Related papers: Anisotropic liquid drop models
In this paper, we prove the existence of classical solutions for the anisotropic surface diffusion with elasticity in the plane using a minimizing movements scheme, provided that the initial set is sufficiently regular. This scheme is…
Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviors contingent on field strength and material properties. These…
In this work we study the influence of isotropic and anisotropic fluids on the spherically symmetric warp metric. We evaluate the energy conditions and the influence of including a cosmological constant type term. We find that, considering…
Droplet impact on solid surfaces is a fluid phenomenon widely involved in additive manufacturing, heat management, and coating, in which the ability to exert control over the impact dynamics and duration is critical. While past studies have…
We study surfaces with constant anisotropic mean curvature which are invariant under a helicoidal motion. For functionals with axially symmetric Wulff shapes, we generalize the recently developed twizzler representation of Perdomo to the…
The liquid drop model was introduced by Gamow in 1928 and Bohr-Wheeler in 1938 to model atomic nuclei. The model describes the competition between the surface tension, which keeps the nuclei together, and the Coulomb force, corresponding to…
In this paper we study the morphology of drops formed on partially wetting substrates, whose footprint is not circular. This type of drops is a consequence of the breakup processes occurring in thin films when anisotropic contact line…
Quantitative stability for crystalline anisotropic perimeters, with control on the oscillation of the boundary with respect to the corresponding Wulff shape, is proven for $n\geq 3$. This extends a result of [Neu16] in $n=2$.
We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also…
We study uniaxial energy-minimizers within the Landau-de Gennes theory for nematic liquid crystals on a three-dimensional spherical droplet subject to homeotropic boundary conditions. We work in the low-temperature regime and show that…
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations…
The structural and interfacial properties of a nanoscopic liquid drops are assessed by means of mechanical, thermodynamical, and statistical mechanical approaches that are discussed in detail, including original developments at both the…
Reduced fluid models for collisionless plasmas including electron inertia and finite Larmor radius corrections are derived for scales ranging from the ion to the electron gyroradii. Based either on pressure balance or on the…
We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features…
Inspired by recent works on the threshold dynamics scheme for multi-phase mean curvature flow (by Esedo\={g}lu-Otto and Laux-Otto), we introduce a novel framework to approximate solutions of the Muskat problem with surface tension. Our…
A numerical model is proposed to simulate the adhesion, compression, and subsequent detachment of a micro-liter droplet from a superhydrophobic surface composed of chemically homogeneous pillars arranged in a periodic fashion, replicating a…
The early stages of drop impact onto a solid surface are considered. Detailed numerical simulations and detailed asymptotic analysis of the process reveal a self-similar structure both for the velocity field and the pressure field. The…
We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is…
Inspired by a planar partitioning problem involving multiple improper chambers, this article investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint…
The recent literature has intensively studied two classes of nonlocal variational problems, namely the ones related to the minimisation of energy functionals that act on functions in suitable Sobolev-Gagliardo spaces, and the ones related…