Uncertainty Relations in the Madelung Picture

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

Design of a Characterisation Environment for a MEMS Ultrasound Sensor under Guided Ultrasonic Wave Excitation

Microelectromechanical Systems (MEMS) are a current subject of research in the field of structural health monitoring (SHM) for the detection of guided ultrasonic waves (GUW). The dispersive behaviour of GUW, reflections and other kinds of wave interactions might result in a complex wave field that requires a specific analysis and interpretation of the recorded signals. This makes it difficult or impossible to interpret the sensor signal regarding the distinguishability between the sensor transfer behaviour and the specific behaviour of the test structure. Therefore, a proper application-suited design of the tested structure is crucial for reliable sensor characterisation. The aim of this contribution is the design and evaluation of a setup that allows a representative situation for a GUW application and provides a defined vibration energy for a MEMS sensor characterisation. Parameters such as the specimen’s geometry, material properties and the sensor specifications are taken into account as well as the experimental settings of the GUW excitation. Furthermore, the requirements for the test application case are discussed.

Finite Element Simulation of Axisymmetric Elastic and Electroelastic Wave Propagation Using Local-Domain Wave Packet Enrichment

A local-domain wave packet enriched multiphysics finite element (FE) formulation is employed for accurately solving axisymmetric wave propagation problems in elastic and piezoelastic media, involving complex wave modes and sharp jumps at the wavefronts, which pose challenges to the conventional FE solutions. The conventional Lagrangian interpolations for the displacement and electric potential fields are enriched with the element-domain sinusoidal functions that satisfy the partition of unity condition. The extended Hamilton’s principle is employed to derive the coupled system of equations of motion which is solved using the simple Newmark-β direct time integration scheme without resorting to any remeshing near the wavefronts or post-processing. The performance of the enrichment is assessed for the axisymmetric problems of impact waves in elastic and piezoelectric cylinders and elastic half-space, bulk and Rayleigh waves in the semi-infinite elastic domain and ultrasonic Lamb wave actuation and propagation in plate-piezoelectric transducer system. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for all problems, including those involving multiple complex wave modes and sharp discontinuities in the fields at the wavefronts.

Deep learning enables accurate sound redistribution via nonlocal metasurfaces

Conventional acoustic metasurfaces are constructed with gradiently "local" phase shift profiles provided by subunits. The local strategy implies the ignorance of the mutual coupling between subunits, which limits the efficiency of targeted sound manipulation, especially in complex environments. By taking into account the "nonlocal" interaction among subunits, nonlocal metasurface offers an opportunity for accurate control of sound propagation, but the requirement of the consideration of gathering coupling among all subunits, not just the nearest-neighbor coupling, greatly increases the complexity of the system and therefore hinders the explorations of functionalities of nonlocal metasurfaces. In this work, empowered by deep learning algorithms, the complex gathering coupling can be learned efficiently from the preset dataset so that the functionalities of nonlocal metasurfaces can be significantly uncovered. As an example, we demonstrate that nonlocal metasurfaces, which can redirect an incident wave into multi-channel reflections with arbitrary energy ratios, can be accurately predicted by deep learning algorithms. Compared to the theory, the relative error of the energy ratios is less than 1\%. Furthermore, experiments witness three-channel reflection with three types of energy ratios of (1, 0, 0), (1/2, 0, 1/2), and (1/3, 1/3, 1/3), proving the validity of the deep learning enabled nonlocal metasurfaces. Our work might blaze a new trail in the design of acoustic functional devices, especially for the cases containing complex wave-matter interactions.

Multicolor Holographic Display of 3D Scenes Using Referenceless Phase Holography (RELPH)

In this paper, we present a multicolor display via referenceless phase holography (RELPH). RELPH permits the display of full optical wave fields (amplitude and phase) using two liquid crystal phase-only spatial light modulators in a Michelson-interferometer-based arrangement. Complex wave fields corresponding to arbitrary real or artificial 3D scenes are decomposed into two mutually coherent wave fields of constant amplitude whose phase distributions are modulated onto the wave fields reflected by the respective light modulators. Here, we present the realization of that concept in two different ways: firstly, via temporal multiplexing using a single setup, switching between wavelengths for temporal integration of the respective wavefields; secondly, using spatial multiplexing of different wavelengths with multiple Michelson-based setups; and finally, we present an approach to magnify the 3D scenes displayed by light modulators with limited space–bandwidth product for a comfortable viewing experience.

Synthesis and Characterization of a Cobalt(III) Corrole with an Sbound DMSO Ligand

A cobalt(III) corrole complex with an apical dmso ligand is presented. Crystallographic and spectroscopic data are used to unequivocally establish the dmso(O) vs. dmso(S) coordination in this complex. Wave function based methods were used to calculate the frontier orbitals for the complexes with O-bound and S-bound dmso ligands. Electrochemical properties of the complex is presented as well.<br>

Synthesis and Characterization of a Cobalt(III) Corrole with an Sbound DMSO Ligand

A cobalt(III) corrole complex with an apical dmso ligand is presented. Crystallographic and spectroscopic data are used to unequivocally establish the dmso(O) vs. dmso(S) coordination in this complex. Wave function based methods were used to calculate the frontier orbitals for the complexes with O-bound and S-bound dmso ligands. Electrochemical properties of the complex is presented as well.<br>