dicadmium], [Cd(C₄H₄O₄)(C₉H₈N₆)]_n, each Cd^II ion exhibits an irregular octahedral CdO₄N₂ coordination geometry and is coordinated by four O atoms from three carboxylate groups of three succinate (butanedioate) ligands and two N atoms from two 1‐[(1H‐benzimidazol‐2‐yl)methyl]‐1H‐tetrazole (bimt) ligands. Cd^II ions are connected by two kinds of crystallographically independent succinate ligands to generate a two‐dimensional layered structure with bimt ligands located on each side of the layer. Adjacent layers are further connected by hydrogen bonding, leading to a three‐dimensional supramolecular architecture in the solid state. Thermogravimetric analysis of the title polymer shows that it is stable up to 529 K and then loses weight from 529 to 918 K, corresponding to the decomposition of the bimt ligands and succinate groups. The polymer exhibits a strong fluorescence emission in the solid state at room temperature.     

Positive solutions for Lotka–Volterra competition system with large cross-diffusion in a spatially heterogeneous environment

In this paper, we study the stationary problem for the Lotka–Volterra competition system with cross-diffusion in a spatially heterogeneous environment. Although some sufficient conditions for the existence of positive solutions are obtained by using global bifurcation theory, the information for their structure is far from complete. In order to get better understanding of the competition system with cross-diffusion, we focus on the asymptotic behaviour of positive solutions and derive two shadow systems as the cross-diffusion coefficient tends to infinity, moreover, the structure of positive solutions of the limiting system is analysed. The result of asymptotic behaviour also reveals different phenomena from that studied in Wang and Li (2013).     

Secondary-flow-aided single-train elastic-inertial focusing in low elasticity viscoelastic fluids

Elastic-inertial focusing has attracted increasing interest in recent years due to the three-dimensional (3D) single-train focusing ability it offers. However, multi-train focusing, instead of single-train focusing, was observed in viscoelastic fluids with low elasticity as a result of the competition between inertia effect and viscoelasticity effect. To address this issue, we employed the secondary flow to facilitate single-train elastic-inertial focusing in low elasticity viscoelastic fluids. A three-section contraction-expansion channel was designed to induce the secondary flow to pinch the multiplex focusing trains into a single one exactly at the channel centerline. After demonstrating the focusing process and mechanism in our device, we systematically explored and discussed the effects of particle diameter, operational flow rate, polymer concentration, and channel dimension on particle focusing performances. Our device enables single-train focusing of particles in viscoelastic fluids with low elasticity, and offers advantages of planar single-layer structure, and sheathless, external-field free operation.     

Investigation of viscoelastic focusing of particles and cells in a zigzag microchannel

Microfluidic particle focusing has been a vital prerequisite step in sample preparation for downstream particle separation, counting, detection, or analysis, and has attracted broad applications in biomedical and chemical areas. Besides all the active and passive focusing methods in Newtonian fluids, particle focusing in viscoelastic fluids has been attracting increasing interest because of its advantages induced by intrinsic fluid property. However, to achieve a well-defined focusing position, there is a need to extend channel lengths when focusing micrometer-sized or sub-microsized particles, which would result in the size increase of the microfluidic devices. This work investigated the sheathless viscoelastic focusing of particles and cells in a zigzag microfluidic channel. Benefit from the zigzag structure of the channel, the channel length and the footprint of the device can be reduced without sacrificing the focusing performance. In this work, the viscoelastic focusing, including the focusing of 10 μm polystyrene particles, 5 μm polystyrene particles, 5 μm magnetic particles, white blood cells (WBCs), red blood cells (RBCs), and cancer cells, were all demonstrated. Moreover, magnetophoretic separation of magnetic and nonmagnetic particles after viscoelastic pre-focusing was shown. This focusing technique has the potential to be used in a range of biomedical applications.