Reply to: “Comment on: ‘Epidemic spreading on heterogeneous networks with identical infectivity’ [Phys. Lett. A 364 (2007) 189]” [Phys. Lett. A 372 (2008) 1722]

In a recent Letter [R. Yang, B.H. Wang, J. Ren, W.J. Bai, Z.W. Shi, W.X. Wang, T. Zhou, Phys. Lett. A 364 (2007) 189], we proposed a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contact, A, at each time step. We found a threshold value λc=1/A in uncorrelated and unlocalized networks. A corresponding Comment, raised by Alberto d'Onofrio, claimed that (i) our model is not biologically relevant; (ii) our model does not have a threshold behavior for recovered population; (iii) the analytical result λc=1/A is incorrect being considered as a threshold for epidemic outbreak, because of an improper approximation of the initial configuration. In this Reply, I show that, by debating from point to point, our analysis and conclusion are solid and reasonable.     

Deformation of an elastic substrate by a three-phase contact line

Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it is expected that this unresolved force is balanced by the elastic response of the solid, a definitive analysis has remained elusive because of an apparent divergence of stress at the contact line. While a number of theories have been presented to cut off the divergence, none of them have provided reasonable agreement with experimental data. We measure surface and bulk deformation of a thin elastic film near a three-phase contact line using fluorescence confocal microscopy. The out-of-plane deformation is well fit by a linear elastic theory incorporating an out-of-plane restoring force due to the surface tension of the solid substrate. This theory predicts that the deformation profile near the contact line is scale-free and independent of the substrate elastic modulus.     

A displacement sensing nanoindentation study of tribo-mechanical properties of the Ni-Co system

An analysis of the tribo-mechanical properties of the Ni-Co system, at the submicrometric contact scale, is conducted using displacement sensing nanoindentation. In particular, the influence of contact depth and surface finishing methods on the hardness, H, and Young's modulus, E, of the materials is analysed. Mechanically and electrolitically polished samples were tested with a conospherical indenter using a range of loads between 0.05 and 10 mN. It is shown that the hardness of these materials depends on the surface finishing method and increases with decreasing contact depth, while the Young's modulus is relatively insensitive to contact depth. Furthermore, sample polycrystallinity leads to a large scattering of hardness values in Co-rich samples and of Young's modulus values in Ni-rich ones. The combined parametric ratio H/E, which can be related to the tribological behaviour of the material, was found to be higher in samples with Co content larger than 80 wt.%.     

An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces

This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.     

Contact line moving on a solid

The moving contact line problem can be summarized as follows: consider the triple line where a solid, a liquid and its vapor meet. This contact line may be the perimeter of a liquid droplet standing on a solid. Suppose now that, because of gravity for instance, the droplet and so its perimeter slides on the solid surface. The boundary conditions for viscous fluids impose that the flow velocity on an immobile solid is zero. If one assumes that the liquid/vapor surface is a material surface, i.e. that it is convected by the fluid, the contact line cannot move with respect to the solid, contrary to what is observed. Over the years many suggestions have been made to solve this problem. I show that solutions relying on the introduction of microscopic length scales are not consistent within the general framework of continuum mechanics. To get consistent solutions, one needs to introduce evaporation/condensation near the moving line, in agreement with experimental findings.     

On the elasticity of transverse isotropic soft tissues (L)

Quantitative elastography techniques have recently been developed to estimate the shear modulus μ of soft tissues in vivo. In the case of isotropic and quasi-incompressible media, the Young's modulus E is close to 3 μ, which is not true in transverse anisotropic tissues such as muscles. In this letter, the transverse isotropic model established for hexagonal crystals is revisited in the case of soft solids. Relationships between elastic constants and Young's moduli are derived and validated on experimental data found in the literature. It is shown that 3 μ(⊥) ≤ E(⊥) ≤ 4 μ(⊥) and that E(//) cannot only be determined from the measurements of μ(//) and μ(⊥).     

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase(MCMP) pseudopotential lattice Boltzmann(LB) model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young's equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie's law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.     

固体杨氏模量的测量

通过测量超声波在固体介质中传播的纵波传播速度,进一步测量该固体的杨氏模量,得到了测量固体杨氏模量的一种新方法。     

Vibration analysis on electromagnetic-resonance-ultrasound microscopy (ERUM) for determining localized elastic constants of solids

In this paper we present a new acoustic-resonance microscopy, Electromagnetic-Resonance-Ultrasound Microscopy (ERUM), to measure the localized elastic stiffness of a solid material. It visualizes the resonance-frequency shift of vibrating piezoelectric crystal (langasite, La3Ga5SiO14) excited by an electric field from a solenoid coil. The acoustic coupling is made only at the tip of the crystal touching the specimen surface. Being based on the calibration for the specimen's effective stiffness, the local elasticity is determined from the resonance frequencies of the crystal with the Rayleigh-Ritz method. An approximate model for the specimen's effective stiffness predicts the shift of resonance frequencies, for which the conventional Hertz-contact model is improved. As an illustrating example, the mapping of Young's modulus of a duplex stainless steel is presented, which shows good agreement with the existing study.     

掺杂单晶硅纳米薄膜杨氏模量的多尺度理论模型

硅纳米材料物理性能的研究对其在半导体技术中的应用是十分重要的. 而掺杂有利于改善硅纳米材料的物理特性, 提高应用价值, 所以本文基于半连续体模型运用Keating形变势, 通过模型计算, 研究了不同位置及不同掺杂浓度的单晶硅纳米薄膜[100]方向的杨氏模量, 分析了掺杂浓度及掺杂位置不同时硅膜杨氏模量与膜厚关系, 结果表明, 与纯硅膜杨氏模量相比, 不同位置的掺杂对硅膜杨氏模量的影响并不明显, 不同浓度的掺杂对硅膜杨氏模量的影响较小. 而随着硅膜厚度的不断增加, 掺杂硅膜杨氏模量与纯硅膜杨氏模量的变化趋势一致, 特别是较小尺寸时的硅膜杨氏模量变化较大. 说明影响硅膜杨氏模量的主要因素是硅膜厚度. 该计算结果对研究硅纳米材料的其他力学特性有一定的参考价值, 也为进一步研究掺杂对纳米硅材料力学性能的影响提供一种全新思路.     

Exact SO(5) symmetry in the spin-3/2 fermionic system

The spin-3/2 fermion models with contact interactions have a generic SO5 symmetry without any fine-tuning of parameters. Its physical consequences are discussed in both the continuum and lattice models. A Monte Carlo algorithm free of the sign problem at any doping and lattice topology is designed when the singlet and quintet interactions satisfy U0< or = U2< or = -3/5 U0 (U0< or = 0), thus making it possible to study different competing orders with high numerical accuracy. This model can be accurately realized in ultracold atomic systems.     

The influence of defects on the effective Young’s modulus of a defective solid

It is difficult to establish structure-property relationships in a defective solid because of its inhomogeneous-geometry microstructure caused by defects. In the present research, the effects of pores and cracks on the Young’s modulus of a defective solid are studied. Based on the law of the conservation of energy, mathematical formulations are proposed to indicate how the shape, size, and distribution of defects affect the effective Young’s modulus. In this approach, detailed equations are illustrated to represent the shape and size of defects on the effective Young’s modulus. Different from the results obtained from the traditional empirical analyses, mixture law or statistical method, for the first time, our results from the finite element method (FEM) and strict analytical calculation show that the influence of pore radius and crack length on the effective Young’s modulus can be quantified. It is found that the longest crack in a typical microstructure of ceramic coating dominates the contribution of the effective Young’s modulus in the vertical direction of the crack.     

Simulation of laser-generated ultrasonic wave propagation in solid media and air with application to NDE

Ultrasonic methods are well known as powerful and reliable tool for defect detection. In the previous decades focus and interest have been directed to non-contact sensors and methods, showing many advantages over contact techniques where inspection depends on contact conditions (pressure, coupling medium, contact area). The non-contact hybrid ultrasonic method described here is of interest for many applications, requiring periodic inspection in service or after manufacturing. Despite the potential impact of laser-generated ultrasound in many areas of industry, robust tools for studying the phenomenon are lacking and thus limit the design and optimization of non-destructive testing and evaluation techniques. Here a specific numerical method is presented to efficiently and accurately solve ultrasound wave propagation problems with frequencies in the MHz range traveling in relatively large bodies and through air. This work improves a previous numerical model where propagation of the acoustic waves through air had not been considered, allowing us to simulate the presence of a non-contact transducer in reception in order to simulate numerically the complete experimental setup. It is very important to limit the amount of air to be considered in the FE analyses; otherwise the computational cost would often exceed the resources available. A way to solve the problem is to implement non-reflecting boundary conditions. A non-reflecting boundary condition allows all outgoing waves to exit the domain at the boundary where they have been imposed without reflection; thus, it is possible to model only the portion of air between the non-contact transducer and the solid under testing. Several numerical and experimental analyses were conducted on a 136 lb AREMA rail; here we study in detail two fully non-contact testing configurations for the rail head and web. The information that can be acquired is very valuable for choosing the right setup and configuration when performing non-contact hybrid ultrasonic inspection.     

稳定超疏水性表面的理论进展

自然界中很多动植物都具有稳定的超疏水性, 它们既拥有高接触角, 又拥有低滚动角, 且能长期稳定存在.通过对它们的研究, 发现表面的润湿性与表面的化学成分、表面的几何形貌有关, 并且表面几何结构的影响更为显著, 甚至可以实现由亲水性表面向超疏水转变. 虽然目前在这个领域已经有大量的实验验证了表面粗糙结构的重要作用, 但是对于表面微纳米结构对表面疏水性机理的理论研究还并不完善. 本文详细介绍了超疏水表面的基本理论及其适用性、 接触角滞后现象, 分别从经典理论和能量的观点探讨了润湿状态转化发生的条件, 重点介绍了通过仿生理念对表面几何形貌的优化设计, 包括单尺度和多尺度表面结构对于设计稳定超疏水表面的作用. 最后, 对超疏水理论的不足和未来发展进行了展望. 关键词： 超疏水 仿生 接触角 滞后     

Phase field modeling of hysteresis in sessile drops

We propose a novel approach to describe wetting of plane solid surfaces by liquid drops. A two-dimensional nonconserved phase field variable is employed to distinguish between wetted and nonwetted regions on the surface. The imbalance in the Young's force provides for the exchange of relative stability of the two phases. The three-phase contact line tension arises from the gradient energy and contact angle hysteresis from the kinetic coefficient. Using this theory, we discuss contact angle hysteresis on chemically heterogeneous surfaces. We show significant departure from the classical Cassie theory, which is attributed to defect pinning of the continuous triple line.     

Magnetic properties of <Superscript>3</Superscript>He on the recursive lattices

We considered the Heisenberg model on the recursive lattices with multi-spin interaction in a strong magnetic field as an approximation of the two-dimensional kagome lattice, as well as hexagonal recursive lattices as an approximation of triangular lattice, for solid ³He. In a strong magnetic field it is possible to approximate the Heisenberg model with the Izing one. Using dynamic approach, we obtain exact recursion relations for partition functions. Diagrams of the magnetization versus external magnetic field with different spin-exchange parameters and temperatures are presented. Magnetization plateaux, bifurcation points, and doublings are obtained.     

Characterization of English ivy (<Emphasis Type="Italic">Hedera helix</Emphasis>) adhesion force and imaging using atomic force microscopy

English ivy (Hedera helix) is well known for its ability to climb onto and strongly adhere to a variety of solid substrates. It has been discovered that the ivy aerial rootlet secretes an adhesive composed of polysaccharide and spherical nanoparticles. This study aims to characterize the mechanical properties of the nanocomposite adhesive using atomic force microscopy (AFM). The adhesive was first imaged by AFM to visualize the nanocomposite. Mechanical properties were then determined at various time points, from secretion to hardening. The experimental results indicate that the ivy adhesive exhibited strong adhesion strength and high elasticity. There was a decrease in adhesive force over time, from 298 to 202 nN during the 24-h study. Accompanying with it were the limited changes in extension length and Young’s modulus. The limited curing process of the ivy adhesive helps fill gaps in the attaching surface, leading to more intimate contact and increased van der Waals interactions with the surface. However, study based on a mechanical model indicated that van der Waals force alone is not significant enough to account for all of the measured force. Other chemical interactions and cross linking likely contribute to the strong adhesion strength of ivy.     

Fitting models to correlated data (large samples)

The study of the ordered series of residuals of a fit proved to be useful in evaluating separately the pure experimental error and the model bias leading to a possible improvement of the modeling [J. Mol. Spectrosc. 217 (2003) 32]. In the present work this procedure is extended to homogeneous correlated data. This new method allows a separate estimation of pure experimental error, model bias, and data correlation; furthermore, it brings a new insight into the difference between goodness of fit and model relevance. It can be considered either as a study of ‘random systematic errors’ or as an extended approach of the Durbin-Watson problem [Biometrika 37 (1950) 409] taking into account the model error. In the present work an empirical approach is proposed for large samples (n?500) where numerical tests are done showing the accuracy and the limits of the method.     

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.