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End date: 2023 × Start date: 2023 × Start date: 2023 × DDC: 510 ×

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Now showing 1 - 6 of 6
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    Differentiability Properties for Boundary Control of Fluid-Structure Interactions of Linear Elasticity with Navier-Stokes Equations with Mixed-Boundary Conditions in a Channel
    (New York, NY : Springer, 2023) Hintermüller, Michael; Kröner, Axel
    In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from (Lasiecka et al. in Nonlinear Anal 44:54–85, 2018). An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generalizing the results of (Wollner and Wick in J Math Fluid Mech 21:34, 2019) to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners.
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    Function spaces, time derivatives and compactness for evolving families of Banach spaces with applications to PDEs
    (Orlando, Fla. : Elsevier, 2023) Alphonse, Amal; Caetano, Diogo; Djurdjevac, Ana; Elliott, Charles M.
    We develop a functional framework suitable for the treatment of partial differential equations and variational problems on evolving families of Banach spaces. We propose a definition for the weak time derivative that does not rely on the availability of a Hilbertian structure and explore conditions under which spaces of weakly differentiable functions (with values in an evolving Banach space) relate to classical Sobolev–Bochner spaces. An Aubin–Lions compactness result is proved. We analyse concrete examples of function spaces over time-evolving spatial domains and hypersurfaces for which we explicitly provide the definition of the time derivative and verify isomorphism properties with the aforementioned Sobolev–Bochner spaces. We conclude with the proof of well posedness for a class of nonlinear monotone problems on an abstract evolving space (generalising the evolutionary p-Laplace equation on a moving domain or surface) and identify some additional problems that can be formulated with the setting developed in this work.
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    Topology- and Geometry-Controlled Functionalization of Nanostructured Metamaterials
    (Basel : MDPI, 2023) Fomin, Vladimir M.; Marquardt, Oliver
    [no abstract available]
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    Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement
    (Basel : MDPI, 2023) Mertens, Lotte; van Wezel, Jasper
    The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does not imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear.
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    Can One Series of Self-Organized Nanoripples Guide Another Series of Self-Organized Nanoripples during Ion Bombardment: From the Perspective of Power Spectral Density Entropy?
    (Basel : MDPI, 2023) Li, Hengbo; Li, Jinyu; Yang, Gaoyuan; Liu, Ying; Frost, Frank; Hong, Yilin
    Ion bombardment (IB) is a promising nanofabrication tool for self-organized nanostructures. When ions bombard a nominally flat solid surface, self-organized nanoripples can be induced on the irradiated target surface, which are called intrinsic nanoripples of the target material. The degree of ordering of nanoripples is an outstanding issue to be overcome, similar to other self-organization methods. In this study, the IB-induced nanoripples on bilayer systems with enhanced quality are revisited from the perspective of guided self-organization. First, power spectral density (PSD) entropy is introduced to evaluate the degree of ordering of the irradiated nanoripples, which is calculated based on the PSD curve of an atomic force microscopy image (i.e., the Fourier transform of the surface height. The PSD entropy can characterize the degree of ordering of nanoripples). The lower the PSD entropy of the nanoripples is, the higher the degree of ordering of the nanoripples. Second, to deepen the understanding of the enhanced quality of nanoripples on bilayer systems, the temporal evolution of the nanoripples on the photoresist (PR)/antireflection coating (ARC) and Au/ARC bilayer systems are compared with those of single PR and ARC layers. Finally, we demonstrate that a series of intrinsic IB-induced nanoripples on the top layer may act as a kind of self-organized template to guide the development of another series of latent IB-induced nanoripples on the underlying layer, aiming at improving the ripple ordering. The template with a self-organized nanostructure may alleviate the critical requirement for periodic templates with a small period of ~100 nm. The work may also provide inspiration for guided self-organization in other fields.
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    Genealogical properties of spatial models in Population Genetics
    (Hannover : Technische Informationsbibliothek, 2023-09) Wirtz, Johannes
    At the interface between Phylo- and Population Genetics, and recently heavily inspired by Epidemonology, the discipline of Phylogeography comprises modelling techniques from classical theoretical biology and combines them with a spatial (2D or 3D) aspect, with the purpose of utilizing geographical information in the analysis to understand the evolutionary history of a biological system or aspects of virology such as directionality and seasonality in pandemic outbreaks [1, 2, 3, 4]. An prime example of this are datasets that take into account the sampling locations of its components (geo-referenced genomic data). In this project, we have focused on the model called "spatial Lambda-Fleming-Viot process" ( V [5, 6]) and analzed its statistical properties forward in time as well as in the ancestral (dual) process, with results that may be used for parameter inference. Of particlar interest was the spatial variance, denoted , a parameter controlling the speed at which genetic information is spread across space and therefore an analog of the reproduction number (R0) used in epidemonology e.g. to assess the infectiousness of differing viral strains. We explored the relation of this parameter to the time to coalescence between lineage pairs in this model and described methods of estimating it from sampled data under different circumstances. We have furthermore investigated similarities and differences between this model and classical models in Population Genetics, particularly Birth-Death processes, which are heavily used for all kinds of biological inference problems, but do not by themselves feature a spatial component. We compared the Vto a variant of the Birth-Death process where the location of a live individual changes over the course of its lifetime according to a Brownian motion. This process is not as easily viewed backward in time as the V, but the genalogical process is accessible by Markov-Chain Monte Carlosimulation, as the likelihoods of ancestral positions and branch lengths are easily calculated, making this model easily applicable to data. Our analysis highlights the analogy between the two processes forward in time as well as backward in time; on the other hand, we also observed a divergent behavior of the two models when no prior on the phylogenetic time scale was assumed. Lastly, this project has given rise to a study of combinatorial properties of tree shapes relevant to the V, the Birth-Death and other biological processes. In particular, we were able to identify the combinatorial class genealogical trees generated from these processes belong to and verify a conjecture regarding their enumeration. Preliminary versions of software tools for the aforementioned inference have also been provided.