3D phase-field simulation results showing dendritic and liquid morphologies during growth at rotational misorientations θ_R of 45° (A–C), 30° (D–F), 15° (G–I), and 0° (J–L). The grand-chemical potential model demonstrates that secondary dendrite arms develop and persist at higher misorientation angles.

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Comparison of experimental and phase-field simulated solute segregation in a quaternary Fe-Cr-Ni-C austenitic stainless steel. Concentration distributions of alloying elements—nickel (A,B) and chromium (C,D)—across dendritic and interdendritic regions, with local distribution fields for quantitative comparison.

Heat distribution in the air–aluminum domain for the experimental (left) and the synthetic (right) open-cell foam model. https://doi.org/10.1108/MMMS-03-2016-0012

Heat distribution including temperature isolines in air–aluminum domains of different porosity after 5 s of physical time. Learn more...

Example application of the developed method for calculating fluid flow and heat transfer in cellular solids: a quarter of an encapsulated foam structure exposed to a fluid flow and heated at the cylindrical shell; (left) temperature distribution in a cross-section and (right) temperature distribution on the surface of the foam structure as well as velocity vectors in a cross-section. Learn more...

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Impact of a rigid sphere onto the interface between two immiscible fluids. The two-dimensional simulations compare different surface wettabilities, represented by varying equilibrium contact angles, illustrating their influence on interface deformation and fluid–solid interaction during impact. The simulations are performed with Pace3D using a two-phase flow formulation coupled with phase-field evolution and rigid body motion, including capillary effects and contact-angle modeling according to Young’s law.

Simulation of the compression of a two-phase foam structure mimicking an aerogel undergoing large deformations. The model describes elastic behavior within an Eulerian framework, enabling robust simulations of porous materials subject to significant deformation.

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Concentration in uncracked (left) and cracked (right) secondary particle during PITT simulation.

Evolution of Li concentration and phases during 1C CC-CV charge: Top row shows a dense agglomerate where concentration gradients form in the radial direction and the phase transitions follow a shrinking core behaviour. The nanoporous agglomerate in the bottom row exhibits a more homogenous lithium distribution and follows a mosaic pattern during the phase transition. Patches of each phase have been labelled for reference.

Secondary particle morphology of NMC811 with colors marking primary particles (a) and (b), crack order-parameter φc (b) and Li-ion concentration 𝑐 after electrolyte infiltration (c). The black vectors in (a) indicate the c-lattice axis of the primary particles.

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