Related papers: Microscopic Patterns in the 2D Phase-Field-Crystal…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
The formation of microstructures in metallic alloys during hot metal forming involves simultaneous metallurgical complex phenomena. Traditional high-fidelity numerical frameworks used on the polycrystalline scale tend to focus on…
Solidification pattern during nonequilibrium crystallization is among the most important microstructures in the nature and technical realms. Phase field crystal (PFC) model could simulate the pattern formation during equilibrium…
As a continuation of our preceding work [R. Erdem and N. Alata, Eur. Phys. J. Plus 135, 911 (2020), https://doi.org/10.1140/epjp/s13360-020-00934-3], we used the thermodynamic geometry in the Ruppeiner formalism to study the geometrical…
Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture…
We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing defects. We focus on the prototypical settings of one or two spherical defects (particles of…
Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here the nucleation of quasicrystals is investigated by using an efficient computational method…
In this contribution we investigate the application of phase-field fracture models on non-linear multiscale computational homogenization schemes. In particular, we introduce different phase-fields on a two-scale problem and develop a…
We study a Phase-Field-Crystal model described by a free energy functional involving second order derivatives of the order parameter in a periodic setting and under a fixed mass constraint. We prove a $\Gamma$-convergence result in an…
We consider fixed-point models for topological phases of matter formulated as discrete path integrals in the language of tensor networks. Such zero-correlation length models with an exact notion of topological invariance are known in the…
The critical dynamics of dislocation avalanches in plastic flow is examined using a phase field crystal (PFC) model. In the model, dislocations are naturally created, without any \textit{ad hoc} creation rules, by applying a shearing force…
Rapid solidification leads to unique microstructural features, where a less studied topic is the formation of various crystalline defects, including high dislocation densities, as well as gradients and splitting of the crystalline…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical…
We study a $\mathcal PT$-symmetric scalar Euclidean field theory with a complex action, using both theoretical analysis and lattice simulations. This model has a rich phase structure that exhibits pattern formation in the critical region.…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…