Derivation, simulation and validation of poroelastic models in dental biomechanics

Poroelasticity and mechanics of growth are playing an increasingly relevant role in biomechanics. This work is a self- contained and holistic presentation of the modeling and simulation of non-linear poroelasticity with and without growth inhomogeneities. Balance laws of poroelasticity are derived in Cartesian coordinates. These allow to write the governing equations in a form that is general but also readily implementable. Closure relations are formally derived from the study of dissipation. We propose an approximation scheme for the poroelasticity problem based on an implicit Euler method for the time discretization and a finite element method for the spatial discretization. The non-linear system is solved by means of Newton's method. Time integration of the growth tensor is discussed for the specific case in which the rate of inelastic deformations is prescribed. We discuss the stability of the mixed finite element discretization of the arising saddle-point problem. We show that a linear finite element approximation of both the unknowns, that is not LBB compliant for the elasticity problem, is nevertheless stable when applied to the linearized poroelasticity problem. This choice enables a fast assembling phase. The discretization of the poroelastic system may present unphysical oscillations if the spatial and temporal step-sizes are not properly chosen. We study the source of these wiggles by comparing the pressure Schur complement to a reaction- diffusion problem. From our analysis, we define a novel Péclet number for the poroelastic system and we show how it depends on the shear and bulk moduli of the solid phase. This number allows to introduce a stability condition that ensures that the solution is free of unphysical oscillations. If this condition on the Péclet number is not met, we introduce a fluid pressure Laplacian stabilization in order to remove the wiggles. This stabilization technique depends on a numerical parameter, whose optimal value is given by the derived Péclet number. Finally, we propose a coupled elastic-poroelastic model for the simulation of a tooth-periodontal ligament system. Because of the high resolution required by this system, we develop an efficient multigrid Newton's method for the non-linear poroelasticity system. The stability condition has again a significant influence on the performances of this solver. If the condition on the Péclet number is not satisfied on all levels of the multigrid algorithm, poor convergence rates or even divergence of the solver can be observed. The stabilization of the coarse grid operators with the optimal fluid pressure Laplacian method is a simple and efficient method to improve the convergence rate of the multigrid solver applied to this saddle-point system. We validate our coupled model against experimental measurements realized by the group of Prof. Bourauel at the University of Bonn

Complex temperature dependence of coupling and dissipation of cavity-magnon polaritons from milliKelvin to room temperature

Hybridized magnonic-photonic systems are key components for future information processing technologies such as storage, manipulation or conversion of data both in the classical (mostly at room temperature) and quantum (cryogenic) regime. In this work, we investigate a YIG sphere coupled strongly to a microwave cavity over the full temperature range from $290\,\mathrm{K}$ down to $30\,\mathrm{mK}$. The cavity-magnon polaritons are studied from the classical to the quantum regime where the thermal energy is less than one resonant microwave quanta, i.e. at temperatures below $1\,\mathrm{K}$. We compare the temperature dependence of the coupling strength $g_{\rm{eff}}(T)$, describing the strength of coherent energy exchange between spin ensemble and cavity photon, to the temperature behavior of the saturation magnetization evolution $M_{\rm{s}}(T)$ and find strong deviations at low temperatures. The temperature dependence of magnonic disspation is governed at intermediate temperatures by rare earth impurity scattering leading to a strong peak at $40\,$K. The linewidth $\kappa_{\rm{m}}$ decreases to $1.2\,$MHz at $30\,$mK, making this system suitable as a building block for quantum electrodynamics experiments. We achieve an electromagnonic cooperativity in excess of $20$ over the entire temperature range, with values beyond $100$ in the milliKelvin regime as well as at room temperature. With our measurements, spectroscopy on strongly coupled magnon-photon systems is demonstrated as versatile tool for spin material studies over large temperature ranges. Key parameters are provided in a single measurement, thus simplifying investigations significantly.Comment: 10 pages , 9 figures in tota

Multigrid for two-sided fractional differential equations discretized by finite volume elements on graded meshes

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite volume elements discretization approach over a generic non-uniform mesh. We focus on grids mapped by a smooth function which consist in a combination of a graded mesh near the singularity and a uniform mesh where the solution is smooth. Such a choice gives rise to Toeplitz-like discretization matrices and thus allows a low computational cost of the matrix-vector product and a detailed spectral analysis. The obtained spectral information is used to develop an ad-hoc parameter free multigrid preconditioner for GMRES, which is numerically shown to yield good convergence results in presence of graded meshes mapped by power functions that accumulate points near the singularity. The approximation order of the considered graded meshes is numerically compared with the one of a certain composite mesh given in literature that still leads to Toeplitz-like linear systems and is then still well-suited for our multigrid method. Several numerical tests confirm that power graded meshes result in lower approximation errors than composite ones and that our solver has a wide range of applicability

Integrating Multi-Preconditioned Conjugate Gradient with Additive Multigrid Strategy

Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of standard MG methods, which are inherently multiplicative, suffers from increasing communication complexity. In such cases, the additive variants of MG methods provide a good alternative due to their inherently parallel nature, although they exhibit slower convergence. This work combines the additive multigrid method with the multipreconditioned conjugate gradient (MPCG) method. In the proposed approach, the MPCG method employs the corrections from the different levels of the MG hierarchy as separate preconditioned search directions. In this approach, the MPCG method updates the current iterate by using the linear combination of the preconditioned search directions, where the optimal coefficients for the linear combination are computed by exploiting the energy norm minimization of the CG method. The idea behind our approach is to combine the $A$-conjugacy of the search directions of the MPCG method and the quasi $H_1$-orthogonality of the corrections from the MG hierarchy. In the numerical section, we study the performance of the proposed method compared to the standard additive and multiplicative MG methods used as preconditioners for the CG method

Speaker Distance Estimation in Enclosures from Single-Channel Audio

Distance estimation from audio plays a crucial role in various applications, such as acoustic scene analysis, sound source localization, and room modeling. Most studies predominantly center on employing a classification approach, where distances are discretized into distinct categories, enabling smoother model training and achieving higher accuracy but imposing restrictions on the precision of the obtained sound source position. Towards this direction, in this paper we propose a novel approach for continuous distance estimation from audio signals using a convolutional recurrent neural network with an attention module. The attention mechanism enables the model to focus on relevant temporal and spectral features, enhancing its ability to capture fine-grained distance-related information. To evaluate the effectiveness of our proposed method, we conduct extensive experiments using audio recordings in controlled environments with three levels of realism (synthetic room impulse response, measured response with convolved speech, and real recordings) on four datasets (our synthetic dataset, QMULTIMIT, VoiceHome-2, and STARSS23). Experimental results show that the model achieves an absolute error of 0.11 meters in a noiseless synthetic scenario. Moreover, the results showed an absolute error of about 1.30 meters in the hybrid scenario. The algorithm's performance in the real scenario, where unpredictable environmental factors and noise are prevalent, yields an absolute error of approximately 0.50 meters. For reproducible research purposes we make model, code, and synthetic datasets available at https://github.com/michaelneri/audio-distance-estimation.Comment: Accepted for publication in IEEE/ACM Transactions on Audio, Speech, and Language Processin

Bau und Vermessung einer laminaren Trennstelle von Flügelvorderkanten

In dieser Arbeit wird ein Demonstrator gebaut und untersucht, um damit eine Methode zur Reduzierung des Umschlags der Grenzschicht am Höhenleitwerk eines langstrecken Flugzeugs zu testen. Dazu sollen aerodynamisch ungünstige Spalte auf der Flügeloberfläche mit einem Titanblech überdeckt werden. Dieser Demonstrator bildet den Ausschnitt eines Höhenleitwerks nach, der ein HLFC System besitzt. Der Demonstrator ist eine ca. 300 x 500 x 108 mm große Niet- und Klebekonstruktion aus CFK-Komponenten, die mittels CFK-Prepregfaserlagen und Vakuumpressen hergestellt werden. Mit dieser Arbeit soll der Nachweis erbracht werden, dass diese Methode bei -10°C Betriebstemperatur funktionstüchtig ist und keine weiteren Spalte aufwirft. Zusätzlich wird der vorangegangene Fertigungsablauf dokumentiert

Zeitbereichs-Nahfeld-Immunitätsprüfung auf PCB-Ebene

Das Nahfeld-Immunitätstestverfahren ist ein zusätzliches diagnostisches Werkzeug, um sensitive Bereiche und Koppelpfade auf Leiterplattenebene zu lokalisieren und zu bewerten. Dabei ist es möglich, mit der entsprechenden Feldsonde die Empfindlichkeit gegenüber elektrischen und magnetischen Feldern separat zu testen. Eine Kalibriermethode wurde entwickelt, um Tests mit definierter Feldstärkeamplitude am Prüfling durchführen zu können. Dies ermöglicht eine reproduzierbare Bewertung des Störvermögens unterschiedlicher Impulsformen. Die Kalibriermethode wurde anhand exakter numerischer Feldsimulationen der Einkopplung in eine Leitung validiert. Die Anwendungsbeispiele veranschaulichen den Zusammenhang zwischen Störwirkung und Störfeldstärke, Repetitionsrate, Sondenposition und Signal-Datenrate anhand des Bitfehlerverhältnisses