Conveners
Phase Field Methods in Real-World Applications: MS-7-1
- Robert Lasarzik (WIAS)
Phase Field Methods in Real-World Applications: MS-7-2
- Robert Lasarzik (WIAS)
Phase Field Methods in Real-World Applications: MS-7-3
- Elisabetta Rocca (Università di Pavia)
Phase Field Methods in Real-World Applications: MS-7-4
- Robert Lasarzik (WIAS)
Description
Organisers: Cecilia Cavaterra, Robert Lasarzik, Elisabetta Rocca, Hao Wu
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Prof. Helmut Abels (Universität Regensburg)08/09/2026, 10:30Phase Field Methods in Real-World Applications
We consider the linearized system for the sharp interface limit of a Navier-Stokes/Allen-Cahn system around a suitable approximate solution.
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With the aid of a suitable weight taking the distance to the interface and the interfacial thickness into account we obtain optimal regularity estimates, which are uniformy in the interfacial thickness. This enables to improve previous convergence... -
Fan Cheng (Freie Universität Berlin)08/09/2026, 11:00Phase Field Methods in Real-World Applications
We study the homogenisation of an incompressible viscoelastoplastic fluid in randomly perforated domains. The mesoscopic model couples the balance of momentum with the evolution of a deviatoric internal stress tensor. The latter is transported by the flow through the Zaremba–Jaumann derivative and is subject to a non-smooth plastic dissipation law as well as stress diffusion. This model is...
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Jonas Stange (Universität Regensburg)08/09/2026, 11:30Phase Field Methods in Real-World Applications
We consider a general class of convective bulk-surface Cahn-Hilliard systems with singular potentials. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn-Hilliard-type allow for dynamic changes of the contact angle between the diffuse interface and the boundary as well as absorption of material by the boundary. In this talk, I present recent results...
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Yadong Liu (Nanjing Normal University)08/09/2026, 12:00Phase Field Methods in Real-World Applications
In this talk, I will report a recent work on a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum mixture theory. It adopts a mass-averaged (barycentric) velocity so that the two-phase flow is quasi-incompressible: the...
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Jürgen Sprekels (Weierstrass Institute, Anton-Wilhelm-Amo-Strasse 39, 10117 Berlin, Germany)08/09/2026, 16:30Phase Field Methods in Real-World Applications
In this talk, we study the optimal control of a phase field system of viscous Cahn-Hilliard type modeling tumor growth, in which a hyperbolic relaxation of the chemical potential is added to the equation governing the phase evolution. In addition to well-posedness results for the state system, we analyze the differentiability properties of the associated control-to-state operator and derive...
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Monica Conti08/09/2026, 17:00Phase Field Methods in Real-World Applications
In this talk, we consider a class of Cahn–Hilliard equations with nonlinear diffusion, arising in the description of complex materials.
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We discuss recent results on existence, regularization, stability, and convergence to equilibrium under very general assumptions. In particular, we show that the strong convexity assumption on the interfacial energy, which underlies much of the existing... -
Abramo Agosti (University of Pavia)08/09/2026, 17:30Phase Field Methods in Real-World Applications
In this talk I will present new results about the Active Cahn-Hilliard equation, which is a variant of the Cahn-Hilliard equation not derivable from variational principles which describes active materials constituted by particles that can convert energy into directed motion. This model has multiple applications in biomedicine and engineering. I will show quantitative results about the...
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RICCARDA ROSSI (Università degli studi di Brescia)08/09/2026, 18:00Phase Field Methods in Real-World Applications
Several phase-field models have the underlying structure of
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generalized gradient systems in Banach spaces, whose evolutions
are generated by the interplay between an energy functional
and a dissipation potential. We focus on the case in which the dual
dissipation potential is given by a sum of two functionals and show
that solutions of the associated gradient-flow evolution... -
Erica Ipocoana (Freie Universität Berlin)08/09/2026, 18:30Phase Field Methods in Real-World Applications
We introduce an isothermal phase-field model for the coupled evaporation and crystallization of an aerosol droplet containing dissolved solutes: as the liquid evaporates, the dissolved solute, for example salt, becomes increasingly concentrated and, once it exceeds a saturation threshold, precipitates by forming a crystalline phase.
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The model is described by a three-phase (liquid,... -
Ulisse Stefanelli (Unviersity of Vienna)10/09/2026, 10:30Phase Field Methods in Real-World Applications
I will present some existence result for a mathematical model of accretive growth in confined environments. Accretive growth occurs ubiquitously in most biological systems, as well as in many natural and technological ones. The model describes the growth process through a level-set formulation, leading to a free-boundary problem combined with a stationary Hamilton-Jacobi equation in a...
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Dennis Trautwein (Universität Regensburg)10/09/2026, 11:00Phase Field Methods in Real-World Applications
In this talk, we study a phase-field model for curvature-driven pattern formation in biomembranes. The model is derived as a gradient flow of an energy functional that approximates the two-phase Canham--Helfrich energy. This leads to a Cahn--Hilliard-type equation with cross diffusion for the relative chemical concentration of one lipid phase, coupled to a fourth-order reaction-diffusion...
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65. Nonlocal-to-local convergence of convolution operators and its application to phase-field modelsPatrik Knopf (Karlsruher Institut für Technologie (KIT))10/09/2026, 11:30Phase Field Methods in Real-World Applications
The goal of nonlocal-to-local convergence is to show that certain singular, nonlocal convolution-type integral operators converge to a local differential operator as the convolution kernel concentrates at zero. This can be a useful tool in the physical justification of mathematical models (e.g., the Cahn-Hilliard equation), especially when a desired local differential operator cannot be...
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Sebastian Aland (HTW Dresden & TU Freiberg)10/09/2026, 12:00Phase Field Methods in Real-World Applications
Growing tumors generate and respond to stress in their local environment. On the one hand, local cell divisions and death lead to complex strain patterns in the tissue. On the other hand, tissue re-arrangements can relax the resulting mechanical shear stresses and make the tissue more fluid-like. To predict the outcomes of these nonlinear visco-elastic interactions, we introduce the framework...
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Prof. Pierluigi Colli (University of Pavia)10/09/2026, 14:00Phase Field Methods in Real-World Applications
We consider a phase-field model for multiphase flows in porous media coupling a Brinkman equation for the fluid motion with a generalized Cahn–Hilliard equation accounting for curvature-driven effects and mass exchange. We discuss existence results for the coupled system and, under suitable assumptions, uniqueness and continuous dependence properties. We further investigate the asymptotic...
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Andrea Giorgini (Politecnico di Milano)10/09/2026, 14:30Phase Field Methods in Real-World Applications
We consider a thermodynamically consistent Navier–Stokes/Cahn–Hilliard system describing the motion of two incompressible fluids with unmatched densities coupled to a soluble chemical species. The model incorporates both chemotactic effects induced by the chemical species and mass transport within the mixture. For the two-dimensional initial-boundary value problem, we discuss the existence of...
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Kei Fong Lam (Hong Kong Baptist University)10/09/2026, 15:00Phase Field Methods in Real-World Applications
Recent studies have shown that chemical reactions in phase separating systems can lead to growth and division of droplets. The fuel from chemical reactions can lead to a sequence of growth and splitting that mimics the behavior in the transition of protocells from nonliving to living systems. Such systems where energy is externally supplied and the governing equations do not fulfil a free...
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Giulia Cavalleri (WIAS)10/09/2026, 15:30Phase Field Methods in Real-World Applications
A diffuse interface model for tumour growth in the presence of a nutrient is introduced, incorporating mechanical effects and reversible tissue damage. The highly nonlinear PDE system consists of a Cahn–Hilliard equation governing the phase separation between healthy and tumour cells, coupled to a parabolic reaction-diffusion equation for the nutrient and a hyperbolic equation for the balance...
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