Efficient model predictive control for parabolic PDEs with goal oriented error estimation. - In: SIAM journal on scientific computing, ISSN 1095-7197, Bd. 44 (2022), 1, S. A471-A500
We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a model predictive control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context. To this end, we present a truncated cost functional as an objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity. This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.
https://doi.org/10.1137/20M1356324
Spatial and temporal modulation of cell instructive cues in a filamentous supramolecular biomaterial. - In: ACS applied materials & interfaces, ISSN 1944-8252, Bd. 14 (2022), 15, S. 17042-17054
Supramolecular materials provide unique opportunities to mimic both the structure and mechanics of the biopolymer networks that compose the extracellular matrix. However, strategies to modify their filamentous structures in space and time in 3D cell culture to study cell behavior as encountered in development and disease are lacking. We herein disclose a multicomponent squaramide-based supramolecular material whose mechanics and bioactivity can be controlled by light through co-assembly of a 1,2-dithiolane (DT) monomer that forms disulfide cross-links. Remarkably, increases in storage modulus from ∼200 Pa to >10 kPa after stepwise photo-cross-linking can be realized without an initiator while retaining colorlessness and clarity. Moreover, viscoelasticity and plasticity of the supramolecular networks decrease upon photo-irradiation, reducing cellular protrusion formation and motility when performed at the onset of cell culture. When applied during 3D cell culture, force-mediated manipulation is impeded and cells move primarily along earlier formed channels in the materials. Additionally, we show photopatterning of peptide cues in 3D using either a photomask or direct laser writing. We demonstrate that these squaramide-based filamentous materials can be applied to the development of synthetic and biomimetic 3D in vitro cell and disease models, where their secondary cross-linking enables mechanical heterogeneity and shaping at multiple length scales.
https://doi.org/10.1021/acsami.1c24114
Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 6 (2022), S. 2443-2448
In this letter we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.
https://doi.org/10.1109/LCSYS.2022.3161054
Revealing the truncated conical geometry of nanochannels in anodic aluminium oxide membranes. - In: Nanoscale, ISSN 2040-3372, Bd. 14 (2022), 14, S. 5356-5368
Anodic aluminium oxide (AAO) membranes with self-ordered nanochannels have become promising candidates for applications in the aspects such as structural coloration, photonic crystals, upconversion luminescence and nanofluidic transport. Also, self-ordered AAO membranes have been extensively used for the fabrication of functional nanostructures such as nanowires, nanotubes, nanoparticles, nanorods and nanopillars. Geometries of nanochannels are crucial for the applications of AAO membranes as well as controlling growth (e.g., nucleation, direction and morphology) and in applications (e.g., optics, magnetics, thermoelectrics, biology, medicine, sensing, and energy conversion and storage) of the functional nanostructures fabricated via AAO template-based methods. However, observation of whole nanochannels with nanometer-resolution in thick AAO membranes remains a fundamental challenge, and the nanochannel geometry has not yet been sufficiently elucidated. Here, for the first time, we use depth-profiling transmission electron microscopy to reveal the truncated conical geometry of whole nanochannels of 70 [my]m in length. Such shape nonuniformity of the nanochannels leads to different reflectance properties of the different depths of the nanochannels along their long axis for one AAO membrane, which suggests that the nonuniformity result in some effects on applications of the nanostructures. Furthermore, we introduce a shape factor to evaluate the shape nonuniformity and demonstrate that the nonuniformity can be remarkably removed by an effective etching method based on a temperature gradient regime.
https://doi.org/10.1039/D2NR01006B
Well-defined nanostructuring with designable anodic aluminum oxide template. - In: Nature Communications, ISSN 2041-1723, Bd. 13 (2022), 2435, S. 1-11
Well-defined nanostructuring over size, shape, spatial configuration, and multi-combination is a feasible concept to reach unique properties of nanostructure arrays, while satisfying such broad and stringent requirements with conventional techniques is challenging. Here, we report designable anodic aluminium oxide templates to address this challenge by achieving well-defined pore features within templates in terms of in-plane and out-of-plane shape, size, spatial configuration, and pore combination. The structural designability of template pores arises from designing of unequal aluminium anodization rates at different anodization voltages, and further relies on a systematic blueprint guiding pore diversification. Starting from the designable templates, we realize a series of nanostructures that inherit equal structural controllability relative to their template counterparts. Proof-of-concept applications based on such nanostructures demonstrate boosted performance. In light of the broad selectivity and high controllability, designable templates will provide a useful platform for well-defined nanostructuring.
https://doi.org/10.1038/s41467-022-30137-6
Balanced states and closure relations: the fluid dynamic limit of kinetic models. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2022. - 1 Online-Ressource (20 Seiten). - (Preprint ; M22,03)
The paper is concerned with closure relations for moment hierarchies of gaskinetic systems in the uid dynamic limit. We develop the concept of balanced solutions which provides a more detailed description of kinetic solutions that the classical approaches. This allows to compare di_erent models in use like the nonlinear Boltzmann equation, its linearization, and the BGK model and their relation to the classical Navier-Stokes equations.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2022200188
Stationary, continuous, and sequential surface-enhanced raman scattering sensing based on the nanoscale and microscale polymer-metal composite sensor particles through microfluidics: a review. - In: Advanced optical materials, ISSN 2195-1071, Bd. 10 (2022), 7, 2102757, S. 1-25
Surface-enhanced Raman scattering (SERS) is a label-free and accurate analytical technique for the detection of a broad range of various analytes such as, biomolecules, pesticides, petrochemicals, as well as, cellular and other biological systems. A key component for the SERS analysis is the substrate which is required to be equipped with plasmonic features of metal nanostructures that directly interact with light and targeted analytes. Either metal nanoparticles can be deposited on the solid support (glass or silicon) which is suitable for stationary SERS analysis or dispersed in the solution (freely moving nanoparticles). Besides these routinely utilizing SERS substrates, polymer-metal composite particles are promising for sustained SERS analysis where metal nanoparticles act as plasmon-active (hence SERS-active) components and polymer particles act as support to the metal nanoparticles. Composite sensor particles provide 3D interaction possibilities for analytes, suitable for stationary, continuous, and sequential analysis, and they are reusable/regenerated. Therefore, this review is focused on the experimental procedures for the development of multiscale, uniform, and reproducible composite sensor particles together with their application for SERS analysis. The microfluidic reaction technique is highly versatile in the production of uniform and size-tunable composite particles, as well as, for conducting SERS analysis.
https://doi.org/10.1002/adom.202102757
Nanoscale surface morphology modulation of graphene - i-SiC heterostructures. - In: Materials today, ISSN 2214-7853, Bd. 53 (2022), 2, S. 289-292
A multitude gratings design consists of gratings with different pitches ranging from the micrometre down to sub 40 nm scale combined with sub 10 nm step heights modulating the surface morphology for length scale measurements is proposed. The surface morphology modulation was performed using electron beam lithography incorporating a standard semiconductor processing technology. The critical dimension, edge roughness, step heights and line morphology in dependence on the grating pitch is studied.
https://doi.org/10.1016/j.matpr.2021.06.427
Relative oscillation theory and essential spectra of Sturm-Liouville operators. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2022. - 1 Online-Ressource (15 Seiten). - (Preprint ; M22,02)
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank one perturbations.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2022200169
On characteristic invariants of matrix pencils and linear relations. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2022. - 1 Online-Ressource (35 Seiten). - (Preprint ; M22,01)
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank one perturbations.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2022200140