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Related papers: Microscopic Patterns in the 2D Phase-Field-Crystal…

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We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the…

Soft Condensed Matter · Physics 2023-02-02 Robert F. B. Weigel , Michael Schmiedeberg

The phase field crystal (PFC) model captures the elastic and topological properties of crystals with a single scalar field at small undercooling. At large undercooling, new foam-like behavior emerges. We characterize this foam phase of the…

Pattern Formation and Solitons · Physics 2015-05-18 Nicholas Guttenberg , Nigel Goldenfeld , Jonathan Dantzig

The phase field crystal (PFC) approach extends the notion of phase field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance…

Materials Science · Physics 2016-05-18 V. Heinonen , C. V. Achim , T. Ala-Nissila

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological…

Mesoscale and Nanoscale Physics · Physics 2023-08-22 Sachin Vaidya , Ali Ghorashi , Thomas Christensen , Mikael C. Rechtsman , Wladimir A. Benalcazar

The three-dimensional (3D) microstructures of polycrystalline materials exert a critical influence on their mechanical and physical properties. Realistic, controllable construction of these microstructures is a key step toward elucidating…

Computer Vision and Pattern Recognition · Computer Science 2026-03-13 Chi Chen , Tianle Jiang , Xiaodong Wei , Yanming Wang

We introduce a mesocopic modeling approach for active systems. The continuum model allows to consider microscopic details as well as emerging macroscopic behavior and can be considered as a minimal continuum model to describe generic…

Soft Condensed Matter · Physics 2016-08-24 Francesco Alaimo , Simon Praetorius , Axel Voigt

The phase-field-crystal (PFC) modeling paradigm is rapidly emerging as the model of choice when investigating materials phenomena with atomistic scale effects over diffusive time scales. Recent variants of the PFC model, so-called…

Materials Science · Physics 2015-06-16 Nana Ofori-Opoku , Jonathan Stolle , Zhi-Feng Huang , Nikolas Provatas

We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…

Materials Science · Physics 2021-10-14 D. Tourret , H. Liu , J. LLorca

We study the 2d-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large…

Probability · Mathematics 2008-12-01 Raphael Cerf , Reda Messikh

The primary factors controlling defect stability in phase-field crystal (PFC) models are examined, with illustrative examples involving several existing variations of the model. Guidelines are presented for constructing models with stable…

Materials Science · Physics 2015-06-11 Joel Berry , Nikolas Provatas , Jörg Rottler , Chad W. Sinclair

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…

Metric Geometry · Mathematics 2011-10-24 Ciprian S. Borcea , Ileana Streinu

We study the nonlinear driven response and sliding friction behavior of the phase-field-crystal (PFC) model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed…

Materials Science · Physics 2016-09-08 J. A. P. Ramos , E. Granato , S. C. Ying , C. V. Achim , K. R. Elder , T. Ala-Nissila

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

Dynamical Systems · Mathematics 2014-04-21 Jesús San Martín , Mason A. Porter

A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where…

Soft Condensed Matter · Physics 2012-08-31 Mark J. Robbins , Andrew J. Archer , Uwe Thiele , Edgar Knobloch

We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…

Soft Condensed Matter · Physics 2021-01-22 Max Philipp Holl , Andrew J. Archer , Uwe Thiele

We review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is…

Soft Condensed Matter · Physics 2007-05-23 L. Granasy , T. Pusztai , T. Borzsonyi

Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an It\^o stochastic…

Computation · Statistics 2026-04-24 Utku Erdogan , Gabriel J. Lord , Joaquin Miguez

Effects of scale coupling between mesoscopic slowly-varying envelopes of liquid-solid profile and the underlying microscopic crystalline structure are studied in the phase-field-crystal (PFC) model. Such scale coupling leads to nonadiabatic…

Materials Science · Physics 2015-06-12 Zhi-Feng Huang

We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic…

Soft Condensed Matter · Physics 2016-09-21 E. S. Nascimento , A. P. Vieira , S. R. Salinas

We present a mesoscale description of deformations and defects in thin, flexible sheets with crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation, as well as dislocation nucleation and motion. Our…

Materials Science · Physics 2025-02-26 Lucas Benoit--Maréchal , Ingo Nitschke , Axel Voigt , Marco Salvalaglio