Broadband Fields Radiated in a Solid by Water-Coupled Transducers: A Comparison of Approximate Models, Numerical Approaches and Experiments

In number of configurations, ultrasonic tests in the French nuclear industry are made using water-coupled focused transducers. To study the influence of the various parameters involved in transducer/piece configurations, model-based predictions of the field radiated by transducers are very useful. A model (called Champ-Sons) has been developed at the French Atomic Energy Commission (CEA) to calculate the field radiated by focused or unfocused transducer through liquid/solid interface at normal or oblique incidence [1]. It can deal with radiating surface of complex (3-D) shape (spherical focusing, Fermat’s surfaces, multiple-elements [2] etc.). The calculation is done directly in the time domain for broadband sources and in the frequency domain for narrowband sources. In its present form Champ-Sons deals with either plane or cylindrical interfaces between a fluid and an isotropic solid. It is implemented in a user-friendly software developed at the CEA called CIVA [3] for NDT data processing (eddy-current, ultrasonics, neutrongraphy, radiography). Since non-canonical configurations are considered and pure numerical schemes are too computer intensive, the model treats the refraction at the fluid/solid interface in an approximate way. It has been validated experimentally [1]

Calculation of Wideband Ultrasonic Fields Radiated by Immersed Transducers into Solids Through Curved Interfaces

In ultrasonic nondestructive testing (NDT), configurations of immersion techniques where transducers radiate through non-planar interfaces are often encountered, e.g., pipe inspection where the probe can be scanned either inside or outside the pipe. When local radii of curvature are far larger than typical wavepaths in the coupling fluid and into the piece, field predictions can often be made assuming a plane interface. For smaller radii, such an approximation is not valid

Broadband Fields Radiated in a Solid by Water-Coupled Transducers: A Comparison of Approximate Models, Numerical Approaches and Experiments

In number of configurations, ultrasonic tests in the French nuclear industry are made using water-coupled focused transducers. To study the influence of the various parameters involved in transducer / piece configurations, model-based predictions of the field radiated by transducers are very useful. A model (called Champ-Sons) has been developed at th

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces

An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which also go under other names such as Spoof Surface Plasmon Polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered and an implicit long-scale wavelength is identified and compared to full numerical simulations. We also investigate non-periodic situations where a long-scale geometric variation in the structure is introduced and show that localised defect states emerge which the asymptotic theory explains

Quantum Point Contacts and Coherent Electron Focusing

I. Introduction II. Electrons at the Fermi level III. Conductance quantization of a quantum point contact IV. Optical analogue of the conductance quantization V. Classical electron focusing VI. Electron focusing as a transmission problem VII. Coherent electron focusing (Experiment, Skipping orbits and magnetic edge states, Mode-interference and coherent electron focusing) VIII. Other mode-interference phenomenaComment: #3 of a series of 4 legacy reviews on QPC'