相关论文: Towards analytical solutions of the alloy solidifi…
We model buoyancy-driven convection with chimneys -- channels of zero solid fraction -- in a mushy layer formed during directional solidification of a binary alloy in two-dimensions. A large suite of numerical simulations is combined with…
We consider local solutions of the two-phase Stefan problem with a "mushy" region. We show that if a (distributional) solution u is locally square integrable then the temperature is continuous.
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical…
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to…
We take a numerical approach to analyze the mechanisms controlling the spacing of chimneys -- channels devoid of solid -- in two-dimensional mushy layers formed by solidifying a binary alloy. Chimneys are the principal conduits through…
The simultaneous determination of two unknown thermal coefficients for a semi-infinite material under a phase-change process with a mushy zone according to the Solomon-Wilson-Alexiades model is considered. The material is assumed to be…
Planar solidification from an undercooled melt has been considered using the phase-field model. The solute and the phase fields have been found in the limit of small impurity concentration. These solutions in the limit of vanishing velocity…
In this paper a 3-phase Stefan problem solution method for 1D semi-infinity alloy is developed. The problem is first solved for full enthalpy of the system and then the thermal diffusivity has been eliminated from the divergence operator by…
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…
In this paper, we present a mathematical and numerical model for blood solidification and its rupture in stenosed arteries. The interaction between the blood flow and an existing stenosis in the arterial wall is modeled as a three…
We introduce a new phase-field formulation of rapid alloy solidification that quantitatively incorporates nonequilibrium effects at the solid-liquid interface over a very wide range of interface velocities. Simulations identify a new…
Many alloys made by Additive Manufacturing (AM) require careful design of post-heat treatment as an indispensable step of microstructure engineering to further enhance the performance. We developed a high-throughput approach by fabricating…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue,…
Treating a boundary value problem in analytical fluid dynamics, translation of 2D steady Navier-Stokes equations to ordinary differential form leads to a second order equation of Riccati type. In the case of a compressible fluid with…
This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial…
Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively…
In this study, novel exact solutions of the Duffing equation with their phase portraits have been proposed and reasoned. It is shown that phase trajectories are initially elliptical and become distorted in the unstable area within the…
We present an approach to calculate the atomic bulk solubility in binary alloys based on the statistical-thermodynamic theory of dilute lattice gas. The model considers all the appropriate ground states of the alloy and results in a simple…