Article
Mathematics
Charles Elbar, Jakub Skrzeczkowski
Summary: There has been a recent interest in rigorously deriving the Cahn-Hilliard equation from the nonlocal equation, particularly with regards to degenerate mobilities. In this study, a new method is presented to show the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation, using nonlocal Poincare and compactness inequalities. This research is motivated by models for the biomechanics of living tissues.(c)2023 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Mechanical
Junxiang Yang, Yibao Li, Chaeyoung Lee, Hyun Geun Lee, Soobin Kwak, Youngjin Hwang, Xuan Xin, Junseok Kim
Summary: In this paper, an explicit conservative Saul'yev finite difference scheme for the Cahn-Hilliard equation is presented. The proposed scheme has four main merits and outperforms in computational experiments.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Eylem Ozturk, Joseph L. Shomberg
Summary: In this study, a viscous Cahn-Hilliard phase-separation model with memory and a nonlocal fractional Laplacian operator in the chemical potential is examined. The existence of global weak solutions is proven using a Galerkin approximation scheme. Continuous dependence estimate provides uniqueness of weak solutions and existence of a compact connected global attractor in the weak energy phase space.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Keiichiro Kagawa, Mitsuharu Otani
Summary: This paper investigates the asymptotic behavior of solutions for the viscous Cahn-Hilliard equations as parameters tend to zero. It is shown that solutions of the viscous Cahn-Hilliard equations converge to solutions of the Allen-Cahn equation, the Cahn-Hilliard equation, and the viscous diffusion equation as suitable parameters tend to zero. Compared to existing results, a wider range of chemical potentials can be analyzed within our framework.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Correction
Mathematics
Sebastian Scholtes, Maria G. Westdickenberg
Summary: This article corrects a dissipation estimate from the original article, but the main result remains unchanged.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Pierluigi Colli, Gianni Gilardi, Andrea Signori, Juergen Sprekels
Summary: This note studies the optimal control of a nonisothermal phase field system with a conserved order parameter. The heat flux constitutive law assumes a possible thermal memory. The system also has a source term in the order parameter equation and the mass conservation of the order parameter is no longer satisfied. The paper analyzes the differentiable cases of the double-well potential and establishes the necessary optimality conditions for the optimal control problem.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Erlend Storvik, Jakub Wiktor Both, Jan Martin Nordbotten, Florin Adrian Radu
Summary: In this paper, a solution strategy for the Cahn-Larche equations is proposed. The system combines the Cahn-Hilliard regularized interface equation and linearized elasticity, and is non-convex and nonlinear. a semi-implicit discretization in time is proposed, and the resulting discrete system is equivalent to a convex minimization problem. Numerical experiments show the effectiveness of the proposed method compared to standard techniques.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Marco Salvalaglio, Axel Voigt, Steven M. Wise
Summary: In this study, we discuss two doubly degenerate Cahn-Hilliard models for isotropic surface diffusion, focusing on degeneracy in the mobility function and a restriction function associated with the chemical potential. Our computational results indicate that the restriction functions provide more accurate approximations of surface diffusion. We also explore a slight generalization of a non-variational model and introduce a new variational and energy dissipative model, both of which can be related to the generalized non-variational model and show convergence to the sharp-interface limit of surface diffusion through formal matched asymptotics.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Seokjun Ham, Yibao Li, Darae Jeong, Chaeyoung Lee, Soobin Kwak, Youngjin Hwang, Junseok Kim
Summary: In this study, an explicit adaptive finite difference method is proposed for solving the Cahn-Hilliard equation. The method utilizes a narrow-band domain to improve the accuracy of the numerical calculations. Comparisons with previous methods demonstrate the superior performance of the proposed method.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Mechanics
S. Sampaoli, A. Agosti, G. Pozzi, P. Ciarletta
Summary: This study proposes a toy partial differential model that considers both the short-term dynamics of misfolded proteins and the long-term evolution of tissue damage in neurodegenerative diseases. By using mixture theory, the brain is considered as a biphasic material consisting of misfolded protein aggregates and healthy tissue. Numerical simulations show that the spreading front of neural damage follows the direction of the largest eigenvalue of the mobility tensor.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2022)
Article
Mathematics, Applied
Junseok Kim, Zhijun Tan, Junxiang Yang
Summary: This article proposes linear temporally first- and second-order accurate methods for simulating phase change in binary fluid mixtures, and proves mass conservation and unconditional energy stability of the proposed schemes. The methods are efficient and easy to implement, and capable of simulating spinodal decomposition in irregular domains.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Revanth Mattey, Susanta Ghosh
Summary: A physics informed neural network (PINN) is a method that incorporates the physics of a system into a neural network's loss function by satisfying the system's boundary value problem. To address the accuracy issue for highly non-linear and higher-order time-varying partial differential equations, a novel backward compatible PINN (bc-PINN) scheme is proposed, which solves the PDE sequentially over successive time segments using a single neural network and re-trains the network to satisfy the already obtained solutions for previous time segments. Two techniques, using initial conditions and transfer learning, are introduced to improve the accuracy and efficiency of the bc-PINN scheme.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Andrej Novak, Nora Reinic
Summary: This paper focuses on the problem of digital image inpainting using the modified Cahn-Hilliard equation and a shock filter. The existence and uniqueness of the solution are proven using fixed point arguments and Aubin-Lions lemma. Additionally, a numerical method based on convexity splitting is introduced to approximate the solutions. The method is applied to various binary images, demonstrating its ability to extend image features and preserve edges.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Mechanical
Xiaofang Zhou, Changxin Qiu, Wenjing Yan, Biao Li
Summary: This paper presents a cell-average-based neural network (CANN) method for approximating the solutions of nonlinear Cahn-Hilliard equation and Camassa-Holm equation. The CANN method utilizes neural networks to approximate the evolution of solutions, allowing for larger time steps and the ability to handle corrupted data.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Yaoyao Chen, Yunqing Huang, Nianyu Yi
Summary: This paper carries out error analysis for a totally decoupled, linear, and unconditionally energy stable finite element method to solve the Cahn-Hilliard-Navier-Stokes equations. The a priori error analysis is derived for the phase field, velocity field, and pressure variable in the fully discrete scheme.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mechanics
Verena Becker, Marc Kamlah
Summary: This paper presents a theoretical model for normal contact force of elastoplastic ellipsoidal bodies for use in mechanical discrete element method. The model is an extension of the Thornton model, incorporating elliptical contact areas and focusing on normal contact force description as a continuous function of time.
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2021)
Article
Nuclear Science & Technology
M. Moscardini, S. Pupeschi, M. Kamlah
Summary: The research focuses on defining the macroscopic plastic strain of the bed by simulating the plastic deformation of individual pebbles, investigating different theories, and validating numerical results in the development of tritium breeder and neutron multiplier in the solid blanket concept.
FUSION ENGINEERING AND DESIGN
(2021)
Article
Chemistry, Physical
Tao Zhang, Marc Kamlah
Summary: A chemo-mechanical phase-field model is developed to capture the complex phase segregation processes in NaxFePO4 (0 < x < 1), along with the structural changes during charging/discharging. The model constructs a multi-well potential for NaxFePO4 for the first time and investigates the microstructure evolution during sodiation and desodiation processes. Results suggest that the formation of an intermediate phase can reduce stress and improve mechanical stability, leading to better battery performance.
JOURNAL OF POWER SOURCES
(2021)
Article
Engineering, Chemical
Oleg Birkholz, Matthias Neumann, Volker Schmidt, Marc Kamlah
Summary: The study investigates the relationships between microstructure characteristics and effective transport properties of granular materials through modeling and simulation of sphere packings. It establishes formulas expressing effective transport properties of the considered sphere packings in terms of the mean contact angle and the standard deviation of the particle radii.
Article
Energy & Fuels
Adrian Schmidt, Elvedin Ramani, Thomas Carraro, Jochen Joos, Andre Weber, Marc Kamlah, Ellen Ivers-Tiffee
Summary: Porous electrode models are crucial for predicting the performance and lifetime of lithium-ion batteries inexpensively, but some simplifications in existing models may lead to limitations in accuracy, especially under high charge and discharge rates. By studying the effects of various microstructural characteristics on the validity of the models, insights are gained to improve the homogenized model and overcome existing limitations of the pseudo-2D approach.
Article
Energy & Fuels
Oleg Birkholz, Marc Kamlah
Summary: The hierarchically structured half-cell model for lithium-ion battery electrodes with porous secondary particles has been developed and validated through experiments. The study shows that the rate-limiting factor in this model differs from classical half-cell models, being the combination of electronic conductivity and inner morphology of the secondary particles.
Article
Energy & Fuels
Verena Becker, Oleg Birkholz, Yixiang Gan, Marc Kamlah
Summary: This article investigates the influence of particle shapes on the micromechanical responses during calendering in lithium-ion battery manufacturing, and their impact on the effective transport properties of battery electrodes. The study presents a novel algorithm for generating stress-free particle assemblies and calculates effective conductivities using a resistor network approach. The research provides insights into the interplay between calendering process, electrode microstructure, and effective conductivities of solid and pore phases.
Article
Materials Science, Multidisciplinary
Friedemann A. Streich, Alexander Martin, Kyle G. Webber, Marc Kamlah
Summary: A fully electromechanically coupled, three-dimensional phenomenological constitutive model was developed for relaxor ferroelectric materials, which can simulate the macroscopic electromechanical response of lead-free and non-lead-free relaxor materials. The model accounts for unique material properties, and its accuracy is validated through comparison with experimental data.
JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
(2022)
Article
Materials Science, Multidisciplinary
Jay Santoki, Simon Daubner, Daniel Schneider, Marc Kamlah, Britta Nestler
Summary: Transport mechanisms in battery systems are influenced by microstructural properties such as particle size, porosity, and tortuosity. A simulation study using a multiple particle model system and ellipsoid-like particles as an example was conducted. Results suggest that electrode structures impact transportation rates, with smaller particles limited by surface reactions and larger particles tending towards bulk-transport limited theory.
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
(2021)
Editorial Material
Energy & Fuels
Thomas Wetzel, Wolfgang G. Bessler, Marc Kamlah, Hermann Nirschl
Article
Instruments & Instrumentation
Alexander Martin, Juliana G. Maier, Friedemann Streich, Marc Kamlah, Kyle G. Webber
Summary: The study examined the impact of ceramic-ceramic composite structures on the electromechanical response of lead-free ferroelectrics by manipulating local electrical and mechanical fields, and separating the relative contributions of PSC mechanisms.
SMART MATERIALS AND STRUCTURES
(2022)
Article
Energy & Fuels
Nils Klasen, Friedemann Heinz, Angela De Rose, Torsten Roessler, Achim Kraft, Marc Kamlah
Summary: This work reports on the cracking mechanism observed on shingle solar cells in PV modules subjected to thermal cycling. Experimental investigations and structural mechanic simulations show that the cracks are limited to the joint area and occur on the rear side of the solar cells. The cracks are caused by the thermal contraction of the encapsulant.
SOLAR ENERGY MATERIALS AND SOLAR CELLS
(2022)
Article
Materials Science, Multidisciplinary
M. Ciavarella, T. Zhang, R. M. McMeeking
Summary: This study analyzes crack growth in viscoelastic material and computes the work done and dissipation per unit area of crack growth under applied load. The results suggest that crack growth models based on quantifying the dissipation per unit area are not applicable to components with finite geometry, while models based on a rupture process zone are easier to implement.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2022)
Article
Chemistry, Physical
Tao Zhang, Mohsen Sotoudeh, Axel Gross, Robert M. McMeeking, Marc Kamlah
Summary: The cathode material NaxFePO4 of sodium-ion batteries exhibits complex phase segregation thermodynamics and large volume change during (dis)charging. A virtual multiscale modeling chain is established to construct a 3D anisotropic electro-chemo-mechanical phase-field model based on first-principles calculations for NaxFePO4, which considers various factors such as phase changes, electrochemical reactions, anisotropic diffusion, anisotropic misfit strain, and anisotropic elasticity. The study investigates the influence of surface reaction kinetics and crystal anisotropy on the microstructure evolution of NaxFePO4 particles and provides insights into engineering desired phase behavior with better mechanical stability.
JOURNAL OF POWER SOURCES
(2023)
