Related papers: Energy scaling law for nanostructured materials
Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or…
The van der Waals (vdW) dispersion interaction between two finite neutral objects typically follows the standard nonretarded $d^{-6}$ law. Here, we reveal an anomalous $d^{-10}$ scaling law between nanostructures with strong geometric or…
A simple theory is proposed for the dispersive molecular binding of unusually high magnitude due to an enhanced polarizability. Two alternative ways have so far been considered in the literature leading to the polarizability enhancement:…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
We consider electrostatic interactions in two classes of nanostructures embedded in a three dimensional space: (1) helical nanotubes, and (2) thin films with uniform bending (i.e., constant mean curvature). Starting from the atomic scale…
We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary…
Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry,…
Entropic forces play a fundamental role in nanoscale phenomena, from colloidal self-assembly to biomolecular disaggregation. Here, we develop an exact analytical theory and find general scaling laws for the entropic separation of…
Recently, it has been experimentally confirmed that non-equilibrium dynamics of phase separation in strongly ferromagnetic Bose-Einstein condensates of $^7$Li atoms obey the dynamic scaling law belonging to the binary-fluid universality…
This report presents a systematic understanding of the nature behind the unusual behavior of a nanosolid, and a surface as well, in mechanics, thermodynamics, acoustics, optoelectronics, magnetism, dielectrics, atomic diffusivity and…
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…
van der Waals stacking of two-dimensional (2D) materials offers a powerful platform for engineering material interfaces with tailored electronic and optical properties. While most van der Waals multilayers have featured inorganic…
A cluster consisting of many atoms or molecules may be considered, in some circustances, to be a single large molecule with a well defined polarizability. Once the polarizability of such a cluster is known, one can evaluate certain…
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…
Energy conservation imposes fundamental bounds on the polarizabilities of nanoparticles (NPs). While such bounds are well established for isotropic and bianisotropic NPs, they remain unexplored for magneto-optical NPs. Here, we derive the…
The electrostatic interaction between metal spheres is an influential component in the assembly of many nanoscale materials in chemistry. Here we derive a method to calculate the energy and polarizations of metal spheres in arbitrary…
We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions. Particles interact via Coulomb potential and electrons have pseudo-relativistic kinetic energy. We prove the van der Waals-London law,…
A universal relationship between scaled size and scaled energy is explored in five-body self-bound quantum systems. The ground-state binding energy and structure properties are obtained by means of the diffusion Monte Carlo method. We use…
Using a unified macroscopic QED formalism, we derive an integral equation for the van der Waals energy of a two-level atomic system near a carbon nanotube. The equation is valid for both strong and weak atom-vacuum-field coupling. By…
The standard DLVO theory offers a limited description of ionic-surfacted magnetic colloids in near aggregation regimes. Correcting the electrical double layer term for ionic surfactants is not enough to successfully simulate the systems.…