Related papers: Unified paradigm for interface dynamics
In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
In the context of scalar-tensor models of dark energy and inflation, the dynamics of vacuum scalar-tensor cosmology are analysed without specifying the coupling function or the scalar field potential. A conformal transformation to the…
We study how the propagation speed of interfaces in the Allen-Cahn phase field model for phase transformations in solids consisting of the elasticity equations and the Allen-Cahn equation depends on two parameters of the model. The two…
We develop a long-wavelength theory for the linear stability of a flat interface between an active nematic and an isotropic fluid. Starting from a diffuse-interface Cahn--Hilliard--Landau--de Gennes description coupled to Brinkman-screened…
The analysis of domain wall dynamics is often simplified to one dimensional physics. For domain walls in thin films, more realistic approaches require the description as two dimensional objects. This includes the study of vortices and…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
In this paper we study the rigorous sharp interface limit of a diffuse interface model related to the dynamics of tumor growth, when a parameter $\epsilon$, representing the interface thickness between the tumorous and non tumorous cells,…
We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be…
Cosmic voids are becoming key players in testing the physics of our Universe. Here we concentrate on the abundances and the dynamics of voids as these are among the best candidates to provide information on cosmological parameters. Cai,…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
The distribution of interface (domain-wall) velocities ${\bf v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v) \sim v^{-p}$ for large v,…
We study the kinetic roughening of a driven domain wall between spin-up and spin-down domains for a model with non-conserved order parameter and quenched disorder. To understand the scaling behavior of this interface we construct an…
We present a model for the dynamics of current- and field-driven domain-wall lines at nonzero temperature. We compute thermally-averaged drift velocities from the Fokker-Planck equation that describes the nonzero-temperature dynamics of the…
We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically…
Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…