Related papers: High order model for describing the pattern format…
We study the self-organized ordering of nanostructures produced by ion-beam sputtering (IBS) of targets amorphizing under irradiation. By introducing a model akin to models of pattern formation in aeolian sand dunes, we extend consistently…
The production of nanopatterns on the surfaces of targets irradiated by ion beams at low and intermediate energies has developed during the present decade to a salient degree of control over the main pattern features. However, there is…
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…
The off-normal ion irradiation of semiconductor materials is seen to induce nanopatterning effects. Different theories are proposed to explain the mechanisms that drive self-reorganization of amorphisable surfaces. One of the prominent…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
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…
Many developmental processes in biology utilize Notch-Delta signaling to construct an ordered pattern of cellular differentiation. This signaling modality is based on nearest-neighbor contact, as opposed to the more familiar mechanism…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
When the surface of a nominally flat binary material is bombarded with a broad, normally-incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled…
The superconducting order parameter and LDOS spectra near an impenetrable surface are studied on the basis of selfconsistent calculations for a two band superconductor with nodeless extended s-+wave order parameter symmetry, as possibly…
Highly ordered one-dimensional arrays of nanodots, or nanobeads, are fabricated by forming nanoripples and nanodots in sequence, entirely by ion-beamsputtering (IBS) of Au(001). This demonstrates the capability of IBS for the fabrication of…
Two-level modeling for nanoscale pattern formation on silicon target by Ar$^+$ ion sputtering is presented. Phase diagram illustrating possible nanosize surface patterns is discussed. Scaling characteristics for the structure wavelength…
Normal incidence ion irradiation at elevated temperatures, when amorphization is prevented, induces novel nanoscale patterns of crystalline structures on elemental semiconductors by a reverse epitaxial growth mechanism: on Ge surfaces…
Ion beam irradiation of semiconductors is a method to produce regular periodic nanoscale patterns self-organized on wafer scale. At low temperatures, the surface of semiconductors is typically amorphized by the ion beam. Above a material…
The generation of high-order harmonics in finite, hexagonal nanoribbons is simulated. Ribbons with armchair and zig-zag edges are investigated by using a tight-binding approach with only nearest neighbor hopping. By turning an alternating…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…