Isogeometric Analysis for Topology Optimization with a Phase Field Model

We consider a phase field model for the formulation and solution of topology optimization problems in the minimum compliance case. In this model, the optimal topology is obtained as the steady state of the phase transition described by the generalized Cahn-Hilliard equation which naturally embeds the volume constraint on the amount of material available for distribution in the design domain. We reformulate the model as a coupled system and we highlight the dependency of the optimal topologies on dimensionless parameters. We consider Isogeometric Analysis for the spatial approximation which facilitates encapsulating the exactness of the representation of the design domain in the topology optimization and is particularly suitable for the analysis of phase field problems. We demonstrate the validity of the approach and numerical approximation by solving two and three-dimensional topology optimization problems. © 2012 CIMNE, Barcelona, Spain

Isogeometric analysis of the advective Cahn-Hilliard equation: Spinodal decomposition under shear flow

We present a numerical study of the spinodal decomposition of a binary fluid undergoing shear flow using the advective Cahn-Hilliard equation, a stiff, nonlinear, parabolic equation characterized by the presence of fourth-order spatial derivatives. Our numerical solution procedure is based on isogeometric analysis, an approximation technique for which basis functions of high-order continuity are employed. These basis functions allow us to directly discretize the advective Cahn-Hilliard equation without resorting to a mixed formulation. We present steady state solutions for rectangular domains in two-dimensions and, for the first time, in three-dimensions. We also present steady state solutions for the two-dimensional Taylor-Couette cell. To enforce periodic boundary conditions in this curved domain, we derive and utilize a new periodic Bézier extraction operator. We present an extensive numerical study showing the effects of shear rate, surface tension, and the geometry of the domain on the phase evolution of the binary fluid. Theoretical and experimental results are compared with our simulations. © 2013 Elsevier Inc

SARS-CoV-2 infects the human kidney and drives fibrosis in kidney organoids

This work was supported by grants of the German Research Foundation (DFG: KR 4073/11-1; SFBTRR219, 322900939; and CRU344, 428857858, and CRU5011 InteraKD 445703531), a grant of the European Research Council (ERC-StG 677448), the Federal Ministry of Research and Education (BMBF NUM-COVID19, Organo-Strat 01KX2021), the Dutch Kidney Foundation (DKF) TASK FORCE consortium (CP1805), the Else Kroener Fresenius Foundation (2017_A144), and the ERA-CVD MENDAGE consortium (BMBF 01KL1907) all to R.K.; DFG (CRU 344, Z to I.G.C and CRU344 P2 to R.K.S.); and the BMBF eMed Consortium Fibromap (to V.G.P, R.K., R.K.S., and I.G.C.). R.K.S received support from the KWF Kankerbestrijding (11031/2017–1, Bas Mulder Award) and a grant by the ERC (deFiber; ERC-StG 757339). J.J. is supported by the Netherlands Organisation for Scientific Research (NWO Veni grant no: 091 501 61 81 01 36) and the DKF (grant no. 19OK005). B.S. is supported by the DKF (grant: 14A3D104) and the NWO (VIDI grant: 016.156.363). R.P.V.R. and G.J.O. are supported by the NWO VICI (grant: 16.VICI.170.090). P.B. is supported by the BMBF (DEFEAT PANDEMIcs, 01KX2021), the Federal Ministry of Health (German Registry for COVID-19 Autopsies-DeRegCOVID, www.DeRegCOVID.ukaachen.de; ZMVI1-2520COR201), and the German Research Foundation (DFG; SFB/TRR219 Project-IDs 322900939 and 454024652). S.D. received DFG support (DJ100/1-1) as well as support from VGP and TBH (SFB1192). M.d.B,R.R., N.S., and A.A. are supported by an ERC Advanced Investigator grant (H2020-ERC-2017-ADV-788982-COLMIN) to N.S. A.A. is supported by the NWO (VI.Veni.192.094). We thank Saskia de Wildt, Jeanne Pertijs (Radboudumc, Department of Pharmacology), and Robert M. Verdijk (Erasmus Medical Center, Department of Pathology) for providing tissue controls (Erasmus MC Tissue Bank) and Christian Drosten (Charite´ Universitatsmedizin Berlin, Institute of € Virology) and Bart Haagmans (Erasmus Medical Center, Rotterdam) for providing the SARS-CoV-2 isolate. We thank Kioa L. Wijnsma (Department of Pediatric Nephrology, Radboud Institute for Molecular Life Sciences, Amalia Children’s Hospital, Radboud University Medical Center) for support with statistical analysis regarding the COVID-19 patient cohort.Peer reviewedPublisher PD