Related papers: Additional scaling regions of ion-sputtered surfac…
The failure of roughness parameters to predict surface properties stems from their inherent scale-dependence; in other words, the measured value depends on the way it was measured. Here we take advantage of this scale-dependence to develop…
Several, recently proposed methods of surface manufacturing based on ion beam sputtering, which involve dual beam setups, sequential application of ion beams from different directions, or sample rotation, are studied with the method of…
We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its "conserved" variants, anisotropic perturbations are found to be relevant in d > 2 dimensions, leading to…
We present a phase-field model for simulating the solid-state dewetting of anisotropic crystalline films on non-planar substrates. This model exploits two order parameters to trace implicitly the crystal free surface and the substrate…
On the proper timescale, amorphous solids can flow. Solid flow can be observed macroscopically in glaciers or lead pipes, but it can also be artificially enhanced by creating defects. Ion Beam Sputtering (IBS) is a technique in which ions…
We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…
An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of…
The critical dynamics of conformal field theories on random surfaces is investigated beyond the previously studied dynamics of the overall area and the genus. It is found that the evolution of the order parameter in physical time performs a…
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
We study the morphological evolution of surfaces during ion sputtering and we compare their dynamical roughening with aeolian ripple formation in sandy deserts. We show that, although the two phenomena are physically different, they must…
In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers.…
We propose a novel approach to continuum modeling of the dynamics of crystal surfaces. Our model follows the evolution of an ensemble of step configurations, which are consistent with the macroscopic surface profile. Contrary to the usual…
A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom…
We investigate the kinetic roughening of Ar$^+$ ion-sputtered Pd(001) surface both experimentally and theoretically. \textit{In situ} real-time x-ray reflectivity and \textit{in situ} scanning tunneling microscopy show that nanoscale adatom…
We use continuum elasticity theory to revise scaling laws for radial breathing-like and shear-like vibration modes in quasi-2D nanostructures including finite-width nanoribbons and finite-size thin circular discs. Such modes can be observed…
Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin,…
The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in…
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…