A note on boundary conditions for quantum hydrodynamic equations

AbstractThe asymptotic behavior of the thermal equilibrium state of a bipolar quantum hydrodynamic model is considered. The quantum limit L → 0, L denoting a characteristic device length, is carried out rigorously. It shows that the classical assumption of charge neutrality at the boundary becomes invalid for ultra small semiconductor devices, whereas the assumption of vanishing boundary quantum effects will be confirmed. Furthermore, numerical simulations are presented, which give insight in the quantitative behavior

Reduced basis catalogs for gravitational wave templates

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for non-spinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about $10-10^5$ fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.Comment: Minor changes in some of the phrasing to match the version as published in PR

Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning

We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime

Polymer ultrapermeability from the inefficient packing of 2D chains

The promise of ultrapermeable polymers, such as poly(trimethylsilylpropyne) (PTMSP), for reducing the size and increasing the efficiency of membranes for gas separations remains unfulfilled due to their poor selectivity. We report an ultrapermeable polymer of intrinsic microporosity (PIM-TMN-Trip) that is substantially more selective than PTMSP. From molecular simulations and experimental measurement we find that the inefficient packing of the two-dimensional (2D) chains of PIM-TMN-Trip generates a high concentration of both small (<0.7 nm) and large (0.7–1.0 nm) micropores, the former enhancing selectivity and the latter permeability. Gas permeability data for PIM-TMN-Trip surpass the 2008 Robeson upper bounds for O2/N2, H2/N2, CO2/N2, H2/CH4 and CO2/CH4, with the potential for biogas purification and carbon capture demonstrated for relevant gas mixtures. Comparisons between PIM-TMN-Trip and structurally similar polymers with three-dimensional (3D) contorted chains confirm that its additional intrinsic microporosity is generated from the awkward packing of its 2D polymer chains in a 3D amorphous solid. This strategy of shape-directed packing of chains of microporous polymers may be applied to other rigid polymers for gas separations

Quantum Energy-Transport and Drift-Diffusion Models

We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an � expansion of these models, � 2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the Drift-Diffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

Unravelling surface and interfacial structures of a metal–organic framework by transmission electron microscopy

Metal-organic frameworks (MOFs) are crystalline porous materials with designable topology, porosity and functionality, having promising applications in gas storage and separation, ion conduction and catalysis. It is challenging to observe MOFs with transmission electron microscopy (TEM) due to the extreme instability of MOFs upon electron beam irradiation. Here, we use a direct-detection electron-counting camera to acquire TEM images of the MOF ZIF-8 with an ultralow dose of 4.1 electrons per square ångström to retain the structural integrity. The obtained image involves structural information transferred up to 2.1 Å, allowing the resolution of individual atomic columns of Zn and organic linkers in the framework. Furthermore, TEM reveals important local structural features of ZIF-8 crystals that cannot be identified by diffraction techniques, including armchair-type surface terminations and coherent interfaces between assembled crystals. These observations allow us to understand how ZIF-8 crystals self-assemble and the subsequent influence of interfacial cavities on mass transport of guest molecules

On adjoint-based optimization of a free surface Stokes flow

This work deals with the optimal control of a free surface Stokes flow which responds to an applied outer pressure. Typical applications are fiber spinning or thin film manufacturing. We present and discuss two adjoint-based optimization approaches that differ in the treatment of the free boundary as either state or control variable. In both cases the free boundary is modeled as the graph of a function. The PDE-constrained optimization problems are numerically solved by the BFGS method, where the gradient of the reduced cost function is expressed in terms of adjoint variables. Numerical results for both strategies are finally compared with respect to accuracy and efficiency

Adjoint based optimal control using mesh-less discretizations

An easy numerical handling of time-dependent problems with complicated geometries, free moving boundaries and interfaces, or oscillating solutions is of great importance for many applications, e.g., in fluid dynamics (free surface and multiphase flows, fluid-structure interactions [22, 18, 24]), failure mechanics (crack growth and propagation [4]), magnetohydrodynamics (accretion disks, jets and cloud simulation [6]), biophysics and -chemistry. Appropriate discretizations, so-called mesh-less methods, have been developed during the last decades to meet these challenging demands and to relieve the burden of remeshing and successive mesh generation being faced by the conventional mesh-based methods, [16, 10, 3]. The prearranged mesh is an artificial constraint to ensure compatibility of the mesh-based interpolant schemes, that often conflicts with the real physical conditions of the continuum model. Then, remeshing becomes inevitable, which is not only extremely time- and storage consuming but also the source for numerical errors and hence the gradual loss of computational accuracy. Apart from this advantage, mesh-less methods also lead to fundamentally better approximations regarding aspects, such as smoothness, nonlocal interpolation character, flexible connectivity, refinement and enrichment procedures, [16]. The common idea of mesh-less methods is the discretization of the domain of interest by a finite set of independent, randomly distributed particles moving with a characteristic velocity of the problem. Location and distribution of the particles then account for the time-dependent description of the geometry, data and solution. Thereby, the global solution is linearly superposed from the local information carried by the particles. In classical particle methods [20, 21], the respective weight functions are Dirac distributions which yield solutions in a distributional sense

Model reduction of nonlinear problems in structural mechanics

This contribution presents a model reduction method for nonlinear problems in structural mechanics. Emanating from a Finite Element model of the structure, a subspace and a lookup table are generated which do not require a linearisation of the equations. The method is applied to a model created with commercial FEM software. In this case, the terms describing geometrical and material nonlinearities are not explicitly known