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The morphology and dynamics of polymerization-induced phase separation in the initially homogeneous solution of a non-reactive component in reactive monomers are investigated by incorporating the reaction kinetics into the time-dependent…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical…
In the framework of the Ginzburg-Landau harmonic potential approximation, we present a possible modeling of the time-dependence of the frequency of the order parameter mode suitable to account for the formation of correlated domains in…
The time-dependent Ginzburg-Landau (TDGL) equation for a single component non-conservative structural order parameter is used to study the spatio-temporal evolution of a second phase in the vicinity of an edge dislocation in an elastic…
In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
The confluence of quantum mechanics and complexity, which leads to the emergence of rich, exotic states of matter, motivates the extension of our concepts of quantum ordering. The twin concepts of spontaneously broken symmetry, described in…
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…
The problem of heterogeneous nucleation of second-phase in alloys in the vicinity of elastic defects is considered. The defect can be a dislocation line or a crack tip residing in a crystalline solid. We use the Ginzburg-Landau equation to…
Many of the systems that appear in various signal processing applications are non-linear, for example, due to hardware impairments such as non-linear amplifiers and finite-resolution quantization. The Bussgang decomposition is a popular…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
We present a microscopic theory of nonlinear damping and dephasing of low-frequency eigenmodes in nano- and micro-mechanical systems. The mechanism of the both effects is scattering of thermally excited vibrational modes off the considered…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
We study the dynamics of phase ordering of a non-conserved, scalar order parameter in one dimension, with long-range interactions characterized by a power law $r^{-d-\sigma}$. In contrast to higher dimensional systems, the point nature of…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…