In this paper, a multidisciplinary design optimization algorithm, the Normal Boundary Intersection (NBI) method, is applied to the design of some devices of a sailing yacht. The full Pareto front is identified for two different design problems, and the optimal configurations are compared with standard devices. The great efficiency of the optimization algorithm is demonstrated by the wideness and density of the identified Pareto front.

To retrieve surface and atmospheric temperature profiles, together with trace species concentrations is a fundamental challenge in numerical weather prediction and Earth monitoring. Over the last 20 years, the development of high-resolution infrared sensors on board Earth observation satellites has opened new remote sensing opportunities, providing an unprecedented source of information. However, infrared sensors cannot probe into thick cloud layers, rendering their observations insensitive to surface under cloudy conditions. This results in spatial fields flagged with missing data, disrupting the continuity of inferred information and hindering accurate modeling of energy fluxes between the surface and the atmosphere. Consequently, advanced interpolation techniques and spatial statistics are essential to process the available (very large) data sets and produce satellite products on a regular grid mesh. This paper reviews and presents the physical modeling of radiative transfer in the atmosphere and the related mathematics of inversion, tailored for high spectral-resolution infrared sensors.

Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents. The Klausmeier-Gray-Scott 2D model for semi-arid ecosystems on a sloped terrain is considered with the addition of a nonlinear cross-diffusion term. Pattern formation driven by cross-diffusion is studied in the resulting system. A weakly nonlinear analysis around the critical value of the cross-diffusion is performed, and the asymptotic expansion is validated by numerical solution of the full system.

In this work, we introduce a quadratically convergent and dynamically consistent integrator specifically designed for the replicator dynamics. The proposed scheme combines a two-stage rational approximation with a normalization step to ensure confinement to the probability simplex and unconditional preservation of non-negativity, invariant sets and equilibria. A rigorous convergence analysis is provided to establish the scheme’s second-order accuracy, and an embedded auxiliary method is devised for adaptive time-stepping based on local error estimation. Furthermore, a discrete analogue of the quotient rule, which governs the evolution of component ratios, is shown to hold. Numerical experiments validate the theoretical results, illustrating the method’s ability to reproduce complex dynamics and to outperform well-established solvers in particularly challenging scenarios.

This Special Issue of Mathematics and Computers in Simulation collects a selection of peer-reviewed original articles on research topics developed in connection with IMACS2023, the IMACS World Congress, held in Rome (Italy) at the Faculty of Engineering, Sapienza University of Rome on September 11 - 15, 2023, that we organized, in the role of Local Scientific Committee, together with Rosa Maria Spitaleri, Congress Chair.

Phase separation in the presence of external forces has attracted considerable attention since the initial works for solid mixtures. Despite this, only very few studies are available which address the segregation process of liquid-vapor systems under gravity. We present here an extensive study which takes into account both hydrodynamic and gravitational effects on the coarsening dynamics. An isothermal formulation of a lattice Boltzmann model for a liquid-vapor system with the van der Waals equation of state is adopted. In the absence of gravity, the growth of domains follows a power law with the exponent 2 / 3 of the inertial regime. The external force deeply affects the observed morphology accelerating the coarsening of domains and favoring the liquid accumulation at the bottom of the system. Along the force direction, the growth exponent is found to increase with the gravity strength still preserving sharp interfaces since Porod’s law is found to be verified. The time evolution of the average thickness L of the layers of accumulated material at confining walls shows a transition from an initial regime where L ≃ t 2/3 (t: time) to a late-time regime L ≃ g t 5/33 with g the gravitational acceleration. The final steady state, made of two overlapped layers of liquid and vapor, shows a density profile in agreement with theoretical predictions.

In this manuscript, we present a comprehensive theoretical and numerical framework for the control of production-destruction differential systems. The general finite horizon optimal control problem is formulated and addressed through the dynamic programming approach. We develop a parallel in space semi-Lagrangian scheme for the corresponding backward-in-time Hamilton-Jacobi-Bellman equation. Furthermore, we provide a suitable conservative reconstruction algorithm for optimal controls and trajectories. The application to two case studies, specifically enzyme catalyzed biochemical reactions and infectious diseases, highlights the advantages of the proposed methodology over classical semi-Lagrangian discretizations.

The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and time-integration to yield the final update. An important concern is how the scheme modifies the solution through the notions of numerical dissipation-dispersion. As far as we know, no analysis of these artifacts has been considered for implicit integration of DG methods. The first part of this work intends to fill this gap, showing that the choice of the implicit Runge-Kutta impacts deeply on the quality of the solution. We analyze one-dimensional dissipation-dispersion to select the best combination of the space-time discretization for high Courant numbers. Then, we apply our findings to the integration of one-dimensional stiff hyperbolic systems. Implicit schemes leverage superior stability properties enabling the selection of time-steps based solely on accuracy requirements. High-order schemes require the introduction of local space limiters which make the whole implicit scheme highly nonlinear. To mitigate the numerical complexity, we propose to use appropriate space limiters that can be precomputed on a first-order prediction of the solution. Numerical experiments explore the performance of this technique on scalar equations and systems.

We further investigate the properties of an approach to topological singularities through free discontinuity functionals of Mumford-Shah type proposed in De Luca et al. (Indiana Univ Math J 73:723–779, 2024). We prove the variational equivalence between such energies, Ginzburg-Landau, and Core-Radius for anti-plane screw dislocations energies in dimension two, in the relevant energetic regimes,, where denotes the linear size of the process zone near the defects. Further, we remove the a priori restrictive assumptions that the approximating order parameters have compact jump set. This is obtained by proving a new density result for -valued functions, approximated through functions with essentially closed jump set, in the strong BV norm.

This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vallée Poussin (VP) interpolation at Cheby- shev nodes. Unlike classical wavelets, which are constructed on the real line, these VP wavelets are defined on a bounded interval, offering the advantage of handling boundaries naturally while maintaining computational efficiency. In addition, the structure of these wavelets enables the use of fast algorithms for decomposition and reconstruction. Furthermore, the flexibility offered by a free parameter allows a better control of localized singularities, such as edges in images. On the basis of previous theoretical foundations, we show the effectiveness of the VP wavelets for basic signal denoising and image compression, emphasizing their potential for more advanced signal and image processing tasks.

Medical implant-related infections remain notoriously difficult to treat due to the formation of bacterial biofilms. Systemic antibiotic delivery is often ineffective and antibiotic-eluting technologies remain immature in this field, at least in part due to limitations in adequately controlling the antibiotic release rate. A confounding factor is the lack of understanding of the most efficacious antibiotic release profile. In this paper, we introduce a novel theoretical framework that leverages functionally graded materials to achieve tunable, spatially controlled antibiotic delivery – addressing both of these key challenges. Specifically, we develop a new coupled nonlinear partial differential equation model that simultaneously captures antibiotic release from a functionally graded material coating and its transport dynamics within an evolving biofilm. Our results reveal that functionally graded material coatings can outperform homogeneous coatings in sustaining local antibiotic concentrations and suppressing biofilm growth. This study thus establishes functionally graded materials as a promising, previously underexplored design paradigm for infection-resistant medical implants and provides a quantitative basis for optimizing antibiotic release profiles in biofilm-prone environments.

Human behavior plays a critical role in shaping epidemic trajectories. During health crises, people respond in diverse ways in terms of self-protection and adherence to recommended measures, largely reflecting differences in how individuals assess risk. This behavioral variability induces effective heterogeneity into key epidemic parameters, such as infectivity and susceptibility. We introduce a minimal extension of the susceptible-infected-removed (SIR) model, denoted HeSIR, that captures these effects through a simple bimodal scheme, where individuals may have higher- or lower-transmission-related traits. We derive a closed-form expression for the epidemic threshold in terms of the model parameters, and the network's degree distribution and homophily, defined as the tendency of like-risk individuals to preferentially interact. We identify a resurgence regime just beyond the classical threshold, where the number of infected individuals may initially decline before surging into large-scale transmission. Through simulations on homogeneous and heterogeneous network topologies we corroborate the analytical results and highlight how variations in susceptibility and infectivity influence the epidemic dynamics. We further show that, under suitable assumptions, the HeSIR model maps onto a standard SIR process on an appropriately modified contact network, providing a unified interpretation in terms of structural connectivity. Our findings quantify the effect of heterogeneous behavioral responses, especially in the presence of homophily, and caution against underestimating epidemic potential in fragmented populations, which may undermine timely containment efforts. The results also extend to heterogeneity arising from biological or other nonbehavioral sources.

Optimal embeddings for fractional Orlicz-Sobolev spaces into (generalized) Campanato spaces on the Euclidean space are exhibited. Embeddings into vanishing Campanato spaces are also characterized. Sharp embeddings into BMO(R-n) and VMO(R-n) are derived as special instances. Dissimilarities to corresponding embeddings for classical fractional Sobolev spaces are pointed out.

In this editorial the historical premises of the world Congress IMACS2023 are delineated in order to appreciate the development of IMACS as a scientific association keeping up with the ultimate scientific aspirations of society in the fields of Applied Mathematics and Scientific Computing. The World Congress, IMACS2023, the last considered step, celebrates successfully such a prestigious story.

In this manuscript, we propose a stable algorithm for computing the zeros of Althammer polynomials. These polynomials are orthogonal with respect to a Sobolev inner product, and are even if their degree is even, odd otherwise. Furthermore, their zeros are real, distinct, and located inside the interval (−1, 1). The Althammer polynomial p_n(x) of degree n satisfies a long recurrence relation, whose coefficients can be arranged into a Hessenberg matrix of order n, with eigenvalues equal to the zeros of the considered polynomial. Unfortunately, the eigenvalues of this Hessenberg matrix are very ill–conditioned, and standard balancing procedures do not improve their condition numbers. Here, we introduce a novel algorithm for computing the zeros of p_n(x), which first transforms the Hessenberg matrix into a similar symmetric tridiagonal one, i.e., a matrix whose eigenvalues are perfectly conditioned, and then computes the zeros of p_n(x) as the eigenvalues of the latter tridiagonal matrix. Moreover, we propose a second algorithm, faster but less accurate than the former one, which computes the zeros of p_n(x) as the eigenvalues of a truncated Hessenberg matrix, obtained by properly neglecting some diagonals in the upper part of the original matrix. The computational complexity of the proposed algorithms are, respectively, O( n^3/ 6 ), and O(l^2 n), with l<

Over the last decade, the Lattice Boltzmann method has found major scope for the simulation of a large spectrum of problems in soft matter, from multiphase and multi-component microfluidic flows, to foams, emulsions, colloidal flows, to name but a few. Crucial to many such applications is the role of supramolecular interactions which occur whenever mesoscale structures, such as bubbles or droplets, come in close contact, say of the order of tens of nanometers. Regardless of their specific physico-chemical origin, such near-contact interactions are vital to preserve the coherence of the mesoscale structures against coalescence phenomena promoted by capillarity and surface tension, hence the need of including them in Lattice Boltzmann schemes. Strictly speaking, this entails a complex multiscale problem, covering about six spatial decades, from centimeters down to tens of nanometers, and almost twice as many in time. Such a multiscale problem can hardly be taken by a single computational method, hence the need for coarse-grained models for the near-contact interactions. In this review, we shall discuss such coarse-grained models and illustrate their application to a variety of soft flowing matter problems, such as soft flowing crystals, strongly confined dense emulsions, flowing hierarchical emulsions, soft granular flows, as well as the transmigration of active droplets across constrictions. Finally, we conclude with a few considerations on future developments in the direction of quantum-nanofluidics, machine learning, and quantum computing for soft flows applications.

In this paper, we explore the determination of a spectral emissivity profile that closely matches real data, intended for use as an initial guess and/or a priori information in a retrieval code. Our approach employs a Bayesian method that integrates the CAMEL (Combined ASTER MODIS Emissivity over Land) emissivity database with the MODIS/Terra+Aqua Yearly Land Cover Type database. The solution is derived as a convex combination of high-resolution Huang profiles using the Bayesian framework. We test our method on IASI (Infrared Atmospheric Sounding Interferometer) data and find that it outperforms the linear spline interpolation of the CAMEL data and the Huang emissivity database itself.

An X-ray diffraction pattern consists of relevant information (the signal) and noisy background. Under the assumption that they behave as the components of a two-dimensional mixture (bicomponent fluid) having slightly different physical properties related to the density gradients, a Lattice Boltzmann Method is applied to disentangle the two different diffusive dynamics. The solution is numerically stable, not computationally demanding, and, it also provides an efficient increase in the signal-to-noise ratio for patterns blurred by Poissonian noise and affected by collection data anomalies (fiber-like samples, experimental setup, etc.). The model is succesfully applied to different resolution images.

Mechanotransduction is the process that enables the conversion of mechanical cues into biochemical signaling. While all our cells are well known to be sensitive to such stimuli, the details of the systemic interaction between mechanical input and inflammation are not well integrated. Often, indeed, they are considered and studied in relatively compartmentalized areas, and we therefore argue here that to understand the relationship of mechanical stimuli with inflammation – with a high translational potential - it is crucial to offer and analyze a unified view of mechanotransduction. We therefore present here pathway representation, recollected with the standard systems biology markup language (SBML) and explored with network biology approaches, offering RAC1 as an exemplar and emerging molecule with potential for medical translation.

A reaction–diffusion system governing the predator–prey interaction with specialist predator and herd behavior for prey is investigated. Linear stability of the interior equilibrium is studied, and conditions guaranteeing the occurrence of Turing instability, induced by cross-diffusion, are found, with a full characterization of the Turing instability region in the parameter space. Numerical simulations on the obtained results are provided.