Related papers: Willmore regularized sharp-interface model for str…
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the…
We consider a closed Willmore surface properly immersed in ${\R}^m$ (m>2) with square-integrable second fundamental form, and with one point-singularity of finite arbitrary integer order. Using the "conservative" reformulation of the…
Isoscalar and isovector particle densities are derived analytically by using the approximation of a sharp edged nucleus within the local energy density approach with the proton-neutron asymmetry and spin-orbit effects. Equations for the…
Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as…
Solid-state dewetting is the process by which thin solid films break up and retract on a substrate, forming nanostructures. While dewetting of single-crystalline films is understood as a surface-energy-driven process mediated by surface…
We study isometric immersions of a Riemannian surface $(\Omega,\frak{g})$, where $\Omega \subset \mathbb{R}^2$, into $\mathbb{R}^3$. We consider their bending energy, i.e., the square of the $L^2$-norm of their second fundamental form,…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary…
Experimental determination of absolute surface energies remains a challenge. We propose a simple method based on two independent measurements on 3D and 2D equilibrium shapes completed by the analysis of the thermal fluctuation of an…
We study the sublevel sets of the Willmore energy on the space of smoothly immersed $ 2 $-spheres in Euclidean $ 3 $-space. We show that the subset of immersions with energy at most $ 12\pi $ consists of four regular homotopy classes.…
A study of properties of the symmetry energy of nuclei is presented based on density functional theory. Calculations for finite nuclei are given so that the study includes isospin dependent surface symmetry considerations as well as isospin…
The significance of wettability between solid and liquid substances in different fields encourages scientists to develop accurate models to estimate the resultant apparent contact angles. Surface free energy (SFE), which is principally…
In the framework of nuclear energy density functional (EDF) methods, many nuclear phenomena can be related to the deformation of intrinsic states. Their accurate modeling relies on the correct description of the change of nuclear binding…
Solid-state dewetting phenomenon in silver thin films offers a straightforward method to obtain structures having controlled shape or size -this latter in principle spanning several orders of magnitudes -- with potentially strong interest…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Surface energy is fundamental in controlling surface properties and surface-driven processes like heterogeneous catalysis, as adsorption energy is. It is thus crucial to establish an effective scheme to determine surface energy and its…
Magnetic equilibrium reconstruction is a crucial simulation capability for interpreting diagnostic measurements of experimental plasmas. Equilibrium reconstruction has mostly been applied to systems with isotropic pressure and relatively…
This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the…
Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…