Abstract This paper presents research conducted at the University of Trento addressing an industrial challenge from Fater S.p.A. regarding the thermal bonding of non-woven fabrics for diaper production. The problem consists in a possible analysis of the behavior of the bonding process of a non-woven fabric. In particular, the bonding process is not given by the use of some kind of glue, but just by the pressure of two fiber webs through two high-velocity steel-made rollers. The research comprised the formulation and theoretical as well as numerical analysis of analytical, mechanical and thermal models for the stress-strain behavior of the non-woven fabric’s fibers and for the bonding process with heating effects.

Abstract The present study focuses on particular properties of transonic flows through a planar channel featuring a circular bump on the lower wall. The selected geometry is reminiscent of the region surrounding the trailing edge of an airfoil at zero angle of attack and the resulting flow pattern is indeed similar to the fishtail shock-pattern that characterizes airfoils flying at nearly sonic speed. Numerical simulations have been conducted by solving the inviscid Euler equations using both a commercial and an in-house CFD code; discontinuities are modeled using shock-capturing in the former and shock-fitting in the latter. Numerical experiments reveal different shock-patterns obtained by independently varying the inlet Mach number and the outlet-to-inlet static pressure ratio. When shock-interactions occur, shock-polar analysis reveals that the branching point can be modeled using either von Neumann’s three-shock-theory or Guderley’s four-wave-theory, depending on the inlet Mach number. Furthermore, for certain pairs of boundary conditions, multiple solutions have been observed.

Abstract We introduce a mathematical model of bread leavening in a warm chamber by coupling heat transfer, yeast growth, and carbon dioxide production and diffusion with the deformation of baking paste. We analyze the corresponding system of partial differential equations. The system is discretized by using a semi-implicit Euler method and the finite-element method in the time and space domain, respectively. Numerical simulations are employed to identify the energy consumption necessary to achieve a target volume under different settings of the leavening chamber and different concentrations of yeast in the baking paste, thereby providing a tool for the identification of cost-effective protocols.

Abstract This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker– Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions, representing density distributions, must be non-negative and satisfy a specific energy dissipation law. We design an arbitrary high-order discontinuous Galerkin (DG) method tailored for these model problems. Both semi-discrete and fully discrete schemes are shown to admit the energy dissipation law for non-negative numerical solutions. To ensure the preservation of positivity in cell averages at all time steps, we introduce a local flux correction applied to the DDG diffusive flux. Subsequently, a hybrid algorithm is presented, utilizing a positivity-preserving limiter, to generate positive and energy-dissipating solutions. Numerical examples are provided to showcase the high resolution of the numerical solutions and the verified properties of the DG schemes.

Abstract This article explores some properties of degenerate hypergeometric Bernoulli polynomials, which are defined through the following generating function t m e λ x ( t ) e λ x ( t ) - ∑ l = 0 m - 1 ( 1 ) l , λ t l l ! = ∑ n = 0 ∞ B n , λ [ m - 1 ] ( x ) t n n ! , | t | < min { 2 π , 1 | λ | } , λ ∈ ℝ \ { 0 } . {{{t^m}e_\lambda ^x\left( t \right)} \over {e_\lambda ^x\left( t \right) - \sum\nolimits_{l = 0}^{m - 1} {\left( 1 \right)l,\lambda{{{t^l}} \over {l!}}} }} = \sum\limits_{n = 0}^{^\infty } {B_{n,\lambda }^{\left[ {m - 1} \right]}} \left( x \right){{{t^n}} \over {n!}},\,\,\,\,\left| t \right| < \min \left\{ {2\pi ,{1 \over {\left| \lambda \right|}}} \right\},\lambda \in \mathbb{R}\backslash \left\{ 0 \right\}. We deduce their associated summation formulas and their corresponding determinant form. Also we focus our attention on the zero distribution of such polynomials and perform some numerical illustrative examples, which allow us to compare the behavior of the zeros of degenerate hypergeometric Bernoulli polynomials with the zeros of their hypergeometric counterpart. Finally, using a monomiality principle approach we present a differential equation satisfied by these polynomials.

Abstract In artificial intelligence applications, the model training phase is critical and computationally demanding. In the graph neural networks (GNNs) research field, it is interesting to investigate how varying the graph topological and spectral structure impacts the learning process and overall GNN performance. In this work, we aim to theoretically investigate how the topology and the spectrum of a graph changes when nodes and edges are added or removed. Numerical results highlight stability issues in the learning process on graphs. In this work, we aim to theoretically investigate how the topology and the spectrum of a graph changes when nodes and edges are added or removed. We propose the topological relevance function as a novel method to quantify the stability of graph-based neural networks when graph structures are perturbed. We also explore the relationship between this topological relevance function, Graph Edit Distance, and spectral similarity. Numerical results highlight stability issues in the learning process on graphs.

Abstract The Weierstrass‘ theory of one-dimensional Lagrangian systems and a quasi-continuum approach are employed to study the propagation of solitary waves in tensegrity mass-spring chains, which exhibit softening-type elastic response in the large displacement regime and are subject to external pre-compression. The presented study analytically derives the shape of the traveling rarefaction pulses, and limiting values of the speeds of such pulses. Use is made of a tensegrity-like interaction potential that captures the main features of the real force-displacement response of the examined units. The Weierstrass approach is validated through numerical applications that establish comparisons between the theory developed in the present work and previous results available in literature.

Abstract Neurophysiological signal analysis is crucial for understanding the complex dynamics of brain function and its deviations in various pathological conditions. Traditional linear methods, while insightful, often fail to capture the full spectrum of inherently non-linear brain dynamics. This review explores the efficacy and applicability of the Higuchi fractal dimension (HFD) in interpreting neurophysiological signals such as scalp electroencephalography (EEG) and stereotactic intracranial encephalography (sEEG). We focus on three case studies: i) distinguishing between Alzheimer’s disease (AD) and healthy controls; ii) classifying neurodynamics across diverse brain parcels looking for a signature of that cortical parcel; and iii) differentiating states of consciousness. Our study highlights the potential of non-linear analysis for deeper insights into brain dynamics and its potential for improving clinical diagnostics.

Abstract This study investigates the use of exploratory data analysis and supervised learning techniques to analyze plant phenotyping traits, with a specific focus on: i) genetic diversity (wild type vs mutant tomato plants); ii) plant-plant interactions (primed vs non-primed plants using volatiles emitted by other stressed plants); and iii) plant stress response (using drought stress and comparing droughted plants with controls). The analyzed data consisted of high-throughput imaging at multiple wavelengths, which allowed for the examination of various morphological traits. The dataset contained the phenotypic characteristics of both wildtype and mutated tomato plants exposed to water stress. Machine learning algorithms were used to identify significant phenotypic indicators and predict plant stress responses. The use of techniques such as K-means clustering and Bayesian classifiers provided valuable insights into the temporal dynamics of plant traits under a variety of experimental conditions. This research emphasizes the importance of employing advanced statistical and machine learning methods to improve the precision and efficacy of phenotypic analysis in plant sciences.

Abstract We investigate the numerical calculation of the general Heun equation using Wolfram Mathematica’s functions, comparing the numerical solutions with hypergeometric and explicit solutions. This exploration sheds light on the efficacy and accuracy of the numerical algorithm implemented in Mathematica for computing Heun functions.