Search Results
A rough path perspective on renormalization
We develop the algebraic theory of rough path translation. Particular attention is given to the case of branched rough paths, whose underlying algebraic structure (Connes-Kreimer, Grossman-Larson) makes it a useful model case of a regularity structure in the sense of Hairer. Pre-Lie structures are seen to play a fundamental rule which allow a direct understanding of the translated (i.e. renormalized) equation under consideration. This construction is also novel with regard to the algebraic renormalization theory for regularity structures due to Bruned–Hairer–Zambotti (2016), the links with which are discussed in detail. © 2019 The Author(s)
Optimal control of multiphase steel production
An optimal control problem for the production of multiphase steel is investigated that takes into account phase transformations in the steel slab. The state equations are a semilinear heat equation coupled with an ordinary differential equation, that describes the evolution of the steel microstructure. The time-dependent heat transfer coefficient serves as a control function. Necessary and sufficient optimality conditions for the control problem are derived. For the numerical solution of the control problem, a reduced sequential quadratic programming method with a primal-dual active set strategy is developed. The numerical results are presented for the optimal control of a cooling line in the production of hot-rolled Mo–Mn dual phase steel. © 2019, The Author(s).
Dynamic maximum entropy reduction
Any physical system can be regarded on different levels of description varying by how detailed the description is. We propose a method called Dynamic MaxEnt (DynMaxEnt) that provides a passage from the more detailed evolution equations to equations for the less detailed state variables. The method is based on explicit recognition of the state and conjugate variables, which can relax towards the respective quasi-equilibria in different ways. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of conjugate variables guarantees that the reduced equations are closed. Moreover, an infinite chain of consecutive DynMaxEnt approximations can be constructed. The method is demonstrated on a particle with friction, complex fluids (equipped with conformation and Reynolds stress tensors), hyperbolic heat conduction and magnetohydrodynamics. © 2020 by the authors.
A monolithic ASIC demonstrator for the Thin Time-of-Flight PET scanner
Time-of-flight measurement is an important advancement in PET scanners to improve image reconstruction with a lower delivered radiation dose. This article describes the monolithic ASIC for the TT-PET project, a novel idea for a high-precision PET scanner for small animals. The chip uses a SiGe Bi-CMOS process for timing measurements, integrating a fully-depleted pixel matrix with a low-power BJT-based front-end per channel, integrated on the same 100 µm thick die. The target timing resolution of the scanner is 30 ps RMS for electrons from the conversion of 511 keV photons. The system will include 1.6 million channels across almost 2000 different chips. A full-featured demonstrator chip with a 3×10 matrix of 500×500 µm2 pixels was fabricated to validate each block. Its design and experimental results are presented here. © 2019 CERN.
Optimizing Variable-Axial Fiber-Reinforced Composite Laminates: The Direct Fiber Path Optimization Concept
The concept of aligning reinforcing fibers in arbitrary directions offers a new perception of exploiting the anisotropic characteristic of the carbon fiber-reinforced polymer (CFRP) composites. Complementary to the design concept of multiaxial composites, a laminate reinforced with curvilinear fibers is called variable-axial (also known as variable stiffness and variable angle tow). The Tailored Fiber Placement (TFP) technology is well capable of manufacturing textile preforming with a variable-axial fiber design by using adapted embroidery machines. This work introduces a novel concept for simulation and optimization of curvilinear fiber-reinforced composites, where the novelty relies on the local optimization of both fiber angle and intrinsic thickness build-up concomitantly. This framework is called Direct Fiber Path Optimization (DFPO). Besides the description of DFPO, its capabilities are exemplified by optimizing a CFRP open-hole tensile specimen. Key results show a clear improvement compared to the current often used approach of applying principal stress trajectories for a variable-axial reinforcement pattern. © 2019 Lars Bittrich et al.
Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans
We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities. © Copyright © 2019 Pournaki, Merfort, Ruiz, Kouvaris, Hövel and Hizanidis.
The invariant distribution of wealth and employment status in a small open economy with precautionary savings
We study optimal savings in continuous time with exogenous transitions between employment and unemployment as the only source of uncertainty in a small open economy. We prove the existence of an optimal consumption path. We exploit that the dynamics of consumption and wealth between jumps can be expressed as a Fuchsian system. We derive conditions under which an invariant joint distribution for the state variables, i.e., wealth and labour market status, exists and is unique. We also provide conditions under which the distribution of these variables converges to the invariant distribution. Our analysis relies on the notion of T-processes and applies results on the stability of Markovian processes from Meyn and Tweedie (1993a, b,c). © 2019 The Author(s)
A distributed control problem for a fractional tumor growth model
In this paper, we study the distributed optimal control of a system of three evolutionary equations involving fractional powers of three self-adjoint, monotone, unbounded linear operators having compact resolvents. The system is a generalization of a Cahn-Hilliard type phase field system modeling tumor growth that has been proposed by Hawkins-Daarud, van der Zee and Oden. The aim of the control process, which could be realized by either administering a drug or monitoring the nutrition, is to keep the tumor cell fraction under control while avoiding possible harm for the patient. In contrast to previous studies, in which the occurring unbounded operators governing the diffusional regimes were all given by the Laplacian with zero Neumann boundary conditions, the operators may in our case be different; more generally, we consider systems with fractional powers of the type that were studied in a recent work by the present authors. In our analysis, we show the Fréchet differentiability of the associated control-to-state operator, establish the existence of solutions to the associated adjoint system, and derive the first-order necessary conditions of optimality for a cost functional of tracking type. © 2019 by the authors.
Increased pore size of scaffolds improves coating efficiency with sulfated hyaluronan and mineralization capacity of osteoblasts
Background: Delayed bone regeneration of fractures in osteoporosis patients or of critical-size bone defects after tumor resection are a major medical and socio-economic challenge. Therefore, the development of more effective and osteoinductive biomaterials is crucial. Methods: We examined the osteogenic potential of macroporous scaffolds with varying pore sizes after biofunctionalization with a collagen/high-sulfated hyaluronan (sHA3) coating in vitro. The three-dimensional scaffolds were made up from a biodegradable three-armed lactic acid-based macromer (TriLA) by cross-polymerization. Templating with solid lipid particles that melt during fabrication generates a continuous pore network. Human mesenchymal stem cells (hMSC) cultivated on the functionalized scaffolds in vitro were investigated for cell viability, production of alkaline phosphatase (ALP) and bone matrix formation. Statistical analysis was performed using student's t-test or two-way ANOVA. Results: We succeeded in generating scaffolds that feature a significantly higher average pore size and a broader distribution of individual pore sizes (HiPo) by modifying composition and relative amount of lipid particles, macromer concentration and temperature for cross-polymerization during scaffold fabrication. Overall porosity was retained, while the scaffolds showed a 25% decrease in compressive modulus compared to the initial TriLA scaffolds with a lower pore size (LoPo). These HiPo scaffolds were more readily coated as shown by higher amounts of immobilized collagen (+ 44%) and sHA3 (+ 25%) compared to LoPo scaffolds. In vitro, culture of hMSCs on collagen and/or sHA3-coated HiPo scaffolds demonstrated unaltered cell viability. Furthermore, the production of ALP, an early marker of osteogenesis (+ 3-fold), and formation of new bone matrix (+ 2.5-fold) was enhanced by the functionalization with sHA3 of both scaffold types. Nevertheless, effects were more pronounced on HiPo scaffolds about 112%. Conclusion: In summary, we showed that the improvement of scaffold pore sizes enhanced the coating efficiency with collagen and sHA3, which had a significant positive effect on bone formation markers, underlining the promise of using this material approach for in vivo studies. © 2019 The Author(s).