In the automotive industry, the absorption coefficient of a porous material layer is usually measured in an alpha cabin, a reverberant chamber of reduced dimensions where the operational frequency range is limited and the absorbent sample size is typically small. Those characteristics are well adapted to the requirements of automotive acoustics but far from the standard reverberant chambers used in building acoustics which ensures the conditions to perform measurements under a diffusive field. Since there are no standard norms to measure the absorption coefficient under non-diffusive fields, this work proposes a time-harmonic/time-domain hybrid approach to compute the absorption coefficient in alpha cabins. For this purpose, pointwise numerical predictions of the sound pressure level decay rate are used to calculate the absorption coefficient associated with a porous sample. To generate the pressure field acting inside the alpha cabin and, subsequently, approximate its decay rate, time-harmonic numerical simulations at a fixed frequency and a full time-dependent discretization of the wave problem have been considered. The proposed methodology is validated in a manufactured scenario where the exact solution is known in closed form. Finally, a realistic three-dimensional alpha cabin is deemed to predict the diffuse field absorption coefficient from the computed reverberation times using the proposed hybrid approach and the heuristic Sabine and Millington formulas.

The micromachined beam fixed at both ends is an essential component of electrostatically-actuated Micro-Electro-Mechanical System (MEMS) based switches. The pull-in voltage and the response time are some of the most important parameters of this system. With physics-based approaches, the challenge of modelling and producing simplified representations comes from the strong nonlinearities involved and the interaction of more than one physical field. Data-driven methods based on recurrent neural networks can be used to obtain simplified, yet accurate models for predicting the minimum gap dynamics for different applied voltages. However, the solution of these black-box models lacks physical connection and can contradict the physical laws. Here, we propose using a hybrid approach, namely a physics-informed machine learning model, and we show the benefits of incorporating initial and boundary conditions into the training process in terms of accuracy without compromising the learning and simulation times. Our neural network models incorporating physics-based constraints are ten times more accurate than the classical neural network architectures for the same problem.

This paper addresses the challenging task of guide wire navigation in cardiovascular interventions, focusing on the parameter estimation of a guide wire system using Ensemble Kalman Inversion (EKI) with a subsampling technique. The EKI uses an ensemble of particles to estimate the unknown quantities. However, since the data misfit has to be computed for each particle in each iteration, the EKI may become computationally infeasible in the case of high-dimensional data, e.g. high-resolution images. This issue can been addressed by randomised algorithms that utilize only a random subset of the data in each iteration. We introduce and analyse a subsampling technique for the EKI, which is based on a continuous-time representation of stochastic gradient methods and apply it to on the parameter estimation of our guide wire system. Numerical experiments with real data from a simplified test setting demonstrate the potential of the method.

In this work we focus on the development of a numerical algorithm for the inverse elastography problem. The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.

The escalating process of urbanization has raised concerns about incidents arising from overcrowding, necessitating a deep understanding of large human crowd behavior and the development of effective crowd management strategies. This study employs computational methods to analyze real-world crowd behaviors, emphasizing self-organizing patterns. Notably, the intersection of two streams of individuals triggers the spontaneous emergence of striped patterns, validated through both simulations and live human experiments. Addressing a gap in computational methods for studying these patterns, previous research utilized the pattern-matching technique, employing the Nelder-Mead Simplex algorithm for fitting a two-dimensional sinusoidal function to pedestrian coordinates. This paper advances the pattern-matching procedure by introducing Simulated Annealing as the optimization algorithm and employing a two-dimensional square wave for data fitting. The amalgamation of Simulated Annealing and the square wave significantly enhances pattern fitting quality, validated through statistical hypothesis tests. The study concludes by outlining potential applications of this method across diverse scenarios.

Hamilton–Jacobi–Bellman equation (HJBE) and backward stochastic differential equation (BSDE) are the two faces of stochastic control. We explore their equivalence focusing on a system of self-exciting and affine stochastic differential equations (SDEs) arising in streamflow dynamics. Our SDE is a finite-dimensional Markovian embedding of an infinite-dimensional jump-driven process called the superposition of continuous-state branching processes (a supCBI process). We formulate new ergodic control problems to evaluate the worst-case streamflow discharge in the long run and derive their HJBEs and ergodic BSDEs. The constant ambiguity aversion classically used in assessing model ambiguity must be modified in our case so that the optimality equations become well-posed. With a suitable modification of the ambiguity-aversion coefficient depending on the distributed reversion speed, we demonstrate that the solutions to the optimality equations are equivalent to each other in the sense that they lead to the same result. Finally, we apply the proposed framework to the computation of realistic cases with an existing record of discharge through a numerical Markovian embedding.

Cloudiness or formation is a concept routinely used in industry to address deviations from homogeneity in nonwovens and papers. Measuring a cloudiness index based on image data is a common task in industrial quality assurance. The two most popular ways of quantifying cloudiness are based on power spectrum or correlation function on the one hand or the Laplacian pyramid on the other hand. Here, we recall the mathematical basis of the first approach comprehensively, derive a cloudiness index, and demonstrate its practical estimation. We prove that the Laplacian pyramid as well as other quantities characterizing cloudiness like the range of interaction and the intensity of small-angle scattering are very closely related to the power spectrum. Finally, we show that the power spectrum can be measured easily by image analysis methods and carries more information than the alternatives.

The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.

Laser-induced thermotherapy (LITT) is a minimally invasive method causing tumor destruction due to heat ablation and coagulative effects. Computer simulations can play an important role to assist physicians with the planning and monitoring of the treatment. Our recent study with ex-vivo porcine livers has shown that the vaporization of the water in the tissue must be taken into account when modeling LITT. We extend the model used for simulating LITT to account for vaporization using two different approaches. Results obtained with these new models are then compared with the measurements from the original study.

Vaccines against varicella-zoster virus (VZV) are under introduction in Hungary into the routine vaccination schedule, hence it is important to understand the current transmission dynamics and to estimate the key parameters of the disease. Mathematical models can be greatly useful in advising public health policy decision making by comparing predictions for different scenarios. First we consider a simple compartmental model that includes key features of VZV such as latency and reactivation of the virus as zoster, and exogeneous boosting of immunity. After deriving the basic reproduction number R_{0}, the model is analysed mathematically and the threshold dynamics is proven: if R_{0}leq 1 then the virus will be eradicated, while if R_{0}>1 then an endemic equilibrium exists and the virus uniformly persists in the population. Then we extend the model to include seasonality, and fit it to monthly incidence data from Hungary. It is shown that besides the seasonality, the disease dynamics has intrinsic multi-annual periodicity. We also investigate the sensitivity of the model outputs to the system parameters and the underreporting ratio, and provide estimates for R_{0}.