A coefficient of restitution model for particle–surface collision of particles with a wide range of mechanical characteristics

The coefficient of restitution describes the energy dissipation resulting from particle-particle and particle–surface interactions in solid–fluid flows. The energy loss depends on the mechanical characteristics of the solid phase, therefore, to correctly predict the behavior of these systems it is necessary to use reliable coefficient values based on the properties of the particles. This paper investigated the energy dissipation in particle–surface collisions using 7 types of particles with a wide range of mechanical properties (Young's modulus between 1.38 × 10⁴ and 2.83 × 10⁹ Pa). Three empirical equations have been proposed to calculate the coefficient of restitution based on the impact velocity and the compressional wave velocity. The experimental results presented an inverse relation between the impact velocity and the coefficient of restitution. This effect was more pronounced for less elastic particles. The models presented an accurate fit to the experimental data and statistical analysis showed that the Power model presented the greater capacity to predict the coefficient of restitution from generic data. The experimental results showed the predominant effect of mechanical characteristics on the coefficient of restitution. In addition, the proposed equations are proved to be precise tools for predicting particle coefficients of restitution with a wide range of elasticity modulus at low velocities.     

A simple model for a minimal environment: the two-atom Tavis–Cummings model revisited

Individual quantum systems may be interacting with surrounding environments having a small number of degrees of freedom. Here we discuss a simple toy model: a system constituted by a two-level atom (atom 1) interacting with a single mode cavity field which is (weakly) coupled to a small environment (atom 2). We investigate the influence of the minimal environment on the dynamics of the linear entropy and the atomic dipole squeezing of atom 1, as well as the entanglement between atom 1 and the field. We also obtain the full analytical solution of the two-atom Tavis–Cummings model for both arbitrary coupling strengths and frequency detunings, necessary to analyse the influence of the field-environment detuning on the evolution of the system’s quantum properties. For complementarity, we discuss the role of the degree of mixedness of the environment by analysing the time-averaged linear entropy of atom 1.     

BEM analysis of crack onset and propagation along fiber–matrix interface under transverse tension using a linear elastic–brittle interface model

The behavior of the fiber–matrix interface under transverse tension is studied by means of a new linear elastic–brittle interface model. Similar models, also called weak or imperfect interface models, are frequently applied to describe the behavior of adhesively bonded joints. The interface is modeled by a continuous distribution of linear-elastic springs which simulates the presence of a thin adhesive layer (interphase). In the present work a new linear elastic–brittle constitutive law for the continuous distribution of springs is introduced. In this law the normal and tangential stresses across the undamaged interface are, respectively, proportional to the relative normal and tangential displacements. This model not only allows for the study of crack growth but also for the study of crack onset. An important feature of this law is that it takes into account the variation of the fracture toughness with the fracture mode mixity of a crack growing along the interface between bonded solids, in agreement with previous experimental results. The present linear elastic–brittle interface model is implemented in a 2D boundary element method (BEM) code to carry out micromechanical analysis of the fiber–matrix interface failure in fiber-reinforced composite materials. It is considered that the behavior of the fiber–matrix interphase can be modeled by the present model although, strictly speaking, there is usually no intermediate material between fiber and matrix. A linear-elastic isotropic behavior of both fiber and matrix is assumed, the fiber being stiffer than the matrix. The failure mechanism of an isolated fiber under transverse tension, i.e., the onset and growth of the fiber–matrix interface crack, is studied. The present model shows that failure along the interface initiates with an abrupt onset of a partial debonding between the fiber and the matrix, caused by presence of the maximum radial stress at the interface, and this debonding further develops as a crack growing along the interface.     

On coordinate-free measures of efficiency of least squares in a linear model

The efficiency of least squares in the linear model y=Xβ+u,where E(u)=0 and V(u)=Г. is considered. Several measures of efficiency have been defined for assessing the relative performance of least squares and best linear unbiased estimates of β, In this paper .far a consistent discussion, we define a doss of measures called coordinate-free measures of efficiency. Within this new framework almost all previous measures can be expressed.Examples of such measures ere given, and their meanings art examined Some results concerning same measares are also given.     

A Molecular Dynamics Simulation Study of the Self-Diffusion Coefficient and Viscosity of the Lennard–Jones Fluid

Self-diffusion coefficients and viscosities for the Lennard–Jones fluid were obtained from extensive equilibrium molecular dynamics simulations using the Einstein plot method. Over 300 simulated state points cover the entire fluid region from the low-density gas to the compressed liquid close to the melting line in the temperature range T*=Tk/=0.7 to 6.0. The translational–translational, translational–configurational, and configurational–configurational contributions to the viscosity are resolved over this broad range of fluid states, thus providing coherent insight into the nature of this transport property. The uncertainties of the simulation data are conservatively estimated to be 0.5% for self-diffusion coefficients and 2% for viscosities in the liquid region, increasing to 15% at low-density gaseous states.     

Study of linear and non-linear optical properties of In–Se doped chalcogenide semiconducting glasses

Journal of Materials Science: Materials in Electronics - The present work focuses on the various linear and non-linear optical properties of antimony (Sb) and gallium (Ga) (both 0.1 at.%) doped...     

Application of Photothermal Techniques in the Determination of the Water–Vapor Diffusion Coefficient and Thermal Effusivity of Hydrogels

The main objective of this work is to determine the effect of different sodium alginate concentrations in hydrogels on their water–vapor diffusion coefficient (WVDC) and thermal effusivity ( $e_\mathrm{s})$ . These physical parameters were measured by photoacoustic and pyroelectric techniques, respectively. The results indicate that the higher values for the WVDC are presented at a concentration of 2 % sodium alginate. At lower concentrations of sodium alginate, the sample thermal effusivity increases, with a value close to the water thermal effusivity.     

The Tl–I phase diagram revisited and the thermodynamic properties of thallium iodides

The Tl–I system has been studied using differential thermal analysis, X-ray diffraction, and emf measurements on TlI concentration cells. A more accurate Tl–I phase diagram is presented, according to which the compounds existing in the Tl–I system are TlI, Tl₂I₃, and TlI₃. Thallium monoiodide melts congruently at 715 K and undergoes a polymorphic transformation at 440 K. The other iodides melt peritectically at 535 and 404 K, respectively. In contrast to what was reported previously, no compound of composition Tl₃I₄ has been obtained. Using experimental emf data, we evaluated relative partial molar thermodynamic functions of the TlI in alloys of the TlI–I system and the standard Gibbs free energy, enthalpy of formation, and standard entropies of TlI₃ (?ΔG ₂₉₈ ⁰ = 142.79 ± 0.73 kJ/mol, ?ΔH ₂₉₈ ⁰ = 135.37 ± 2.85 kJ/mol, and S ₂₉₈ ⁰ = 263.3 ± 7.4 J/(mol K)) and Tl₂I₃ (271.39 ± 1.47, 262.40 ± 5.34, and 322.8 ± 13.2).     

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schl?gl model revisited

Schlögl''s model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.     

Analysis of the compaction behavior of Al–SiC nanocomposites using linear and non-linear compaction equations

The compressibility behavior of Al–SiC nanocomposite powders was examined and the density-pressure data were analyzed by linear and non-linear compaction equations. SiC particles with an average size of 50 nm were mixed with gas-atomized aluminum powder (40 μm average size) at different volume fractions (up to 20 vol%) and compacted in a rigid die at various pressures. In order to highlight the effect of reinforcement particle size, the compressibility of micrometric SiC particles of two sizes (1 and 40 μm) was also examined. Analysis of the compressibility data indicated hindering effect of the hard ceramic particles on the plastic deformability of soft aluminum matrix, particularly at high volume fractions. More pronounced effect on the yield pressure was obtained for the nanometric particles compared with the micrometric ones. Nevertheless, better particles rearrangement was taken place when the ultrafine SiC particles were utilized. In light of the experimental and theoretical analysis, the densification mechanism of aluminum matrix composites and the effect of reinforcement particle size and volume fraction are discussed.     

High and low cycle fatigue behavior of linear friction welded Ti–6Al–4V

Linear friction welded Ti–6Al–4V was investigated in fatigue at various stress amplitudes ranging from the high cycle fatigue (HCF) to the low cycle fatigue (LCF) regime. The base material was composed of hot-rolled Ti–6Al–4V plate that presented a strong crystallographic texture. The welds were characterized in terms of microstructure using electron backscatter diffraction and hardness measurements. The microstructural gradients across the weld zone and thermomechanically affected zone of the linear friction welds are discussed in terms of the crystallographic texture, grain shape and hardness levels, relative to the parent material. The location of crack nucleation under fatigue loading was analyzed relative to the local microstructural features and hardness gradients. Though crack nucleation was not observed within the weld or thermomechanically affected zones, its occurrence within the base material in LCF appears to be affected by the welding process. In particular, by performing high resolution digital image correlation during LCF, the crack nucleation site was related to the local accumulation of plastic deformation in the vicinity of the linear friction weld.     

Hot tensile deformation behaviors and constitutive model of an Al–Zn–Mg–Cu alloy

The hot tensile deformation behaviors of an Al–Zn–Mg–Cu alloy are studied by uniaxial tensile tests under the deformation temperature of 340–460 °C and strain rate of 0.01–0.001 s⁻¹. The effects of deformation temperature and strain rate on the hot tensile deformation behaviors and fracture characteristics are discussed in detail. The Arrhenius-type constitutive model is developed to predict the peak stress under the tested deformation condition. The results show that: (1) The true stress–true strain curves under all the tested deformation conditions are composed of four distinct stages, i.e., elastic stage, uniform deformation stage, diffusion necking stage and localized necking stage. The flow stress decreases with the increase of deformation temperature or the decrease of strain rate. (2) The elongation to fracture increases with the increase of deformation temperature. Under the tested conditions, the strain rate sensitivity coefficient varies between 0.1248 and 0.2059, which indicates that the main deformation mechanism is the lattice diffusion-controlled dislocation climb. (3) The localized necking causes the final fracture of specimens under all the deformation conditions. Microvoids coalescence is the main fracture mechanism under relatively low deformation temperatures. With the increase of deformation temperature, the intergranular fracture occurs. (4) The peak stresses predicted by the developed model well agree with the experimental results, which indicate the validity of the developed model.     

Metal solidification–nucleation–rate model under coupling effects of shearing flow and vibration

This paper proposes the influence factors of coupling effects of shearing flow and vibration on diffusion coefficient and critical nucleation energy during metal solidification. Based on this proposal, a metal solidification–nucleation–rate model under coupling effects of shearing flow and vibration is established. Verification experiment using Al–7Si alloy is carried out. When vibration frequency and melt flow velocity are zero, the results calculated by the above model agree with that calculated by Turnbull’s theory. The results calculated by the above model under coupling effects of shearing flow and vibration agree with the experimental results, with the error within 0·2–14·3%. So the established model can calculate and explain the nucleation rate of melt under coupling effects of shearing flow and vibration.     

A simulation model of the Triple Helix of university–industry–government relations and the decomposition of the redundancy

A Triple Helix (TH) network of bi- and trilateral relations among universities, industries, and governments can be considered as an ecosystem in which uncertainty can be reduced when functions become synergetic. The functions are based on correlations among distributions of relations, and therefore latent. The correlations span a vector space in which two vectors (P and Q) can be used to represent forward “sending” and reflexive “receiving,” respectively. These two vectors can also be understood in terms of the generation versus reduction of uncertainty in the communication field that results from interactions among the three bi-lateral channels of communication. We specify a system of Lotka–Volterra equations between the vectors that can be solved. Redundancy generation can then be simulated and the results can be decomposed in terms of the TH components. Furthermore, we show that the strength and frequency of the relations are independent parameters in the model. Redundancy generation in TH arrangements can be decomposed using Fourier analysis of the time-series of empirical studies. As an example, the case of co-authorship relations in Japan is re-analyzed. The model allows us to interpret the sinusoidal functions of the Fourier analysis as representing redundancies.     

Synergy of cell–cell repulsion and vacuolation in a computational model of lumen formation

A key step in blood vessel development (angiogenesis) is lumen formation: the hollowing of vessels for blood perfusion. Two alternative lumen formation mechanisms are suggested to function in different types of blood vessels. The vacuolation mechanism is suggested for lumen formation in small vessels by coalescence of intracellular vacuoles, a view that was extended to extracellular lumen formation by exocytosis of vacuoles. The cell–cell repulsion mechanism is suggested to initiate extracellular lumen formation in large vessels by active repulsion of adjacent cells, and active cell shape changes extend the lumen. We used an agent-based computer model, based on the cellular Potts model, to compare and study both mechanisms separately and combined. An extensive sensitivity analysis shows that each of the mechanisms on its own can produce lumens in a narrow region of parameter space. However, combining both mechanisms makes lumen formation much more robust to the values of the parameters, suggesting that the mechanisms may work synergistically and operate in parallel, rather than in different vessel types.     

Probabilistic model of fatigue crack propagation and estimation of probability-confidence bounded a–N curves

The fatigue crack growth model is expressed as a function of mechanical properties. The uncertainties associated with the crack growth process are incorporated assuming them as random variable following a statistical distribution. The effect of material nonhomogeneity is included in the model through a random process parameter of Gaussian type. Assuming fatigue life as a random variable, probability-confidence bounded mean crack growth relation is developed and an algorithm is presented. The model is validated through the experimental and predicted results from several data sets.     

Dedicated linear – Voce model and its application in investigating temperature and strain rate effects on sheet formability of aluminum alloys

This paper proposes a method to investigate the effects of temperature and strain rate on the forming limit curves (FLCs) by combining a modified Voce constitutive model (Lin-Voce model) with the numerical simulation of Marciniak test. The tensile tests are firstly carried out at different forming temperatures (20, 230 and 290 °C) and strain rates (2.5, 120 and 150 s⁻¹) for AA5086 sheet. A modified Voce constitutive model (named Lin-Voce model) is proposed to describe the deformation behavior of AA5086 and its material parameters are identified by inverse analysis technique. Then, the proposed constitutive model is verified by comparing numerical and experimental results obtained by tensile tests and Marciniak test, respectively. Finally, the numerical simulation of Marciniak test is carried out at different temperatures (100, 200 and 300 °C) and strain rates (2.5, 120 and 150 s⁻¹), and the effects of temperature and strain rate on the FLCs of AA5086 are investigated and discussed.     

A minimal model of predator–swarm interactions

We propose a minimal model of predator–swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a ‘weak’ predator, the swarm is able to escape the predator completely. As the strength is increased, the predator is able to catch up with the swarm as a whole, but the individual prey is able to escape by ‘confusing’ the predator: the prey forms a ring with the predator at the centre. For higher predator strength, complex chasing dynamics are observed which can become chaotic. For even higher strength, the predator is able to successfully capture the prey. Our model is simple enough to be amenable to a full mathematical analysis, which is used to predict the shape of the swarm as well as the resulting predator–prey dynamics as a function of model parameters. We show that, as the predator strength is increased, there is a transition (owing to a Hopf bifurcation) from confusion state to chasing dynamics, and we compute the threshold analytically. Our analysis indicates that the swarming behaviour is not helpful in avoiding the predator, suggesting that there are other reasons why the species may swarm. The complex shape of the swarm in our model during the chasing dynamics is similar to the shape of a flock of sheep avoiding a shepherd.     

Job Demands–Control–Support model and employee safety performance

The aim of this study was to explore whether work characteristics (job demands, job control, social support) comprising Karasek and Theorell's (1990) Job Demands–Control–Support framework predict employee safety performance (safety compliance and safety participation; Neal and Griffin, 2006). We used cross-sectional data of self-reported work characteristics and employee safety performance from 280 healthcare staff (doctors, nurses, and administrative staff) from Emergency Departments of seven hospitals in the United Kingdom. We analyzed these data using a structural equation model that simultaneously regressed safety compliance and safety participation on the main effects of each of the aforementioned work characteristics, their two-way interactions, and the three-way interaction among them, while controlling for demographic, occupational, and organizational characteristics. Social support was positively related to safety compliance, and both job control and the two-way interaction between job control and social support were positively related to safety participation. How work design is related to employee safety performance remains an important area for research and provides insight into how organizations can improve workplace safety. The current findings emphasize the importance of the co-worker in promoting both safety compliance and safety participation.