On the stiffness of surfaces with non-Gaussian height distribution

In this work, the stiffness, i.e., the derivative of the load-separation curve, is studied for self-affine fractal surfaces with non-Gaussian height distribution. In particular, the heights of the surfaces are assumed to follow a Weibull distribution. We find that a linear relation between stiffness and load, well established for Gaussian surfaces, is not obtained in this case. Instead, a power law, which can be motivated by dimensionality analysis, is a better descriptor. Also unlike Gaussian surfaces, we find that the stiffness curve is no longer independent of the Hurst exponent in this case. We carefully asses the possible convergence errors to ensure that our conclusions are not affected by them.

Molecular Dynamics-Based Cohesive Zone Model for Mg/Mg17Al12 Interface

The fracture of the Mg/Mg17Al12 interface was investigated by molecular dynamics simulations. The interface crack extends in a brittle manner without noticeable plasticity. The distributions of normal stress and separation along the interface were examined to render a quantitative picture of the fracture process. A normal traction–separation curve was extracted from simulation and compared with three cohesive zone models, i.e., cubic polynomial cohesive zone model, exponential cohesive zone model, and bilinear cohesive zone model. The exponential cohesive zone model exhibits the best agreement with simulation results, followed by the bilinear cohesive zone model.

Critical adsorption of multiple polyelectrolytes onto a nanosphere: splitting the adsorption–desorption transition boundary

Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption—the phase-separation curve between the adsorbed and desorbed states of the PEs—as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE–SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption–desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.

Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems

This paper deals with a kind of piecewise smooth equation which is linear in the dependent variable. We study the problem of lower bounds for the maximum number of limit cycles of such equations using Melnikov functions. First of all, using the first order Melnikov function, we prove that these differential equations have a sharp upper bound for the number of the limit cycles which bifurcate from the periodic orbits and cross the separation straight line. Furthermore, in some cases the maximum number of these limit cycles is three, up to any order analysis. In the end, we apply this result on a kind of piecewise smooth planar system which has a separation curve with [Formula: see text] up to homomorphism.

Tensile fracture of a single crack in first-year sea ice

The break-up of sea ice in the Arctic and Antarctic has been studied during three field trips in the spring of 1993 at Resolute, NWT, and the fall of 2001 and 2004 on McMurdo Sound via in situ cyclic loading and fracture experiments. In this paper, the back-calculated fracture information necessary to the specification of an accurate viscoelastic fictitious (cohesive) crack model is presented. In particular, the changing shape of the stress separation curve with varying conditions and loading scenarios is revealed. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

Justification of the air separation curve

The article considers a method for increasing the production efficiency of fine powders. It is shown that modern air separators do not have high efficiency. A method for increasing the efficiency of air separators is proposed. It is noted that the main characteristic of the separation process is the separation curve, with the help of which a dispersed composition of fine and coarse products can be found. The calculation is made taking into account the turbulent diffusion of separation air in the casing of the air separator, and also the constructive features of the separator in question. The separation function is proposed taking into account the proposed technical solution.