A four-field three-phase flow model with both miscible and immiscible components

A three-phase flow model with hybrid miscibility constraints is proposed: three immiscible phases are considered (liquid, solid and gas) but the gaseous phase is composed with two miscible components (steam water and non-condensable gas). The modelling approach is based on the building of an entropy inequality for the system of partial dfferential equations: once an interfacial velocity is given by the user, the model is uniquely defined, up to some relaxation time scales, and source terms complying with the second principle of thermodynamics can then be provided. The convective part of the system is hyperbolic when fulfilling a non-resonance condition and classical properties are studied (Riemann invariants, symmetrization). A key property is that the system possesses uniquely defined jump conditions. Last, preservation of thermodynamically admissible states and pressure relaxation are investigated.

Examining the link between relaxed predation and bird coloration on islands

Insular ecosystems share analogous ecological conditions, leading to patterns of convergent evolution that are collectively termed as the ‘island syndrome’. In birds, part of this syndrome is a tendency for a duller plumage, possibly as a result of relaxed sexual selection. Despite this global pattern, some insular species display a more colourful plumage than their mainland relatives, but why this occurs has remained unexplained. Here, we examine the hypothesis that these cases of increased plumage coloration on islands could arise through a relaxation of predation pressure. We used comparative analyses to investigate whether average insular richness of raptors of suitable mass influences the plumage colourfulness and brightness across 110 pairs of insular endemic species and their closest mainland relatives. As predicted, we find a likely negative relationship between insular coloration and insular predation while controlling for mainland predation and coloration, suggesting that species were more likely to become more colourful as the number of insular predators decreased. By contrast, plumage brightness was not influenced by predation pressure. Relaxation from predation, together with drift, might thus be a key mechanism of species phenotypic responses to insularity.

Numerical simulation of shock wave – dense particles cloud interaction using Godunov solver for Baer–Nunziato equations

Purpose This paper aims to clarify some aspects of the application of the Godunov method for the Baer–Nunziato equations solution on the example of the problem of shock wave – dense particles cloud interaction. Design/methodology/approach The statement of the problem corresponds to the natural experiment. Mathematical model is based on the Baer–Nunziato system of equations with algebraic right-hand side source terms that takes into account the interphase friction force. Two numerical approaches are used: Harten-Lax-van Leer method and Godunov method. Findings For the robust simulation using Godunov method, the application of the pressure relaxation procedure is proposed. The comparative analysis of the simulation results using two methods is carried out. The Godunov method provides significantly smaller numerical diffusion of the solid phase volume fraction in the cloud that leads to the much better agreement of the pressure curves on transducers and the dynamics of the cloud motion with the experimental data. Originality/value Godunov method for the Baer–Nunziato equations is applied for the simulation of the natural experiment on the shock wave particles cloud interaction. Up to now, the examples of the application of the Godunov method for the Baer–Nunziato equations to the investigation of the practical problems have been limited by the works of the authors of the method and the field of detonation in the heterogeneous explosives. For the robust simulations in the presence of interphase boundaries, it is proposed to use the Godunov method together with the pressure relaxation procedure.

The relaxation of residual inclusion pressure and implications to Raman-thermobarometry

Residual pressure can be preserved in mineral inclusions, e.g. quartz-in-garnet, after exhumation due to differential expansion between inclusion and host crystals. Raman spectroscopy has been applied to infer the residual pressure and provides information on the entrapment temperature and pressure conditions. However, the amount of residual pressure relaxation cannot be directly measured. An underestimation of pressure relaxation may lead to significant errors between calculated and actual entrapment pressure. This study focuses on three mechanisms responsible for the residual-pressure relaxation: 1) viscous creep; 2) plastic yield; 3) proximity of inclusion to thin-section surface. Criteria are provided to quantify how much of the expected residual pressure is relaxed due to these three mechanisms. An analytical solution is introduced to demonstrate the effect of inclusion depth on the residual pressure field when the inclusion is close to thin-section surface. It is shown that for quartz-in-garnet system, the distance between thin-section surface and inclusion centre needs to be at least two times the inclusion radius to avoid pressure relaxation. In terms of viscous creep, representative case studies on quartz-in-garnet system show that viscous relaxation may occur from temperatures as low as 600∼700 °C depending on the particular P-T path and various garnet compositions. For quartz entrapped along the prograde P-T path and subject to viscous resetting at peak T above 600∼700 °C, its residual pressure after exhumation may be higher than predicted from its true entrapment conditions. Moreover, such a viscous resetting effect may introduce apparent overstepping of garnet nucleation that is not related to reaction affinity.