Related papers: High order model for describing the pattern format…
Electrochemical etching of semiconductors, apart from many technical applications, provides an interesting experimental setup for self-organized structure formation capable e.g. of regular, diameter-modulated, and branching pores. The…
We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
The order-disorder transition of a sphere-forming block copolymer thin film was numerically studied through a Cahn-Hilliard model. Simulations show that the fundamental mechanisms of pattern formation are spinodal decomposition and…
The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have…
The soliton dressing matrices for the higher-order zeros of the Riemann-Hilbert problem for the $N$-wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric…
The following is a thermodynamic analysis of a III order (and some aspects of a IV order) phase transition. Such a transition can occur in a superconductor if the normal state is a diamagnet. The equation for a phase boundary in an H-T (H…
Order-disorder processes fundamentally determine the structure and properties of many important oxide systems for energy and computing applications. While these processes have been intensively studied in bulk materials, they are less…
We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a…
Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…
We perform a detailed analysis of high-order harmonic generation in diatomic molecules within the strong-field approximation, with emphasis on quantum-interference effects. Specifically, we investigate how the different types of electron…
We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide…
The ways of creating of nanoscale systems (conducting filaments) in the ordered structure of a doped semiconductor in the aspect of the modern problems of nanotechnology to improve solar cells. Nuclear methods and processes of interaction…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…
We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…