Related papers: Pattern size in Gaussian fields from spinodal deco…
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before…
Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary…
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical…
Understanding the large-scale structure of the universe remains a fundamental challenge in cosmology, with computational simulations providing critical insights into non-linear structure growth. Particularly, computational simulations…
The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single…
A Cahn-Hilliard-type theory for hydrodynamic fluctuations is proposed that gives a quantitative description of the slowly evolving spatial correlations and structures in density and flow fields in the early stages of evolution of freely…
Hyperuniform structures are disordered, correlated systems in which density fluctuations are suppressed at large scales. Such a property generalizes the concept of order in patterns and is relevant across diverse physical systems. We…
Results are presented for the phase separation process of a binary mixture subject to an uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the…
We investigate numerically the influence of an homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are…
We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and…
We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when…
The order-disorder transition of a sphere-forming block copolymer thin film was numerically studied through a Cahn-Hilliard model. Simulations show that the fundamental mechanisms of pattern formation are spinodal decomposition and…
We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface…
We study the process of spinodal decomposition in a scalar quantum field theory that is quenched from an equilibrium disordered initial state at $T_i > T_f$ to a final state at $T_f \approx 0$. The process of formation and growth of…
We study spinodal decomposition and coarsening when initiated by localized disturbances in the Cahn-Hilliard equation. Spatio-temporal dynamics are governed by multi-stage invasion fronts. The first front invades a spinodal unstable…
We investigate the dynamical evolution of a thermodynamically unstable crystal surface into a hill-and-valley structure. We demonstrate that, for quasi one-dimensional ordering, the equation of motion maps exactly to the modified…
We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz…
We study the maximum norm behavior of $L^2$-normalized random Fourier cosine series with a prescribed large wave number. Precise bounds of this type are an important technical tool in estimates for spinodal decomposition, the celebrated…
An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field (vortices) and in the density field (clusters), driven by unstable fluctuations. Their spatial correlations, as measured in…
Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…