The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with 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 vertebral body

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 multifrequency 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

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

Scanning-probe spectroscopy of semiconductor donor molecules

Semiconductor devices continue to press into the nanoscale regime, and new applications have emerged for which the quantum properties of dopant atoms act as the functional part of the device, underscoring the necessity to probe the quantum structure of small numbers of dopant atoms in semiconductors[1-3]. Although dopant properties are well-understood with respect to bulk semiconductors, new questions arise in nanosystems. For example, the quantum energy levels of dopants will be affected by the proximity of nanometer-scale electrodes. Moreover, because shallow donors and acceptors are analogous to hydrogen atoms, experiments on small numbers of dopants have the potential to be a testing ground for fundamental questions of atomic and molecular physics, such as the maximum negative ionization of a molecule with a given number of positive ions[4,5]. Electron tunneling spectroscopy through isolated dopants has been observed in transport studies[6,7]. In addition, Geim and coworkers identified resonances due to two closely spaced donors, effectively forming donor molecules[8]. Here we present capacitance spectroscopy measurements of silicon donors in a gallium-arsenide heterostructure using a scanning probe technique[9,10]. In contrast to the work of Geim et al., our data show discernible peaks attributed to successive electrons entering the molecules. Hence this work represents the first addition spectrum measurement of dopant molecules. More generally, to the best of our knowledge, this study is the first example of single-electron capacitance spectroscopy performed directly with a scanning probe tip[9].Comment: In press, Nature Physics. Original manuscript posted here; 16 pages, 3 figures, 5 supplementary figure

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

Designing Cathodes and Cathode Active Materials for Solid‐State Batteries

Solid-state batteries (SSBs) currently attract great attention as a potentially safe electrochemical high-energy storage concept. However, several issues still prevent SSBs from outperforming today\u27s lithium-ion batteries based on liquid electrolytes. One major challenge is related to the design of cathode active materials (CAMs) that are compatible with the superionic solid electrolytes (SEs) of interest. This perspective, gives a brief overview of the required properties and possible challenges for inorganic CAMs employed in SSBs, and describes state-of-the art solutions. In particular, the issue of tailoring CAMs is structured into challenges arising on the cathode-, particle-, and interface-level, related to microstructural, (chemo-)mechanical, and (electro-)chemical interplay of CAMs with SEs, and finally guidelines for future CAM development for SSBs are proposed

Short-pulse frequency stabilization of a MW-class ECRH gyrotron at W7-X for CTS diagnostic

At the Wendelstein 7-X stellarator, a 174 GHz Collective Thomson Scattering (CTS) diagnostic will be implemented. One of the 140 GHz Electron Cyclotron Resonance Heating (ECRH) gyrotrons will be operated at around 174 GHz in a higher cavity mode, using it as source for the CTS mm-wave probing beam. To prevent any damage to the CTS receiver, a notch filter cuts out the high-power gyrotron signal at the entrance of the receiver. The bandwidth of the gyrotron signal determines the notch filter bandwidth. First proof-of-principle experiments on frequency stabilization were conducted on W7-X ECRH gyrotrons employing Phase-Locked Loop techniques. The gyrotron output frequency was controlled with the accelerating voltage, which is applied between the anode and cathode of the gyrotron diode-type Magnetron Injection Gun. Frequency stabilization experiments with 10 ms pulses were conducted at the gyrotron nominal frequency of 140 GHz as well as at 174 GHz. It is concluded that the gyrotron frequency could be stabilized for at least 3 ms at 140 GHz and 8 ms at 174 GHz. In the frequency spectrum, a clear main peak of the gyrotron frequency at 140 GHz with a full -15 dB linewidth of below 500 Hz was achieved

Changes in Plant Species Richness Induce Functional Shifts in Soil Nematode Communities in Experimental Grassland

Changes in plant diversity may induce distinct changes in soil food web structure and accompanying soil feedbacks to plants. However, knowledge of the long-term consequences of plant community simplification for soil animal food webs and functioning is scarce. Nematodes, the most abundant and diverse soil Metazoa, represent the complexity of soil food webs as they comprise all major trophic groups and allow calculation of a number of functional indices.We studied the functional composition of nematode communities three and five years after establishment of a grassland plant diversity experiment (Jena Experiment). In response to plant community simplification common nematode species disappeared and pronounced functional shifts in community structure occurred. The relevance of the fungal energy channel was higher in spring 2007 than in autumn 2005, particularly in species-rich plant assemblages. This resulted in a significant positive relationship between plant species richness and the ratio of fungal-to-bacterial feeders. Moreover, the density of predators increased significantly with plant diversity after five years, pointing to increased soil food web complexity in species-rich plant assemblages. Remarkably, in complex plant communities the nematode community shifted in favour of microbivores and predators, thereby reducing the relative abundance of plant feeders after five years.The results suggest that species-poor plant assemblages may suffer from nematode communities detrimental to plants, whereas species-rich plant assemblages support a higher proportion of microbivorous nematodes stimulating nutrient cycling and hence plant performance; i.e. effects of nematodes on plants may switch from negative to positive. Overall, food web complexity is likely to decrease in response to plant community simplification and results of this study suggest that this results mainly from the loss of common species which likely alter plant-nematode interactions

Development of the 174 GHz collective Thomson scattering diagnostics at Wendelstein 7-X

In this paper, we present the design and commissioning results of the upgraded collective Thomson scattering diagnostic at the Wendelstein 7-X stellarator. The diagnostic has a new radiometer designed to operate between the second and third harmonics of the electron cyclotron emission from the plasma at 171–177 GHz, where the emission background has a minimum and is of order 10–100 eV. It allows us to receive the scattered electromagnetic field with a significantly improved signal-to-noise ratio and extends the set of possible scattering geometries compared to the case of the original instrument operated at 140 GHz. The elements of the diagnostic are a narrowband notch filter and a frequency stabilized probing gyrotron that will allow measuring scattered radiation spectra very close to the probing frequency. Here, we characterize the microwave components applied to the radiometer and demonstrate the performance of the complete system that was achieved during the latest experimental campaign, OP2.1