Over the last decade major progress has been made in developing both theoretical and practical aspects of apatite (U–Th)/He thermochronometry it is now standard practice, generally seen as best to analyse single grain aliquots. These individual prismatic crystals are often broken fragments larger that have during mineral separation along weak basal cleavage apatite. This clearly indicated by common occurrence only 1 or no clear crystal terminations present on separated grains, evidence...

We describe a new numerical inversion approach to deriving thermal history information from range of naturally dispersed single grain apatite (U–Th)/He ages. The explicitly exploits the about shape 4He diffusion profile within individual grains that is inherent in pattern dispersion arises common and routine practice analysing broken crystals. Additional arising differences size U Th concentration grains, resultant changes helium diffusivity caused by differential accumulation annealing...

In this paper we study an inverse problem in convex geometry, inspired by a materials science. Firstly, consider the question of whether Laguerre tessellation (a partition polytopes) can be recovered from only volumes and centroids its cells. We show that has unique solution give constructive way computing it using optimal transport theory optimisation. Secondly, fitting to synthetic volume centroid data. Given some target centroids, seek such difference between cells is minimised. For...

We study steady vertical propagation of a crack filled with buoyant viscous fluid through an elastic solid large effective fracture toughness. For fed by constant flux Q , non-dimensional toughness K = c /(3μ Qm 3 /2) 1/4 describes the relative magnitudes resistance to and flow, where is dimensional toughness, μ viscosity m modulus. Even in limit ≫ 1, rate determined effects. In this requires behind tip form teardrop-shaped head length O ( 2/3 ) width 4/3 ), which much narrower tail. head,...

Understanding the dynamics of growth nanowires by vapor-liquid-solid (VLS) process is essential in order to relate properties wire their processing conditions. A theory for VLS developed that incorporates surface energy solid-liquid, liquid-vapor, and solid-vapor interfaces, allows supersaturation material droplet, employs contact-line We predict profile catalyst concentration degree supersaturation, modification shape solid-liquid interface due growth, as functions parameters. Under typical...

This paper studies dissection propagation subject to internal pressure in a residually-stressed two-layer arterial model. The artery is assumed be infinitely long, and the resultant plane strain problem solved using extended finite element method. layers are modelled anisotropic hyperelastic Holzapfel–Gasser–Ogden model, tissue damage due tear described linear cohesive traction–separation law. Residual stress wall determined by an opening angle $$\alpha $$ stress-free configuration. An...

An arterial dissection is a longitudinal tear in the vessel wall, which can create false lumen for blood flow and may propagate quickly, leading to death. We employ computational model using extended finite element method with cohesive traction-separation law faces. The wall described by anisotropic hyperelastic Holzapfel–Gasser–Ogden material that accounts collagen fibres ground matrix, while evolution of damage governed linear law. simulate propagation both peeling pressure-loading tests....

The propagation of a liquid-filled crack from an over-pressured source into semi-infinite uniform elastic solid is studied. fluid lighter than the and propagates due to its buoyancy over-pressure. role this over-pressure at early late times considered it found that combination leads significantly different behaviour or alone. Lubrication theory used describe flow, where pressure in determined by deformation presence crack. Numerical results for evolution shape speed are obtained. grows...

The requirements for steady nanowire growth under near-equilibrium conditions in the vapor-liquid-solid (VLS) method is examined with particular emphasis on configuration of liquid droplet. It found that final radius a cylindrical wire selected by fixed volume VL and surface-energy ratio γsl/γlv but independent solid-vapor energy γsv. Existing models growth, based balance configurational forces at triple junction, are shown to be consistent principle maximal release free energy. Gibbs’s...

In this paper we develop a numerical method for solving class of optimization problems known as optimal location or quantization problems. The target energy can be written either in terms atomic measures and the Wasserstein distance weighted points power diagrams (generalized Voronoi diagrams). latter formulation is more suitable computation. We show that critical are centroidal diagrams, which generalizations tessellations, they approximated by generalization Lloyd's algorithm (Lloyd's...

The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape individual grains. One major obstacle to wider adoption APDs is computational cost that associated their generation. We propose a novel approach generate prescribed statistical properties, including fine size To this end, we rely on fast optimal transport algorithms stream well Graphics Processing Units (GPU) handle non-uniform, distance functions....

We study the dynamics of a mushy layer in directional solidification for case thin near-eutectic mush with deformable and permeable mush–liquid interface. examine onset convection using linear stability analysis, weakly nonlinear growth liquid inclusions that signal chimneys. This analysis is compared to past analyses which interface replaced by rigid impermeable lid. find qualitative agreement between two models, but rigid-lid approximation gives substantially different quantitative...

Thinning rates of liquid lamellae in surfactant-free non-Newtonian gas–liquid foams, appropriate for ceramic or polymer melts and also metals near the melting point, are derived two dimensions by matched asymptotic analysis valid at small capillary number. The viscosity is modelled (i) as a power-law function shear rate (ii) Ellis law. Equations governing interface dynamics variations within lamellar, transition plateau border regions corner surrounding gas bubble. results show that varies...

In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer melts with dominant phase. The is simple enough to be amenable not only numerics but also analysis, yet sophisticated reproduce hexagonally packed structures that resemble the cylinder observed block experiments. Starting from sharp-interface continuum model, nonlocal energy functional involving Wasserstein cost, derive using Gamma-convergence limit where volume fraction of one phase tends zero....

We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used creating RVEs polycrystalline materials computational homogenisation, or fitting to EBSD XRD measurements metals. Given list desired cell we solve convex optimisation problem find diagram these up any prescribed tolerance. The is built on tools from geometry and optimal transport theory which, as far are aware, have not been applied microstructure modelling before. illustrate the speed...

It is known that freckles form at the sidewalls of directionally solidified materials. We present a weakly nonlinear analysis effects weak and slowly varying background flow formed by non-axial thermal gradients on convection near onset in mushy layer. find two-dimensional case, mush occurs away from walls. However if three-dimensional disturbances are allowed, walls container confining mush. derive amplitude equations governing this behaviour simulate their evolution numerically.

In this paper, we present a new approach based on combination of the Arnoldi and frontal methods for solving large sparse asymmetric generalized complex eigenvalue problems. The eigensolver seeks most unstable eigensolution in Krylov subspace makes use efficiency solver developed finite element methods. is used stability analysis flows collapsible channel found to significantly improve computational compared traditionally QZ or standard method. With approach, are able validate previous...

The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape individual grains. One major obstacle to wider adoption APDs is computational cost that associated their generation. We propose a novel approach generate prescribed statistical properties, including fine size To this end, we rely on fast optimal transport algorithms stream well Graphics Processing Units (GPU) handle non-uniform, distance functions....

In this paper we study an inverse problem in convex geometry, inspired by a materials science. Firstly, consider the question of whether Laguerre tessellation (a partition polytopes) can be recovered from only volumes and centroids its cells. We show that has unique solution give constructive way computing it using optimal transport theory optimisation. Secondly, fitting to synthetic volume centroid data. Given some target centroids, seek such difference between cells is minimised. For...

In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer melts with dominant phase. The is simple enough to be amenable not only numerics but also analysis, yet sophisticated reproduce hexagonally packed structures that resemble the cylinder observed block experiments. Starting from sharp-interface continuum model, nonlocal energy functional involving Wasserstein cost, derive using Gamma-convergence limit where volume fraction of one phase tends zero....

We present a new implementation of the geometric method Cullen & Purser (1984) for solving semi-geostrophic Eady slice equations which model large scale atmospheric flows and frontogenesis. The is Lagrangian discretisation, where PDE approximated by particle system. An important property discretisation that it energy conserving. restate in language semi-discrete optimal transport theory exploit this to develop fast combines latest results from numerical with novel adaptive time-stepping...

In this paper we describe a fast algorithm for generating periodic RVEs of polycrystalline materials. particular, use the damped Newton method from semi-discrete optimal transport theory to generate 3D Laguerre tessellations (or power diagrams) with cells given volumes. Complex, polydisperse up 100,000 grains prescribed volumes can be created in few minutes on standard laptop. The relies Hessian objective function, which derive by extending recent results setting.