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We consider the interaction between a poroelastic structure, described using the Biot model in primal form, and a free-flowing fluid, modelled with the time-dependent incompressible Stokes equations. We propose a diffuse interface model in…

Numerical Analysis · Mathematics 2024-07-09 Francis R. A. Aznaran , Martina Bukač , Boris Muha , Abner J. Salgado

In the present work we introduce a novel graded-material design based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material…

Optimization and Control · Mathematics 2019-06-03 Massimo Carraturo , Elisabetta Rocca , Elena Bonetti , Dietmar Hömberg , Alessandro Reali , Ferdinando Auricchio

Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field…

Numerical Analysis · Mathematics 2025-06-23 Md Mamun Miah , Ryuhei Wakida , Masato Kimura

We study the free energy and dynamics of a closed elastic filament (a one-dimensional curve in two dimensions) whose local internal state is specified by curvature, stretch, and a scalar density field representing, for example, the…

Soft Condensed Matter · Physics 2026-02-27 Hanchun Wang , Ronojoy Adhikari , Michael E. Cates

The phase-field model (PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack…

Computational Engineering, Finance, and Science · Computer Science 2019-02-18 Shuwei Zhou , Timon Rabczuk , Xiaoying Zhuang

We present a new phase-field model for binary fluids exhibiting typical signatures of self-glassiness, such as long-time relaxation, ageing and long-term dynamical arrest. The present model allows the cost of building an interface to become…

Statistical Mechanics · Physics 2015-05-20 R. Benzi , M. Sbragaglia , M. Bernaschi , S. Succi

There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational…

Numerical Analysis · Mathematics 2025-04-24 J. Storm , W. Sun , I. B. C. M. Rocha , F. P. van der Meer

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…

Analysis of PDEs · Mathematics 2022-01-03 Mina Karimi , Mehrdad Massoudi , Noel Walkington , Matteo Pozzi , Kaushik Dayal

Fundamental differences between materials originate from the unique nature of their constituent chemical elements. Before specific differences emerge according to the precise ratios of elements in a given crystal structure, a material can…

In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic…

Biological Physics · Physics 2007-05-23 Xiaoqiang Wang , Qiang Du

Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost…

Materials Science · Physics 2022-07-01 Vivek Oommen , Khemraj Shukla , Somdatta Goswami , Remi Dingreville , George Em Karniadakis

The driven Dicke model, wherein an ensemble of atoms is driven by an external field and undergoes collective spontaneous emission due to coupling to a leaky cavity mode, is a paradigmatic example of a system exhibiting a driven-dissipative…

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

A multiscale scheme combining molecular dynamics (MD) and microscopic phase-field theory is proposed to study the structural phase transformations in solids with inhomogeneous strain field. The approach calculates strain response based on…

Materials Science · Physics 2007-05-23 Zhi-Rong Liu , Huajian Gao

Multiscale modelling is a new paradigm that has emerged in recent times to study the well-known problem of the process-structure-property relationship in the area of materials science and engineering. For obtaining the desired performance…

Materials Science · Physics 2023-10-10 Rupesh Chafle , Vishal Panwar , Kaushik Das , Somnath Bhowmick , Rajdip Mukherjee

Modal synthesis is an important area of physical modeling whose exploration in the past has been held back by a large number of control parameters, the scarcity of general-purpose design tools and the difficulty of obtaining the…

Sound · Computer Science 2007-05-23 Ilia Bisnovatyi

We present a phase-field model based on the Cahn-Hilliard equation to investigate the properties of phase separation in DNA nanostar systems. Leveraging a realistic free-energy functional derived from Wertheim theory, our model captures the…

Soft Condensed Matter · Physics 2025-04-23 Marco Cappa , Francesco Sciortino , Lorenzo Rovigatti

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…

Numerical Analysis · Mathematics 2016-11-03 Guo-Wei Wei , Y. C. Zhou

Knowledge of the underlying mechanisms of multiphase flow dynamics in porous media is crucial for optimizing subsurface engineering applications like geological carbon sequestration. However, studying the micro-mechanisms of multiphase…

Fluid Dynamics · Physics 2025-08-01 Quanwei Dai , Kang Duan , Chung-Yee Kwok

We present a 5-phase equation of state (EOS) for elemental carbon. The phases considered are: diamond, BC8, simple-cubic, simple-hexagonal, and the liquid/plasma state. The solid phase free energies are constrained by density functional…