Domain growth morphology in curvature driven two dimensional coarsening

Abstract

We study the distribution of domain areas, areas enclosed by domain boundaries (''hulls''), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, $n_h(A,t)dA$, with enclosed area in the interval $(A,A+dA)$, is described, for a disordered initial condition, by the scaling function $n_h(A,t)=2c_h/(A+{\lambda }_{h}t{)}^2$, where $c_h=1/8\pi \sqrt{3}\approx 0.023$ is a universal constant and ${\lambda }_h$ is a material parameter. For a critical initial condition, the same form is obtained, with the same ${\lambda }_h$ but with $c_h$ replaced by $c_h/2$. For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form $n_d(A,t)=2c_d({\lambda }_{d}t{)}^{{\tau }^{\prime }-2}/(A+{\lambda }_{d}t{)}^{{\tau }^{\prime }}$, where $c_d=c_h+\mathcal{O}(c_h^2)$, ${\lambda }_d={\lambda }_h+\mathcal{O}(c_h)$, and ${\tau }^{\prime }=187/91\approx 2.055$. For critical initial conditions, one replaces $c_d$ by $c_d/2$ (possibly with corrections of $\mathcal{O}(c_h^2)$) and the exponent is $\tau =379/187\approx 2.027$. These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.

27 pages, 35 figures

References in corpus (10)

• Theory of Phase Ordering Kinetics
• Distribution of domain sizes in the zero temperature Glauber dynamics of the 1 D Potts model
• Exact results for curvature-driven coarsening in two dimensions
• Clusters in Simple Fluids
• Domain Statistics in Coarsening Systems
• Inter-Particle Distribution Functions for One-Species Diffusion-Limited Annihilation, A+A->0
• Fractal Structure of Spin Clusters and Domain Walls in 2D Ising Model
• Domain statistics in a finite Ising chain
• Identification of domain walls in coarsening systems at finite temperature
• Stress-free Spatial Anisotropy in Phase-Ordering

Cited by in corpus (57)

• Kibble-Zurek mechanism and infinitely slow annealing through critical points
• Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation
• Quench dynamics of the 2d XY model
• Fate of 2D Kinetic Ising Ferromagnets and Critical Percolation Crossing Probabilities
• Diffusive Domain Coarsening : Early Time Dynamics and Finite-Size Effects
• Curvature-driven coarsening in the two dimensional Potts model
• Geometry of phase separation
• Fragmentation and Limits to Dynamical Scaling in Viscous Coarsening: An Interrupted in situ X-Ray Tomographic Study
• Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model
• How soon after a zero-temperature quench is the fate of the Ising model sealed?
• Topics in coarsening phenomena
• Simple rules govern the patterns of Arctic sea ice melt ponds
• Experimental test of curvature-driven dynamics in the phase ordering of a two dimensional liquid crystal
• Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model
• Geometric properties of two-dimensional coarsening with weak disorder
• Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line
• Critical percolation in the dynamics of the 2d ferromagnetic Ising model
• Frozen into stripes: fate of the critical Ising model after a quench
• Exact Algorithm for Sampling the 2D Ising Spin Glass
• Coarsening and percolation in a disordered ferromagnet
• Geometrical properties of Potts model during the coarsening regime
• Persistence in the two dimensional ferromagnetic Ising model
• Defects dynamics following thermal quenches in square spin-ice
• Effective mobility and diffusivity in coarsening processes
• Finite-Size Scaling Study of Aging during Coarsening in Non-Conserved Ising Model: The case of zero temperature quench
• Zero-Temperature Coarsening in the 2d Potts Model
• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Percolation and coarsening in the bidimensional voter model
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Coarsening and percolation in the kinetic $2d$ Ising model with spin exchange updates and the voter model
• Critical percolation in the slow cooling of the bi-dimensional ferromagnetic Ising model
• Thermal quenches in the stochastic Gross-Pitaevskii equation: morphology of the vortex network
• Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation
• Limiting Shapes of Ising Droplets, Ising Fingers, and Ising Solitons
• Domain-area distribution anomaly in segregating multicomponent superfluids
• Topological symmetry breaking in viscous coarsening
• Slicing the $3d$ Ising model: critical equilibrium and coarsening dynamics
• Critical Langevin dynamics of the O(N)-Ginzburg-Landau model with correlated noise
• Non-Analytic Non-Equilibrium Field Theory: Stochastic Reheating of the Ising Model
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Voter models with conserved dynamics
• Pattern formation and coarsening dynamics in apparent competition models
• Phase separation and critical percolation in bidimensional spin-exchange models
• Fractal character of the phase ordering kinetics of a diluted ferromagnet
• Dynamical cluster size heterogeneity
• Phase instability and coarsening in two dimensions
• Fate of Ising ferromagnets and antiferromagnets by zero-temperature Glauber dynamics on the two-dimensional Archimedean and 2-uniform lattices
• Opinion inertia and coarsening in the Persistent Voter model
• Critical percolation in the ordering kinetics of twisted nematic phases
• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model
• High-degeneracy Potts coarsening
• Critical clusters in liquid crystals: Fractal geometry and conformal invariance
• Coarsening and percolation in the Ising Model with quenched disorder
• Spatial dynamics of synergistic coinfection in rock-paper-scissors models
• On internal structure of smaller domains in domain coarsening dynamics of spontaneous Z_2-symmetry breaking in two dimensions
• Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet
• Methods for detecting Order-by-Disorder transitions: the example of the Domino model