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Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…

Analysis of PDEs · Mathematics 2025-02-25 S. Kiana Naghibzadeh , Anthony Rollett , Noel Walkington , Kaushik Dayal

Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models coupled with the Navier-Stokes equations are widely used to…

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…

Disordered Systems and Neural Networks · Physics 2026-01-01 A. D. Berezner , V. A. Fedorov , N. S. Perov , G. V. Grigoriev

We study how solidification of model freely rotating polymers under athermal quasistatic compression varies with their bond angle $\theta_0$. All systems undergo two discrete, first-order-like transitions: entanglement at $\phi =…

Soft Condensed Matter · Physics 2020-05-01 Joseph D. Dietz , Robert S. Hoy

We study phase segregation in a model alloy undergoing both ordering and decomposition, using computer simulations of Kawasaki exchange dynamics on a square lattice. Following a quench into the miscibility gap we observe an early stage in…

Statistical Mechanics · Physics 2009-10-30 V. Gorentsveig , P. Fratzl , J. L. Lebowitz

Laser-based additive manufacturing offers a promising route for 3D printing of metallic parts. We evidence experimentally a particular columnar solidification microstructure in a Laser Powder-Bed Fusion processed Inconel 718 nickel-based…

Materials Science · Physics 2019-01-23 G. Boussinot , M. Apel , J. Zielinski , U. Hecht , J. H. Schleifenbaum

The thermal decomposition behavior, the microstructural evolution and its influence on the mechanical properties of a supersaturated Cu Co solid solution with ~100 nm average grain size prepared by severe plastic deformation is investigated…

Materials Science · Physics 2016-11-07 Andrea Bachmaier , Marina Pfaff , Moritz Stolpe , Hisham Aboulfadl , Christian Motz

The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…

Materials Science · Physics 2015-06-05 Hervé Henry , Jesper Mellenthin , Mathis Plapp

This study aimed to explore and develop a new material with high cost-effectiveness, excellent strength, light weight, high hardness, great wear resistance, corrosion resistance, and favorable oxidation resistance. Structural analysis…

Applied Physics · Physics 2020-11-06 Junfeng Wang , Xinran Wang , Zhihao Huang , Ting Li , Yudong Fu

For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…

Numerical Analysis · Mathematics 2021-04-07 Jan Helmig , Fabian Key , Marek Behr , Stefanie Elgeti

Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…

Statistical Mechanics · Physics 2014-08-27 L. S. Metlov

The evaluation of phase stabilities of unstable elemental phases is a long-standing problem in the computational assessment of phase diagrams. Here we tackle this problem by explicitly calculating phase diagrams of intermetallic systems…

Materials Science · Physics 2016-09-20 Shmuel Barzilai , Cormac Toher , Stefano Curtarolo , Ohad Levy

Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…

Materials Science · Physics 2007-05-23 Mathieu Bouville , Shenyang Hu , Long-Qing Chen , Dongzhi Chi , David J Srolovitz

For two-dimensional many-particle systems first-order, second-order, single step continuous, as well as two-step continuous (KTHNY-like) melting transitions have been found in previous studies. Recent computer simulations, using particle…

Materials Science · Physics 2014-06-23 Aranka Derzsi , Kovács Anikó Zsuzsa , Zoltán Donkó , Peter Hartmann

The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…

Materials Science · Physics 2015-10-23 A. V. Khomenko , D. S. Troshchenko , L. S. Metlov

We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary…

Materials Science · Physics 2009-11-10 R. Folch , M. Plapp

The phase stability of fcc and bcc magnetic binary Fe-Cr, Fe-Ni, Cr-Ni alloys and ternary Fe-Cr-Ni alloys is investigated using a combination of density functional theory (DFT), Cluster Expansion (CE) and Magnetic Cluster Expansion (MCE).…

Materials Science · Physics 2015-02-03 Jan S. Wrobel , Duc Nguyen-Manh , Mikhail Yu. Lavrentiev , Marek Muzyk , Sergei L. Dudarev

The Cahn--Hilliard equations are a versatile model for describing the evolution of complex morphologies. In this paper we present a computational pipeline for the numerical solution of a ternary phase-field model for describing the…

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that…

Materials Science · Physics 2009-11-10 Jean-Marc Debierre , Alain Karma , Franck Celestini , Rahma Guerin

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the…

Materials Science · Physics 2015-05-18 Gyula I. Tóth , György Tegze , Tamás Pusztai , László Gránásy