We consider periodic piecewise affine functions, defined on the real line, with two given slopes, one positive and one negative, and prescribed length scale of the intervals where the slope is negative. We prove that, in such a class, the minimizers of s-fractional Gagliardo seminorm densities, with 0<1/2, are in fact periodic with the minimal possible period determined by the prescribed slopes and length scale. Then, we determine the asymptotic behavior of the energy density as the ratio between the length of the two intervals, where the slope is constant, vanishes. Our results, for s=1/2, have relevant applications to the van der Merwe theory of misfit dislocations at semicoherent straight interfaces. We consider two elastic materials having different elastic coefficients and casting parallel lattices having different spacing. As a byproduct of our analysis, we prove the periodicity of optimal dislocation configurations and we provide the sharp asymptotic energy density in the semicoherent limit as the ratio between the two lattice spacings tends to one.

We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge dislocations, which we model as the solutions to minimum problems for isotropic elastic energies under the constraint of kinematic incompatibility. Operating under the assumption of planar linearized kinematics, we formulate the mechanical equilibrium problem in terms of the Airy stress function, for which we introduce a rigorous analytical formulation in the context of incompatible elasticity. Our main result entails the analysis of the energetic equivalence of systems of disclination dipoles and edge dislocations in the asymptotics of their singular limit regimes. By adopting the regularization approach via core radius, we show that, as the core radius vanishes, the asymptotic energy expansion for disclination dipoles coincides with the energy of finite systems of edge dislocations. This proves that Eshelby’s kinematic characterization of an edge dislocation in terms of a disclination dipole is exact also from the energetic standpoint.

We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite system of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy, as the core-radius (in the semi-discrete model) and the lattice spacing (in the purely discrete one) vanish. Our analysis passes through a linearization procedure within the rigorous framework of Γ-convergence.

The conformational and dynamical properties of active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain, driven by tangential forces, put in contact with a heat bath described by the Brownian multiparticle collision dynamics. Both phantom polymers and chains comprising excluded volume interactions are considered for different bending rigidities. The size and shape are found to be dependent on persistence length, driving force, and bead mutual exclusion. The lack of excluded volume interactions is responsible for a shrinkage of active rings when increasing driving force in the flexible limit, while the presence induces a moderate swelling of chains. The internal dynamics of flexible phantom active rings shows activity-enhanced diffusive behavior at large activity values while, in the case of self-avoiding active chains, it is characterized by active ballistic motion not depending on stiffness. The long-time dynamics of active rings is marked by rotational motion whose period scales as the inverse of the applied tangential force, irrespective of persistence length and beads' self-exclusion.

A meticulous description of a real network with respect to its heterogeneous physical infrastructure and properties is necessary for network design assessment. Quantifying the costs of making these structures work together effectively, and taking into account any hidden charges they may incur, can lead to improve the quality of service and reduce mandatory maintenance requirements, and mitigate the cost associated with finding a valid solution. For these reasons, we devote our attention to a novel approach to produce a more complete representation of the overall costs on the reload cost net-work. This approach considers both the cost of reloading due to linking structures and their internal charges, which we refer to as the penalized reload cost. We investigate the complexity and approximability of finding an optimal path, walk, tour, and maxi-mum flow problems under penalized reload cost. All these problems turn out to be NP-complete. We prove that, unless P=NP, even if the reload cost matrix is symmetric and satisfies the triangle inequality, the problem of finding a path, tour, and a maxi-mum flow with a minimum penalized reload cost cannot be approximated within any constant alpha < 2 , and finding a walk is not approximable within any factor beta <= 3.

Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.

The non-equilibrium structural and dynamical properties of a flexible polymer tethered to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as a bead-spring chain immersed in a fluid described by the Brownian multiparticle collision dynamics. At high strain, the polymer is stretched along the flow direction following the applied flow, then recoils at flow inversion before flipping and elongate again. When strain is reduced, it may happen that the chain recoils without flipping when the applied shear changes sign. Conformations are analyzed and compared to stiff polymers revealing more compact patterns at low strains and less stretched configurations at high strain. The dynamics is investigated by looking at the center-of-mass motion which shows a frequency doubling along the direction normal to the external flow. The center-of-mass correlation function is characterized by smaller amplitudes when reducing bending rigidity.

The properties of semiflexible active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain subject to tangential active forces, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. Both phantom polymers and chains with excluded- volume interactions are considered. The size and shape strongly depend on the relative ratio of the persistence length to the ring length as well as on the active force. The long-time dynamics is characterized by a rotational motion whose frequency increases with the active force.

In microfluidic systems, droplets undergo intricate deformations as they traverse flow-focusing junctions, posing a challenging task for accurate measurement, especially during short transit times. This study investigates the physical behavior of droplets within dense emulsions in diverse microchannel geometries, specifically focusing on the impact of varying opening angles within the primary channel and injection rates of fluid components. Employing a sophisticated droplet tracking tool based on deep-learning techniques, we analyze multiple frames from flow-focusing experiments to quantitatively characterize droplet deformation in terms of ratio between maximum width and height and propensity to form liquid with hexagonal spatial arrangement. Our findings reveal the existence of an optimal opening angle where shape deformations are minimal and hexagonal arrangement is maximal. Variations of fluid injection rates are also found to affect size and packing fraction of the emulsion in the exit channel. This paper offers insight into deformations, size, and structure of fluid emulsions relative to microchannel geometry and other flow-related parameters captured through machine learning, with potential implications for the design of microchips utilized in cellular transport and tissue engineering applications.

This work addresses the Knapsack Problem with Forfeit Sets, a recently introduced variant of the 0/1 Knapsack Problem considering subsets of items associated with contrasting choices. Some penalty costs need to be paid whenever the number of items in the solution belonging to a forfeit set exceeds a predefined allowance threshold. We propose an effective metaheuristic to solve the problem, based on the Biased Random-Key Genetic Algorithm paradigm. An appropriately designed decoder function assigns a feasible solution to each chromosome, and improves it using some additional heuristic procedures. We show experimentally that the algorithm outperforms significantly a previously introduced metaheuristic for the problem.

Il rapporto analizza i principi che regolano il Programma HORIZON EUROPE e le modalità di rendicontazione dei costi sostenuti per la realizzazione delle attività progettuali, soffermandosi sulle caratteristiche dello strumento finanziario, sulla tipologia dei costi e sul sistema di controlli attraverso il quale la Commissione Europea vigila sul rispetto delle norme gli obblighi previsti dalla convenzione di sovvenzione.

We analyze the dynamics of the Sun-Earth-Moon system in the context of a particular class of theories of gravity where curvature and matter are nonminimally coupled (NMC). These theories can potentially violate the Equivalence Principle as they give origin to a fifth force and a extra non-Newtonian force that may imply that Earth and Moon fall differently towards the Sun. We show, through a detailed analysis, that consistency with the bound on Weak Equivalence Principle arising from 48 years of Lunar Laser Ranging data, for a range of parameters of the NMC gravity theory, can be achieved via the implementation of a suitable screening mechanism.

In questo report si affrontano gli aspetti tecnici e di sviluppo che hanno portato all’attuale sito web di istituto, all’interno di un approfondimento generale relativo alla comunicazione istituzionale e al posizionamento dell’IAC nel contesto della comunicazione della matematica. Sono, inoltre, discusse le modalità di misurazione delle performance (Analytics) del sito, con una panoramica sulle necessarie attività di miglioramento in termini di Search Engine Optimization (SEO).

The volume collects the long abstracts of the 79 contributions presented during the fourth edition of the “Young Applied Mathematicians Conference” (YAMC, www.yamc.it). Organized in Rome under the sponsorship of the Institute for Applied Mathematics (IAC) of the CNR and the Department of Mathematics at Sapienza, University of Rome, the conference took place from September 16 to 20, 2024, and brought together primarily young researchers (students, PhD candidates, post-docs, etc.) from 37 universities and research centers across 8 countries. This volume is intended to promote the communication of the research presented in the field of applied mathematics, with a primary focus on numerical analysis, artificial intelligence, statistics, and mathematical modeling. Il volume raccoglie i long abstracts dei 79 contributi presentati durante la quarta edizione del convegno "Young Applied Mathematicians Conference" (YAMC, www.yamc.it). Organizzato a Roma sotto il patrocinato dell'Istituto per le Applicazioni del Calcolo (IAC) del CNR e del dipartimento di Matematica di Sapienza, Università di Roma, il convegno si è svolto nelle giornate 16--20 settembre 2024 ed ha riunito principalmente giovani ricercatori (studenti, dottorandi, post-doc, ...) provenienti da 37 fra università e centri di ricerca di 8 nazioni. Il presente volume è indirizzato a favorire la comunicazione delle ricerche presentate nel panorama della matematica applicata, con principale attenzione in analisi numerica, intelligenza artificiale, statistica e modellistica matematica.

Personalized medicine strategies are gaining momentum nowadays, enabling the introduction of targeted treatments based on individual differences that can lead to greater therapeutic efficacy by reducing adverse effects. Despite its crucial role, studying the contribution of the immune system (IS) in this context is difficult because of the intricate interplay between host, pathogen, therapy, and other external stimuli. To address this problem, a multidisciplinary approach involving in silico models can be of great help. In this perspective, we will discuss the use of a well-established agent-based model of the immune response, C-ImmSim, to study the relationship between long-lasting diseases and the combined effects of IS, drug therapies and exogenous factors such as physical activity and dietary habits.

A mixed approach with meta-modelling techniques and machine-learning algorithms is here applied to the minimization of the lap time of a Formula 1 race car. The fine tuning of the front wing is performed in order to optimize the car for each specific racetrack. This task is performed by a simplified model, which is trained by some high-fidelity fluid dynamic simulations and then extended to the complete design space. The resulting tool is reliable, fast and easy to use. The accuracy of the resulting speed profiles of the chosen car in comparison with available measurements is indicating the overall reliability of the procedure.

Numerical optimization of complex systems benefits from the technological development of computing platforms in the last twenty years. Unfortunately, this is still not enough, and a large computational time is still necessary when mathematical models that include richer (and therefore more realistic) physical models are adopted. In this paper we show how the combination of optimization and Artificial Intelligence (AI), in particular the Machine Learning algorithms, can help in strongly reducing the overall computational times, making possible the use of complex simulation systems within the optimization cycle. Original approaches are also proposed.

: We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker-Planck equations in one space dimension, we derive some known exact results in simple physical situations (free run-and-tumble particles and harmonic confinement). We then extend the calculation to the case of anisotropic motion (different speeds and tumbling rates for right- and left-oriented particles), obtaining exact expressions of the entropy production rate. We conclude by discussing the general case of heterogeneous run-and-tumble motion described by space-dependent parameters and extending the analysis to the case of d-dimensional motions.

We present a mapping between a Schrödinger equation with a shifted nonlinear potential and the Navier–Stokes equation. Following a generalization of the Madelung transformations, we show that the inclusion of the Bohm quantum potential plus the laplacian of the phase field in the nonlinear term leads to continuity and momentum equations for a dissipative incompressible Navier–Stokes fluid. An alternative solution, built using a complex quantum diffusion, is also discussed. The present models may capture dissipative effects in quantum fluids, such as Bose–Einstein condensates, as well as facilitate the formulation of quantum algorithms for classical dissipative fluids.

In this paper, we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian neural network and (the law of) a random Gaussian vector. Our main results concern deep random Gaussian neural networks with a rather general activation function. The upper bounds show how the widths of the layers, the activation function, and other architecture parameters affect the Gaussian approximation of the output. Our techniques, relying on Stein's method and integration by parts formulas for the Gaussian law, yield estimates on distances that are indeed integral probability metrics and include the convex distance. This latter metric is defined by testing against indicator functions of measurable convex sets and so allows for accurate estimates of the probability that the output is localized in some region of the space, which is an aspect of a significant interest both from a practitioner's and a theorist's perspective. We illustrated our results by some numerical examples.