MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1268 products
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04/2025 - 01/15/2025
Andrini, D.; Magri, M.; Ciarletta, P.
Nonlinear morphoelastic theory of biological shallow shells with initial stress | Abstract | | Shallow shells are widely encountered in biological structures, especially during embryogenesis, when they undergo significant shape variations. As a consequence of geometric frustration caused by underlying biological processes of growth and remodeling, such thin and moderately curved biological structures experience initial stress even in the absence of an imposed deformation. In this work, we perform a rigorous asymptotic expansion from three-dimensional elasticitiy to obtain a nonlinear morphoelastic theory for shallow shells accounting for both initial stress and large displacements. By application of the principle of stationary energy for admissible variation of the tangent and normal displacement fields with respect to the reference middle surface, we derive two generalised nonlinear equilibrium equations
of the Marguerre-von K´arm´an type. We illustrate how initial stress distributions drive the emergence of spontaneous mean and Gaussian curvatures which are generally not compatible with the existence of a stress free configuration. We also show how such spontaneous curvatures influence the structural behavior in the solutions of two systems: a saddle-like and a cylindrical shallow shell. |
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02/2025 - 01/08/2025
Corda, A.; Pagani, S.; Vergara, C.
Influence of patient-specific acute myocardial ischemia maps on arrhythmogenesis: a computational study | Abstract | | The early phase of acute myocardial ischemia is associated with an elevated risk of ventricular reentrant arrhythmias. After partial or total occlusion of a coronary artery, some regions of the heart experience a reduction in myocardial blood flow. This causes metabolic and cellular processes, such as hypoxia, hyperkalemia and acidosis, which lead to changes in the transmembrane ionic dynamics. The effect of such alterations may result in the formation of electrical loops and reentries.
In this context, digital twins aim at predicting patient-specific arrhythmic propensity to support clinical decision. Due to a lack of available representative data of acute events, digital twins can only rely on differential multiscale models, whose parameters are personalized based on imaging data. Through their numerical approximation, we can quantitatively assess arrhythmic risk by simulating the generation of arrhythmic episodes, possibly persistent, triggered by ectopic beats and in presence of acute myocardial regions. Since quantitative information (extent, localization, ...) about acute ischemic regions are hardly available from clinics, to date, computational models only integrate imaging data from chronic infarcted ventricles. This may not accurately reflect the acute condition. This work presents a novel patient-specific electrophysiological model, based on myocardial blood flow maps acquired during a pharmacologically induced acute ischemic event. The model personalization is obtained with the partitioning of the left ventricle geometries on the basis of the myocardial blood flow maps. First, we aim to numerically investigate the induction and sustainment of reentrant drivers in patient-specific scenarios, in order to assess their arrhythmic propensity. Secondly, we perform an intra-patient sensitivity analysis, where different levels of acute ischemia are virtually depicted for the most arrhythmogenic patient. Our results suggest that the amount of ischemic regions seems to have less influence on arrhythmogenesis than their pattern. |
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01/2025 - 01/04/2025
Dede', L.; Parolini, N.; Quarteroni, A.; Villani, G.; Ziarelli, G.
SEIHRDV: a multi-age multi-group epidemiological model and its validation on the COVID-19 epidemics in Italy | Abstract | | We propose a novel epidemiological model, referred to as SEIHRDV, for the numerical simulation of the COVID-19 epidemic, which we validate using data from Italy starting in September 2020. SEIHRDV features the following compartments: Susceptible (S), Exposed (E), Infectious (I), Healing (H), Recovered (R), Deceased (D) and Vaccinated (V). The model is age-stratified, as it considers the population split into 15 age groups. Moreover, it takes into account 7 different contexts of exposition to the infection (family, home, school, work, transport, leisure, other contexts), which impact on the transmission mechanism. Thanks to these features, the model can address the analysis of the epidemics and the efficacy of non-pharmaceutical interventions, as well as possible vaccination strategies and the introduction of the Green Pass, a containment measure introduced in Italy in 2021. By leveraging on the SEIHRDV model, we successfully analyzed epidemic trends during the COVID-19 outbreak from September 2020 to July 2021. The model proved instrumental in conducting comprehensive what-if studies and scenario analyses tailored to Italy and its regions. Furthermore, SEIHRDV facilitated accurate forecasting of the future potential trajectory of the epidemic, providing critical information for informed decision making and public health strategies. |
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108/2024 - 12/27/2024
Arostica, R.; Nolte, D.; Brown, A.; Gebauer, A.; Karabelas, E.; Jilberto, J.; Salvador, M.; Bucelli, M.; Piersanti, R.; Osouli, K.; Augustin, C.; Finsberg, H.; Shi, L.; Hirschvogel, M.; Pfaller, M.; Africa, P.C.; Gsell, M.; Marsden, A.; Nordsletten, D.; Regazzoni, F.; Plank, G.; Sundnes, J.; Dede’, L.; Peirlinck, M.; Vedula, V.; Wall, W.; Bertoglio, C.
A software benchmark for cardiac elastodynamics | Abstract | | In cardiovascular mechanics, reaching consensus in simulation results within a physiologically relevant range of parameters is essential for reproducibility purposes. Although currently available benchmarks contain some of the features that cardiac mechanics models typically include, some important modeling aspects are missing. Therefore, we propose a new set of cardiac benchmark problems and solutions for assessing passive and active material behaviour, viscous effects, and pericardial boundary condition. The problems proposed include simplified analytical fiber definitions and active stress models on a monoventricular and biventricular domains, allowing straightforward testing and validation with already developed solvers. |
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109/2024 - 12/27/2024
Liverotti, L.; Ferro, N.; Matteucci, M.; Perotto, S.
A PCA and mesh adaptation-based format for high compression of Earth Observation optical data with applications in agriculture | Abstract | | Earth Observation optical data are critical for agriculture, supporting tasks like vegetation health monitoring, crop classification, and land use analysis. However, the large size of multispectral and hyperspectral datasets poses challenges for storage, transmission, and processing, particularly in precision farming and resource-limited contexts. This work presents the H²-PCA-AT (Hilbert and Huffman-encoded Principal Component Analysis-Adaptive Triangular) format, a novel lossy compression framework that combines PCA for spectral reduction with anisotropic mesh adaptation for spatial compression. Adaptive triangular meshes capture image features with fewer elements with respect to a standard pixel grid, while efficient encoding with Hilbert curves and Huffman coding ensures compact storage. Numerical evaluations on data reconstruction, vegetation index computation, and land cover classification demonstrate the H²-PCA-AT format effectiveness, achieving superior compression compared to JPEG while preserving essential agricultural insights. |
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110/2024 - 12/27/2024
Pederzoli, V.; Corti, M.; Riccobelli, D.; Antonietti, P.F.
A coupled mathematical and numerical model for protein spreading and tissue atrophy, applied to Alzheimer's disease | Abstract | | The aim of this paper is to introduce, analyse and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by pathogen diffusion, with applications to neurodegenerative disorders. This study introduces a novel mathematical and computational model comprising a Fisher-Kolmogorov equation for species diffusion coupled with an elasticity equation governing mass loss. These equations intertwine through a logistic law dictating the reduction of the medium's mass. One potential application of this model lies in understanding the onset and development of Alzheimer's disease. Here, the equations can describe the propagation of misfolded tau-proteins and the ensuing brain atrophy characteristic of the disease. To address numerically the inherited complexities, we propose a Polygonal Discontinuous Galerkin method on polygonal/polyhedral grids for spatial discretization, while time integration relies on the theta-method. We present the mathematical model, delving into its characteristics and propose discretization applied. Furthermore, convergence results are presented to validate the model, accompanied by simulations illustrating the application scenario of the onset of Alzheimer's disease. |
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107/2024 - 12/19/2024
Chen, J.; Ballini, E.; Micheletti, S.
Active Flow Control for Bluff Body under High Reynolds Number Turbulent Flow Conditions Using Deep Reinforcement Learning | Abstract | | This study employs Deep Reinforcement Learning (DRL) for active flow
control in a turbulent flow field of high Reynolds numbers at Re = 274000. That is, an agent is trained to obtain a control strategy that can reduce the drag of a cylinder while also minimizing the oscillations of the lift. Probes are placed only around the surface of the cylinder, and a Proximal Policy Optimization (PPO) agent controls nine zero-net mass flux jets on the downstream side of the cylinder. The trained PPO agent effectively reduces drag by 29% and decreases lift oscillations by 18% of amplitude, with the control effect demonstrating good repeatability. Control tests of this agent within the Reynolds number range of Re = 260000 to 288000 show the agent’s control strategy possesses a certain degree of robustness, with very similar drag reduction effects under different Reynolds numbers. Analysis using power spectral energy reveals that the agent learns specific flow frequencies in the flow field and effectively suppressesù low-frequency, large-scale structures. Graphically visualizing the policy, combined with pressure, vorticity, and turbulent kinetic energy contours, reveals the mechanism by which jets achieve drag reduction by influencing reattachment vortices. This study successfully implements robust active flow control in realistically significant high Reynolds number turbulent flows, minimizing time costs (using two-dimensional geometrical models and turbulence models) and maximally considering the feasibility of future experimental implementation. |
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106/2024 - 12/18/2024
Brunati, S.; Bucelli, M.; Piersanti, R.; Dede', L.; Vergara, C.
Coupled Eikonal problems to model cardiac reentries in Purkinje network and myocardium | Abstract | | We propose a novel partitioned scheme based on Eikonal equations to model the coupled propagation of the electrical signal in the His-Purkinje system and in the myocardium for cardiac electrophysiology. This scheme allows, for the first time in Eikonal-based modeling, to capture all possible signal reentries between the Purkinje network and the cardiac muscle that may occur under pathological conditions. As part of the proposed scheme, we introduce a new pseudo-time method for the Eikonal-diffusion problem in the myocardium, to correctly enforce electrical stimuli coming from the Purkinje network. We test our approach by performing numerical simulations of cardiac electrophysiology in a real biventricular geometry, under both pathological and therapeutic conditions, to demonstrate its flexibility, robustness, and accuracy. |
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