A platform for benchmark cases in computational acoustics

Solutions to the partial differential equations that describe acoustic problems can be found by analytical, numerical and experimental techniques. Within arbitrary domains and for arbitrary initial and boundary conditions, all solution techniques require certain assumptions and simplifications. It is difficult to estimate the precision of a solution technique. Due to the lack of a common process to quantify and report the performance of the solution technique, a variety of ways exists to discuss the results with the scientific community. Moreover, the absence of general reference results does hamper the validation of newly developed techniques. Over the years many researchers in the field of computational acoustics have therefore expressed the need and wish to have available common benchmark cases. This contribution is intended to be the start of a long term project, about deploying benchmarks in the entire field of computational acoustics. The platform is a web-based database, where cases and results can be submitted by all researchers and are openly available. Long-term maintenance of this platform is ensured. As an example of good practice, this paper presents a framework for the field of linear acoustic. Within this field, different categories are defined – as bounded or unbounded problems, scattering or radiating problems and time-domain as well as frequency-domain problems – and a structure is proposed how to describe a benchmark case. Furthermore, a way of reporting on the used solution technique and its result is suggested. Three problems have been defined that demonstrate how the benchmark cases are intended to be used

Coupled CFD-CAA approach for rotating systems

We present a recently developed computational scheme for the numerical simulation of flow induced sound for rotating systems. Thereby, the flow is fully resolved in time by utilizing a DES (Detached Eddy Simulation) turbulance model and using an arbitrary mesh interface scheme for connecting rotating and stationary domains. The acoustic field is modeled by a perturbation ansatz resulting in a convective wave equation based on the acoustic scalar potential and the substational time derivative of the incompressible flow pressure as a source term. We use the Finite-Element (FE) method for solving the convective wave equation and apply a Nitsche type mortaring at the interface between rotating and stationary domains. The whole scheme is applied to the numerical computation of a side channel blower

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

The Iteratively Regularized Gau{\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

Annihilation of low energy antiprotons in silicon

The goal of the AE$\mathrm{\bar{g}}$IS experiment at the Antiproton Decelerator (AD) at CERN, is to measure directly the Earth's gravitational acceleration on antimatter. To achieve this goal, the AE$\mathrm{\bar{g}}$IS collaboration will produce a pulsed, cold (100 mK) antihydrogen beam with a velocity of a few 100 m/s and measure the magnitude of the vertical deflection of the beam from a straight path. The final position of the falling antihydrogen will be detected by a position sensitive detector. This detector will consist of an active silicon part, where the annihilations take place, followed by an emulsion part. Together, they allow to achieve 1$$ precision on the measurement of $\bar{g}$ with about 600 reconstructed and time tagged annihilations. We present here, to the best of our knowledge, the first direct measurement of antiproton annihilation in a segmented silicon sensor, the first step towards designing a position sensitive silicon detector for the AE$\mathrm{\bar{g}}$IS experiment. We also present a first comparison with Monte Carlo simulations (GEANT4) for antiproton energies below 5 MeVComment: 21 pages in total, 29 figures, 3 table

Prospects for measuring the gravitational free-fall of antihydrogen with emulsion detectors

The main goal of the AEgIS experiment at CERN is to test the weak equivalence principle for antimatter. AEgIS will measure the free-fall of an antihydrogen beam traversing a moir\'e deflectometer. The goal is to determine the gravitational acceleration g for antihydrogen with an initial relative accuracy of 1% by using an emulsion detector combined with a silicon micro-strip detector to measure the time of flight. Nuclear emulsions can measure the annihilation vertex of antihydrogen atoms with a precision of about 1 - 2 microns r.m.s. We present here results for emulsion detectors operated in vacuum using low energy antiprotons from the CERN antiproton decelerator. We compare with Monte Carlo simulations, and discuss the impact on the AEgIS project.Comment: 20 pages, 16 figures, 3 table

Joint multi-field T1 quantification for fast field-cycling MRI

Acknowledgment This article is based upon work from COST Action CA15209, supported by COST (European Cooperation in Science and Technology). Oliver Maier is a Recipient of a DOC Fellowship (24966) of the Austrian Academy of Sciences at the Institute of Medical Engineering at TU Graz. The authors would like to acknowledge the NVIDIA Corporation Hardware grant support.Peer reviewedPublisher PD

Building the impedance model of a real machine

A reliable impedance model of a particle accelerator can be built by combining the beam coupling impedances of all the components. This is a necessary step to be able to evaluate the machine performance limitations, identify the main contributors in case an impedance reduction is required, and study the interaction with other mechanisms such as optics nonlinearities, transverse damper, noise, space charge, electron cloud, beam-beam (in a collider). The main phases to create a realistic impedance model, and verify it experimentally, will be reviewed, highlighting the main challenges. Some examples will be presented revealing the levels of precision of machine impedance models that have been achieved