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  • 1
    Online Resource
    Online Resource
    Modeling cellular self-organization in strain-stiffening hydrogels (2023)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: We develop a three-dimensional mathematical model framework for the collective evolution of cell populations by an agent-based model (ABM) that mechanically interacts with the surrounding extracellular matrix (ECM) modeled as a hydrogel. We derive effective two-dimensional models for the geometrical set-up of a thin hydrogel sheet to study cell-cell and cell-hydrogel mechanical interactions for a range of external conditions and intrinsic material properties. We show that without any stretching of the hydrogel sheets, cells show the well-known tendency to form long chains with varying orientations. Our results further show that external stretching of the sheet produces the expected nonlinear strainsoftening or stiffening response, with, however, little qualitative variation of the overall cell dynamics for all the materials considered. The behavior is remarkably different when solvent is entering or leaving from strain softening or stiffening hydrogels, respectively.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (37 Seiten, 14,45 MB) , Illustrationen, Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 3076
    URL: https://doi.org/10.20347/WIAS.PREPRINT.3076
    URL: https://edocs.tib.eu/files/e01fn24/1880008424.pdf
    DOI: 10.20347/WIAS.PREPRINT.3076
    Language: English
    Note: Literaturverzeichnis: Seite 31-35
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  • 2
    Online Resource
    Online Resource
    Counterion-controlled phase equilibria in a charge-regulated polymer solution (2023)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: We study phase equilibria in a minimal model of charge-regulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonation-deprotonation processes in the presence of a dissolved acid, whose anions serve as screening counterions. We explicitly account for variability in the polymers’ charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counter-ions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes unimodal and multi-modal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for non-linear responses to the solution acidity: re-entrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions and mixture compositions.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (30 Seiten, 6,15 MB) , Diagramme, Illustrationen
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 3031
    URL: https://doi.org/10.20347/WIAS.PREPRINT.3031
    URL: https://edocs.tib.eu/files/e01fn23/1855024144.pdf
    DOI: 10.20347/WIAS.PREPRINT.3031
    Language: English
    Note: Literaturverzeichnis: Seite 18-21
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  • 3
    Online Resource
    Online Resource
    "Entwicklung einer innovativen Fügetechnologie für neuartige Steuergeräte-Konzepte" : Abschlussbericht MODAL (Modulare Aufbautechnologie für hochkompakte Systeme auf Leiterplattenbasis) : Berichtszeitraum: 01.08.2017-31.10.2020 (2020)
    Nürnberg : Vitesco Technologies
    Details Availability
    Keywords: Forschungsbericht ; Integrierte Schaltung ; Gedruckte Schaltung ; Sintern ; Silber ; Laminieren ; Prepreg
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (47 Seiten, 4,02 MB) , Illustrationen, Diagramme
    URL: https://doi.org/10.2314/KXP:1783577002
    DOI: 10.2314/KXP:1783577002
    Language: German
    Note: Förderkennzeichen BMBF 16ES0714K , Verbundnummer 01180364 , Autoren dem Berichtsblatt entnommen , Unterschiede zwischen dem gedruckten Dokument und der elektronischen Ressource können nicht ausgeschlossen werden
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  • 4
    Online Resource
    Online Resource
    Marangoni driven liquid films rising out of a meniscus onto a nearly horizontal substrate (2004)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
    Details Availability
    Keywords: Forschungsbericht
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (22 Seiten, 379,70 KB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik im Forschungsverbund Berlin e.V. no. 941
    URL: http://webdoc.sub.gwdg.de/ebook/serien/e/wias/2004/2004/wias_preprints_941.pdf
    URL: https://edocs.tib.eu/files/e01fn21/504263390.pdf
    DDC: 530
    RVK:
    SI 304
    Language: English
    Note: Literaturverzeichnis: Seite 18-20
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  • 5
    Online Resource
    Online Resource
    Asymptotic study of the electric double layer at the interface of a polyelectrolyte gel and solvent bath (2020)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: An asymptotic framework is developed to study electric double layers that form at the interface between a solvent bath and a polyelectrolyte gel that can undergo phase separation. The kinetic model for the gel accounts for the finite strain of polyelectrolyte chains, free energy of internal interfaces, and Stefan–Maxwell diffusion. By assuming that the thickness of the double layer is small compared to the typical size of the gel, matched asymptotic expansions are used to derive electroneutral models with consistent jump conditions across the gel-bath interface in twodimensional plane-strain as well as fully three-dimensional settings. The asymptotic framework is then applied to cylindrical gels that undergo volume phase transitions. The analysis indicates that Maxwell stresses are responsible for generating large compressive hoop stresses in the double layer of the gel when it is in the collapsed state, potentially leading to localised mechanical instabilities that cannot occur when the gel is in the swollen state. When the energy cost of internal interfaces is sufficiently weak, a sharp transition between electrically neutral and charged regions of the gel can occur. This transition truncates the double layer and causes it to have finite thickness. Moreover, phase separation within the double layer can occur. Both of these features are suppressed if the energy cost of internal interfaces is sufficiently high. Thus, interfacial free energy plays a critical role in controlling the structure of the double layer in the gel.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (37 Seiten, 2,23 MB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 2751
    URL: https://doi.org/10.20347/WIAS.PREPRINT.2751
    DOI: 10.20347/WIAS.PREPRINT.2751
    Language: English
    Note: Literaturverzeichnis: Seite 33-35
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  • 6
    Online Resource
    Online Resource
    A kinetic model of a polyelectrolyte gel undergoing phase separation (2020)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a thermodynamically consistent model for the salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, as well as finite elasticity and multicomponent transport. The fully time-dependent model describes the evolution of small changes in the mobile ion concentrations and follows their impact on the large-scale solvent flux and the emergence of long-time pattern formation in the gel. We observe a strong acceleration of the evolution of the free surface when the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (48 Seiten, 2,75 MB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no.2802
    URL: https://doi.org/10.20347/WIAS.PREPRINT.2802
    DOI: 10.20347/WIAS.PREPRINT.2802
    Language: English
    Note: Literaturverzeichnis: Seite 42-46
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  • 7
    Online Resource
    Online Resource
    Spinodal decomposition and collapse of a polyelectrolyte gel (2020)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
    Details Availability
    Keywords: Forschungsbericht
    Description / Table of Contents: The collapse of a polyelectrolyte gel in a (monovalent) salt solution is analysed using a new model that includes interfacial gradient energy to account for phase separation in the gel, finite elasticity and multicomponent transport. We carry out a linear stability analysis to determine the stable and unstable spatially homogeneous equilibrium states and how they phase separate into localized regions that eventually coarsen to a new stable state. We then investigate the problem of a collapsing gel as a response to increasing the salt concentration in the bath. A phase space analysis reveals that the collapse is obtained by a front moving through the gel that eventually ends in a new stable equilibrium. For some parameter ranges, these two routes to gel shrinking occur together.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (30 Seiten, 2,22 MB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 2731
    URL: https://doi.org/10.20347/WIAS.PREPRINT.2731
    DOI: 10.20347/WIAS.PREPRINT.2731
    Language: English
    Note: Literaturverzeichnis: Seite 26-28
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  • 8
    Online Resource
    Online Resource
    Signatures of slip in dewetting polymer films (2018)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: Thin liquid polymer films on hydrophobic substrates are susceptable to rupture and formation of holes, which in turn initiate a complex dewetting process that eventually evolves into characteristic stationary droplet patterns. Experimental and theoretical studies suggest that the specific type of droplet pattern largely depends on the nature of the polymer-substrate boundary condition. To follow the morphological evolution numerically over long time scales and for the multiple length scales involved has so far been a major challenge. In this study a highly adaptive finite-element based numerical scheme is presented that allows for large-scale simulations to follow the evolution of the dewetting process deep into the nonlinear regime of the model equations, capturing the complex dynamics including shedding of droplets. In addition, the numerical results predict the previouly unknown shedding of satellite droplets during the destabilisation of liquid ridges, that form during the late stages of the dewetting process. While the formation of satellite droplets is well-known in the context of elongating fluid filaments and jets, we show here that for dewetting liquid ridges this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (19 Seiten, 7.812 KB) , Illustrationen, Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 2538
    URL: https://doi.org/10.20347/WIAS.PREPRINT.2538
    DOI: 10.20347/WIAS.PREPRINT.2538
    Language: English
    Note: Literaturverzeichnis: Seite 15-17
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  • 9
    Online Resource
    Online Resource
    Thin film models for an active gel (2017)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie-Erickson-Parodi theory. Analytic expressions are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (28 Seiten, 322 kB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik No. 2451
    URL: https://doi.org/10.20347/WIAS.PREPRINT.2451
    DOI: 10.20347/WIAS.PREPRINT.2451
    Language: English
    Note: Literaturverzeichnis: Seite 23-26
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  • 10
    Online Resource
    Online Resource
    Gradient structures for flows of concentrated suspensions (2018)
    Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik Leibniz-Institut im Forschungsverbund Berlin e.V.
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    Keywords: Forschungsbericht
    Description / Table of Contents: In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth twohomogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows.
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (22 Seiten, 6.457 KB) , Diagramme
    Series Statement: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 2543
    URL: https://doi.org/10.20347/WIAS.PREPRINT.2543
    DOI: 10.20347/WIAS.PREPRINT.2543
    Language: English
    Note: Literaturverzeichnis: Seite 18-20
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