Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement

An efficient mixed variational reduced order model formulation for non-linear analyses of elastic shells

The Koiter-Newton method had recently demonstrated a superior performance for non-linear analyses of structures, compared to traditional path-following strategies. The method follows a predictor-corrector scheme to trace the entire equilibrium path. During a predictor step a reduced order model is constructed based on Koiter's asymptotic post-buckling theory which is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid-shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger-Reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out-of-balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems

Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

Weak localization and electron-electron interactions in Indium-doped ZnO nanowires

Single crystal ZnO nanowires doped with indium are synthesized via the laser-assisted chemical vapor deposition method. The conductivity of the nanowires is measured at low temperatures in magnetic fields both perpendicular and parallel to the wire axes. A quantitative fit of our data is obtained, consistent with the theory of a quasi-one-dimensional metallic system with quantum corrections due to weak localization and electron-electron interactions. The anisotropy of the magneto-conductivity agrees with theory. The two quantum corrections are of approximately equal magnitude with respective temperature dependences of T^-1/3 and T^-1/2. The alternative model of quasi-two-dimensional surface conductivity is excluded by the absence of oscillations in the magneto-conductivity in parallel magnetic fields.Comment: 13 pages, Corrected forma

Effects of soil warming and nitrogen foliar applications on bud burst of black spruce

Key message: In mature black spruce, bud burst process is anticipated by soil warming, while delayed by foliar applications of nitrogen; however, the effects depend on growth conditions at the site. Abstract: The observation of phenological events can be used as biological indicator of environmental changes, especially from the perspective of climate change. In boreal forests, the onset of the bud burst is a key factor in the length of the growing season. With current climate change, the major factors limiting the growth of boreal trees (i.e., temperature and nitrogen availability) are changing and studies on mature trees are limited. The aim of this study was to investigate the effects of soil warming and increased nitrogen (N) deposition on bud burst of mature black spruce [Picea mariana (Mill.) BSP]. From 2008 onwards, an experimental manipulation of these environmental growth conditions was conducted in two stands (BER and SIM) at different altitudes in the boreal forest of Quebec, Canada. An increase in soil temperature (H treatment) and a canopy application of artificial rain enriched with nitrogen (N treatment) were performed. Observations of bud phenology were made during May–July 2012 and 2013. In BER, H treatment caused an anticipation (estimated as 1–3 days); while N treatment, a delay (estimated as 1–2 days but only in 2012) in bud burst. No treatments effect was significant in SIM. It has been demonstrated that soil temperature and N availability can play an important role in affecting bud burst in black spruce but the effects of these environmental factors on growth are closely linked with site conditions

Automated Generation of High-Order Modes for Tests of Quasi-Optical Systems of Gyrotrons for W7-X Stellarator

A test system for the verification of the quasi-optical converter system is vital in the gyrotron development. For this reason, an automated measurement setup has been developed and is benchmarked with the TE$_{28,8}$ mode operating in the cavities of the gyrotrons of W7-X with a high purity of about 95 % and a counter-rotating amount of about 0.3 %. The time duration for the mode generator adjustment has been reduced to two days for this mode. After a successful mode excitation, the quasi-optical mode converter, consisting of a launcher and three mirrors, is measured having a vectorial Gaussian mode content of 97 %

Quasi-Optical Mode Generator for Excitation of Very High-Order Modes up to 240 GHz

A new quasi-optical mode generator setup has been designed to excite the TE48,26 mode operating at 238 GHz. It will be the mode with the highest eigenvalue , = 146.80) ever measured in cold tests and therefore the successor of the TE40,23 mode operating at 204 GHz. In this paper, the design of the new coaxial cavity for the mode generator setup is presented, which is based on the cavity design of the corresponding gyrotron. Simulations using a scattering matrix code show a mode purity of 99.5 % at the output of the cavity at an operating frequency of 238.101 GHz. Recently, the main components are under manufacturing. After delivery mid-2024, first experiments will be performed

A compact two-frequency notch filter for millimeter wave plasma diagnostics

Sensitive millimeter wave diagnostics in magnetic confinement plasma fusion experiments need protection from gyrotron stray radiation in the plasma vessel. Modern electron cyclotron resonance heating (ECRH) systems take advantage of multi-frequency gyrotrons. This means that the frequency band of some millimeter wave diagnostics contains more than one narrow-band gyrotron-frequency line, which needs to be effectively suppressed. A compact standard waveguide notch filter based on coupled waveguide resonators with rectangular cross-section is presented which can provide very high suppression of several gyrotron frequencies and has low insertion loss of the passband.Projekt DEA