Related papers: Phase-Field Peridynamics
Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their…
Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth…
A phase-field approach to the dynamics of liquid-solid interfaces that evolve due to precipitation and/or dissolution is presented. For the purpose of illustration and comparison with other methods, phase field simulations were carried out…
Due to its computational robustness and versatility, the phase field fracture model has become the preferred tool for predicting a wide range of cracking phenomena. However, in its conventional form, its intrinsic tension-compression…
We study a two-level system coupled to two quantized electromagnetic modes within the Jaynes-Cummings framework. While the single-mode model is exactly solvable due to its conserved excitation number, yielding finite-dimensional invariant…
A non-iterative waveform sensing approach is proposed toward (i) geometric reconstruction of penetrable fractures, and (ii) quantitative identification of their heterogeneous contact condition by seismic i.e. elastic waves. To this end, the…
A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform…
We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
We describe a new model for the study of weakly-collisional, magnetized plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle…
The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a…
We focus our attention on some relevant aspects of the beam-plasma instability in order to refine some features of the linear and non-linear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
This work overviews a new, recent success of phase-field modelling: its application to predicting the evolution of the corrosion front and the associated structural integrity challenges. Despite its important implications for society,…
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Nonequilibrium conditions fundamentally change how systems undergo phase separation. In systems with temperature gradients, attractive particles have been shown to form periodic patterns and steady convective currents, but a clear…
A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic…
This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…
This work develops a low-dimensional nonlinear stochastic model of symmetry-breaking coherent structures from experimental measurements of a turbulent axisymmetric bluff body wake. Traditional model reduction methods decompose the field…