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.

Objectives: Microfluidic cell Co-Culture, Tissue Co-Culture and Organ-on-Chip (OoC) technologies enable modeling of tissues and organs in vitro, facilitating cellenvironment interaction studies and early therapeutic evaluation. The combination of physiology-based models, agent-based models (ABMs), cellular automata, and invitro modelling of complex processes provides a powerful tool to formalize, quantify, and predict observed phenomena. Methods: Estimating parameters for these hybrid computational models using observational data is challenging. Approximate Bayesian computation (ABC) is particularly well suited for this task due to the intractability of the likelihood function. This work extends a hybrid ABM for a cell co-culture experiment on a chip. Cell tracking data is used to estimate model parameters via a Sequential Monte Carlo ABC (ABC-SMC) approach. Results: The resulting model accurately reproduces observed cellular behavior and distinguishes between different experimental conditions. Conclusion: The combination of cell co-culture and microfluidic technology with hybrid computational models and ABC-SMC provides a robust framework for modeling and predicting cellular behavior in vitro, enhancing the potential for early therapeutic evaluation and understanding of cell-environment interactions.

The design of race cars often focuses on the lower portion of the vehicle to achieve aerodynamic advantages by creating an optimal pressure pattern on the car’s underside. In fact, an appropriately shaped underbody can generate significant downforce with minimal aerodynamic drag, allowing for higher speeds during cornering. Unfortunately, no experimental facilities can accurately simulate the airflow around a car while cornering. For this reason, computational fluid dynamics (CFD) has become the primary tool for effectively designing such features. This study focuses on optimizing the shape of a Venturi channel for a highly simplified race car model that embodies the primary characteristics of a Le Mans Hypercar (LHM). We analyze and optimize the forces generated during straight-line travel and cornering, identifying the optimal configurations and their unique characteristics.

Background: A hypersensitivity reaction has been hypothesized as one of the possible pathophysiological mechanisms involved in non-celiac wheat sensitivity (NCWS). Some studies have reported a high frequency of atopic diseases in NCWS patients. Objectives: This study aimed (A) to define the presence and features of atopic diseases and other hypersensitivities in NCWS patients and (B) to search for possible allergic features which could address a NCWS diagnosis. Methods: Clinical, laboratory and histological data from NCWS patients before the start of a wheat-free diet were retrospectively analyzed and compared to control subjects with celiac disease (CeD) or irritable bowel syndrome/functional dyspepsia (IBS/FD). Results: Atopic disease prevalence was higher in the NCWS patients (32.8%) than in those with CeD (19.3%) and IBS/FD (21.5%) (p = 0.001 for both). Similarly, NCWS subjects reported a higher frequency of multiple food sensitivities (MFSs) (39.8%) and self-reported milk intolerance (SRMI) (65.9%) compared to the control groups (p < 0.001 for both). On multiple logistic regression analysis, a coexistent atopic disease (OR 1.481), MFS (OR 3.882) and SRMI (OR 2.259) proved to be variables associated with the NCWS diagnosis. Conclusions: NCWS subjects have a higher frequency of atopic disease, MFS and SRMI when compared to both CeD and IBS/FD patients. All these conditions could be considered as an expression of an underlying hypersensitivity milieu characterizing NCWS and might be of support in the differential diagnosis between NCWS and functional gastrointestinal disorders, if inserted into a broader diagnostic panel.

The development of harmonized, standardized, and integrated environmental observation systems is a key challenge in Earth system science. Such capability is essential for advancing the interdisciplinary research needed to improve understanding of the Earth system and support global sustainability. The Integrated European Long-Term Ecosystem, Critical Zone and Socio-ecological Research Infrastructure (eLTER RI) is a recently developed pan-European network of in situ research sites that facilitates the collection long-term, comprehensive observation, analysis, and modeling of environmental and ecosystem change. This initiative focuses on Europe's primary ecosystems, encompassing the atmosphere, geosphere, hydrosphere, biosphere, and their socio-ecological interactions with the anthroposphere. A fundamental prerequisite for effective environmental monitoring and observation is a standardized and harmonized design that facilitates consistent and comparable environmental data across diverse spatial and temporal scales. The objective of this paper is to introduce the eLTER Framework of Standard Observations (eLTER SO) as a harmonized conceptual and operational standard for long-term, integrated in situ environmental observations, and to demonstrate how it supports consistent cross-sphere monitoring and international collaboration in environmental research. The eLTER SO delineates essential ecosystem variables, their measurement methods, and protocols. These Standard Observations (SOs) constitute the conceptual foundation of eLTER RI and provide a basis for overcoming existing disciplinary barriers to the international harmonization of environmental research and a foundation for cross-sphere observation concepts. The eLTER SO combines the scientific-academic perspective, as known from “classical” Essential Variable concepts, with the operational perspective required for the establishment and long-term operation of in situ observatories.

This technical report provides a detailed description of the reporting and monitoring procedures—both documentary and financial—implemented throughout the entire lifecycle of the 2022 PRIN PNRR projects. The document analyzes the methodologies adopted and the evolution of management procedures, highlighting the gradual consolidation of the monitoring system in relation to regulatory compliance requirements and the traceability of operations. Questo rapporto tecnico descrive nel dettaglio le procedure di rendicontazione e monitoraggio documentale e finanziaria implementate nel corso dell’intero ciclo di vita dei progetti PRIN 2022 PNRR. Il documento analizza le metodologie adottare e l’evoluzione delle procedure gestionali, evidenziando il progressivo consolidamento del sistema di monitoraggio in relazione alle esigenze di conformità normativa e tracciabilità delle operazioni.

Editorial

Editorial