Self-propelled particles include both self-phoretic synthetic colloids and various
microorganisms. By continually consuming energy, they bypass the laws of equilibrium …

Recent theories predict phase separation among orientationally disordered active particles
whose propulsion speed decreases rapidly enough with density. Coarse-grained models of …

We present efficient, second-order accurate and adaptive finite-difference methods to solve
the regularized, strongly anisotropic Cahn–Hilliard equation in 2D and 3D. When the surface …

Mathematical and physical aspects of the applicability of the Onsager, Prigogine as well as
the Glansdorff and Ziegler thermodynamic extremal principles (TEPs) to non-equilibrium …

Rayleigh–Bénard convection in finite-size enclosures exhibits really intricate features when
turbulent states are reached and thermal plumes play a crucial role in a number of them …

In the present contribution we review basic mathematical results for three physical systems
involving self-organizing solid or liquid films at solid surfaces. The films may undergo a …

In this manuscript, singularly perturbed energies with 2, 3, or 4 preferred gradients subject to
incompatible Dirichlet boundary conditions are studied. This extends results on models for …

A new phase-field approach is designed to model surface diffusion of crystals with strongly
anisotropic surface energy. The model can be shown to asymptotically converge toward the …

We introduce a general-purpose computational geometry tool for simulating the evolution of
single-crystal, threefold-symmetric, 2+ 1D coarsening faceted surfaces z= h (x, y, t). By …

Nano-faceted crystals answer the call for self-assembled, physico-chemically tailored
materials, with those arising from a kinetically mediated response to free-energy …