Related papers: High order model for describing the pattern format…
We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
We study noncentrosymmetric superconductors with the tetrahedral $T_d$, tetragonal $C_{4v}$, and cubic point group $O$. The order parameter is computed self-consistently in the bulk and near a surface for several different singlet to…
Apparently conflicting phase-sensitive measurements of the order parameter symmetry in the high-T$_c$ superconductors may be explained by regions near surfaces in which the order parameter symmetry is different than in the bulk. These…
This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…
We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these…
We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the…
Recent work has proven that training large language models with self-supervised tasks and fine-tuning these models to complete new tasks in a transfer learning setting is a powerful idea, enabling the creation of models with many…
When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…
Ultrafast laser irradiation can induce spontaneous self-organization of surfaces into dissipative structures with nanoscale reliefs. These surface patterns emerge from symmetry-breaking dynamical processes that occur in…
The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…
This research thesis presents a novel higher-order spectral element method (SEM) formulated in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex anisotropic media. In this study, we consider a…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
We investigate the morphologies of the Ge(001) surface that are produced by bombardment with a normally incident, broad argon ion beam at sample temperatures above the recrystallization temperature. Two previously-observed kinds of…
The theory of nucleation of nanoscale structures of the adsorbed atoms (adatoms), which occurs as a result of the self-consistent interaction of adatoms with the surface acoustic wave and electronic subsystem is developed. Temperature…
A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it…
Coherent grazing-incidence small-angle X-ray scattering is used to investigate the average kinetics and the fluctuation dynamics during self-organized nanopatterning of silicon by Ar$^+$ bombardment at 65$^{\circ}$ polar angle. At early…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
We report on the production of ordered assemblies of silicon nanostructures by means of irradiation of a Si(100) substrate with 1.2 keV Ar ions at normal incidence. Atomic Force and High-Resolution Transmission Electron microscopies show…
In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…