A vortex–wave interaction theory describing the effect of boundary forcing on shear flows

A strongly nonlinear theory describing the effect of small amplitude boundary forcing in the form of waves on high Reynolds number shear flows is given. The interaction leads to an $O(1)$ change in the unperturbed flow and is relevant to a number of forcing mechanisms. The cases of the shear flow being bounded or unbounded are both considered and the results for the unbounded case apply to quite arbitrary flows. The instability criterion for unbounded flows is expressed in terms of the wall forcing and the friction Reynolds number. As particular examples we investigate wall transpiration or surface undulations as sources of the forcing and both propagating and stationary waves are considered. Results are given for propagating waves with crests perpendicular to the flow direction and for stationary waves with crests no longer perpendicular to the flow direction. In the first of those situations we find the instability induced by transpiration waves is independent of the propagation speed. For wavy walls downstream propagation completely stabilises the flow at a critical speed whereas upstream propagation greatly destabilises the flow. For stationary oblique waves we find that the instability is enhanced and a much wider range of unstable wavenumbers exists. For the bounded case with a wall of fixed wavelength we identify a critical wavelength where the most dangerous mode switches from the aligned to the oblique configuration. For the transpiration problem in the oblique configuration a strong resonance occurs when the vortex wavelength coincides with the spanwise wavelength of the forcing.

Pattern formation from spatially heterogeneous reaction–diffusion systems

First proposed by Turing in 1952, the eponymous Turing instability and Turing pattern remain key tools for the modern study of diffusion-driven pattern formation. In spatially homogeneous Turing systems, one or a few linear Turing modes dominate, resulting in organized patterns (peaks in one dimension; spots, stripes, labyrinths in two dimensions) which repeats in space. For a variety of reasons, there has been increasing interest in understanding irregular patterns, with spatial heterogeneity in the underlying reaction–diffusion system identified as one route to obtaining irregular patterns. We study pattern formation from reaction–diffusion systems which involve spatial heterogeneity, by way of both analytical and numerical techniques. We first extend the classical Turing instability analysis to track the evolution of linear Turing modes and the nascent pattern, resulting in a more general instability criterion which can be applied to spatially heterogeneous systems. We also calculate nonlinear mode coefficients, employing these to understand how each spatial mode influences the long-time evolution of a pattern. Unlike for the standard spatially homogeneous Turing systems, spatially heterogeneous systems may involve many Turing modes of different wavelengths interacting simultaneously, with resulting patterns exhibiting a high degree of variation over space. We provide a number of examples of spatial heterogeneity in reaction–diffusion systems, both mathematical (space-varying diffusion parameters and reaction kinetics, mixed boundary conditions, space-varying base states) and physical (curved anisotropic domains, apical growth of space domains, chemicalsimmersed within a flow or a thermal gradient), providing a qualitative understanding of how spatial heterogeneity can be used to modify classical Turing patterns. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

Research on the Hot Deformation Behavior of the Casting NiTi Alloy

The hot deformation behavior and processing maps of the casting NiTi alloy were studied at the deformation temperature of 650–1050 °C and the strain rate of 5 × 10−3–1 s−1 by Gleeble-3800 thermal simulating tester. The variation of the strain rate sensitivity exponent m and the activation energy Q under different deformation conditions (T = 650–1050 °C, ε˙ = 0.005–1 s−1) were obtained. The formability of the NiTi alloy was the best from 800 °C to 950 °C. The constitutive equation of the casting NiTi alloy was constructed by the Arrhenius model. The processing map of the casting NiTi alloy was plotted according to the dynamic material model (DMM) based on the Prasad instability criterion. The optimal processing areas were at 800–950 °C and 0.005–0.05 s−1. The microstructure of the casting NiTi alloy was analyzed by TEM, SEM and EBSD. The softening mechanisms of the casting NiTi alloy were mainly dynamic recrystallization of the Ti2Ni phase and the nucleation and growth of fine martensite.

Prediction of Crack Initiation Based on Energy Storage Rate during Low-Cycle Fatigue of Austenitic Stainless Steel

The low-cycle deformation of 304L austenitic stainless steel was examined in terms of energy conversion. Specimens were subjected to cyclic loading at the frequency of 2 Hz. The loading process was carried out in a hybrid strain–stress manner. In each cycle, the increase in elongation of the gauge part of the specimen was constant. During experimental procedures, infrared and visible-range images of strain and temperature fields were recorded simultaneously using infrared thermography (IR) and digital image correlation (DIC) systems. On the basis of the obtained test results, the energy storage rate, defined as the ratio of the stored energy increment to the plastic work increment, was calculated and expressed in reference to selected sections of the specimen. It was shown that, before the specimen fracture in a specific area, the energy storage rate is equal to zero (the material loses the ability to store energy), and the energy stored during the deformation process is released and dissipated as heat. Negative and close-to-zero values of the energy storage rate can be used as a plastic instability criterion on the macroscale. Thus, the loss of energy storage ability by a deformed material can be treated as an indicator of fatigue crack initiation.

Study on Web Pillar Stability in Open-Pit Highwall Mining

When highwall mining technology is applied to recover large amounts of residual coal left under the highwall of a big open-pit mine, reasonable coal pillar width is the premise for maintaining the stability of web pillars. By adopting the numerical simulation method, the characteristics of the abutment stress distributions in the web pillars under different slope angles and mining depths are studied, and the function of the stress distribution in the web pillar is established. The relationship between the abutment stress and the ultimate strength of the web pillar under different widths is also analyzed and used in combination with the failure characteristics of the pillar yield zone to explore the instability mechanism of the web pillar. The retaining widths of the web pillars are determined. Based on the modeling results, a mechanical bearing model of the web pillar is established, a cusp catastrophe model of pillar-overburden is constructed, and the formula for the web pillar instability criterion is obtained. By analyzing and calculating the ultimate strength of the web pillar, the formula for calculating the yield zone width at both sides of the pillar is achieved. Using the instability criterion of web pillars in highwall mining, a reasonable pillar width can be deduced theoretically, which provides significant guidance on the application of highwall mining technology.

Transverse Thermal Instability of Radiative Plasma with FLR Corrections for Star Formation in ISM

Impact of porosity, rotation and finite ion Larmor radius (FLR) corrections on thermal instability of immeasurable homogeneous plasma has been discovered incorporating the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is carried out with the help of the normal mode analysis scheme taking the suitable linearized perturbation equations of the difficulty. This general dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field. Thermal instability criterion establishes the stability of the medium. Mathematical calculations have been performed to represent the impact of different limitations on the growth rate of thermal instability. It is found that rotation, FLR corrections and medium porosity stabilize the growth rate of the medium in the transverse mode of propagation. Our outcome of the problem explains that the rotation, porosity and FLR corrections affect the dens molecular clouds arrangement and star configuration in interstellar medium.

Instability of the printing jet during the three-dimensional-printing process

Euler’s instability criterion is widely used in engineering to design a column. However, this criterion is not suitable for judging the instability of a three-dimensional printing process because the axial motion of the printing jet has to be considered. A variational principle is established, and an equivalent Eulerian load is obtained. The theoretical results show that a higher printing velocity makes the moving jet much more stable, and an experiment is designed to verify our theoretical prediction.