Related papers: Formation and Evolution of Target Patterns in Cahn…
We combine matrix-product state (MPS) and Mean-Field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between…
A fully three-dimensional (3D) magnetohydrodynamical (MHD) model is applied to simulate the evolution of the large-scale magnetic field in cluster galaxies interacting with the intra-cluster medium (ICM). As the model input we use a time…
The Cahn-Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss…
Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this…
We model the evolution of tokens within a deep stack of Transformer layers as a continuous-time flow on the unit sphere, governed by a mean-field interacting particle system, building on the framework introduced in (Geshkovski et al.,…
The effects of an external electric field on the formation of Liesegang patterns are investigated. The patterns are assumed to emerge from a phase separation process in the wake of a diffusive reaction front. The dynamics is described by a…
Experiments on a thin layer of cohesive wet granular matter under vertical vibrations reveal kink separated domains that collide with the container at different phases. Due to the strong cohesion arising from the formation of liquid bridges…
We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…
We present numerical simulations of the growth and saturation of the Kelvin-Helmholtz instability in a compressible fluid layer with and without a weak magnetic field. In the absence of a magnetic field, the instability generates a single…
We consider the Cahn-Hilliard equation, which models phase separation in binary fluids, on the two-dimen\-sional torus in the presence of advection by a given background shear flow, satisfying certain conditions and of sufficiently large…
Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition. Recently, SHD has been observed in confined…
The recently developed two-stage growth model of synthesis of monodispersed polycrystalline colloidal particles is utilized and improved to explain growth of uniform cadmium sulfide spheres. The model accounts for the coupled processes of…
After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant solutions, we present flow phase diagrams spanned by shear stress (or strain-rate) and concentration in the two-fluid,…
The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is…
We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between…
Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench periodic stripe patterns are generated behind the quench front.…
We show that the rate of separation of two phases of different densities (e.g. gas and solid) can be radically altered by the presence of a metastable intermediate phase (e.g. liquid). Within a Cahn-Hilliard theory we study the growth in…
Magnetic field evolution in neutron star cores is not fully understood. We describe the field evolution both for one barotropic fluid as well as two collisionally coupled barotropic fluids with different density profiles using the anelastic…
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…
Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface…