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The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Analysis of PDEs · Mathematics 2021-04-27 Patrik Knopf , Kei Fong Lam , Chun Liu , Stefan Metzger

In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid…

Analysis of PDEs · Mathematics 2025-03-12 Yinghua Li , Yuanxiang Yan , Xijun Yin

We propose a refined scheme of deriving an effective low-energy Hamiltonian for materials with strong electronic Coulomb correlations beyond density functional theory (DFT). By tracing out the electronic states away from the target degrees…

Strongly Correlated Electrons · Physics 2017-08-09 Motoaki Hirayama , Takashi Miyake , Masatoshi Imada , Silke Biermann

We consider a multi-component version of the conserved Allen-Cahn equation proposed by J. Rubinstein and P. Sternberg in 1992 as an alternative model for phase separation. In our case, the free energy is characterized by a mixing entropy…

Analysis of PDEs · Mathematics 2023-08-23 Maurizio Grasselli , Andrea Poiatti

In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…

Computational Physics · Physics 2026-04-14 Ye-Hang Qin , Ye Feng

We obtain a cohesive fracture model as a $\Gamma$-limit of scalar damage models in which the elastic coefficient is computed from the damage variable $v$ through a function $f_k$ of the form $f_k(v)=min\{1,\varepsilon_k^{1/2} f(v)\}$, with…

Analysis of PDEs · Mathematics 2018-05-01 Sergio Conti , Matteo Focardi , Flaviana Iurlano

We investigate the role of architected thin films in the interfacial failure properties of bi-layer composites. Our results show that, while graded structures can be used to prescribe failure at the interface, they do not offer significant…

Materials Science · Physics 2026-03-10 Christian Greff , Leon Pyka , Michael Zaiser , Paolo Moretti

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

Analysis of PDEs · Mathematics 2023-10-25 Andrea Giorgini , Patrik Knopf

We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…

Analysis of PDEs · Mathematics 2011-03-24 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Juergen Sprekels

New experimental results for the elastic scattering of 6He on 64Zn at incident energies of 15.0 and 18.0 MeV and 4He at 17.5 MeV along with results already published at 10.0 and 13.6 MeV, are presented. Elastic and alpha experimental cross…

In this paper, we study numerical methods for solving the coupled Allen-Cahn/Cahn-Hilliard system associated with a free energy functional of logarithmic type. To tackle the challenge posed by the special free energy functional, we propose…

Numerical Analysis · Mathematics 2020-07-15 Jizu Huang , Chao Yang , Ying Wei

A chemo-mechanical model for a finite-strain elasto-viscoplastic material containing multiple chemical components is formulated and an efficient numerical implementation is developed to solve the resulting transport relations. The numerical…

Computational Physics · Physics 2020-04-22 Pratheek Shanthraj , Chuanlai Liu , Amirhassan Akbarian , Bob Svendsen , Dierk Raabe

We present a modified form of the Functionalized Cahn Hilliard (FCH) functional which models highly amphiphilic systems in solvent. A molecule is highly amphiphilic if the energy of a molecule isolated within the bulk solvent molecule is…

Analysis of PDEs · Mathematics 2020-09-08 Shibin Dai , Keith Promislow

We present a generalization of the Debye-H\"uckel free-energy-density functional of simple fluids to the case of two-component systems with arbitrary interaction potentials. It allows one to obtain the two-component Debye-H\"uckel integral…

Plasma Physics · Physics 2018-10-24 T. Blenski , R. Piron

Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived…

Materials Science · Physics 2009-11-13 Gunnar Pruessner , A. P. Sutton

We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…

We consider one dimensional generalized parabolic Cahn-Hilliard equation $$ u_t=-\partial_{xx}\big[\partial_{xx}u-W'(u)\big]+W''(u)\big[\partial_{xx} u -W'(u)\big], \qquad \forall\, (t,x)\in [0,+\infty)\times {\mathbb R}, $$ where the…

Analysis of PDEs · Mathematics 2023-03-31 Chao Liu , Jun yang

We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by…

Analysis of PDEs · Mathematics 2023-02-13 Martin Kalousek , Sourav Mitra , Šárka Nečasová

The Cahn-Hilliard equation is one of the most common models to describe phase separation processes in mixtures of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…

Numerical Analysis · Mathematics 2023-01-23 Stefan Metzger

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With…

Materials Science · Physics 2007-05-23 J. E. Guyer , W. J. Boettinger , J. A. Warren , G. B. McFadden
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