We study a family of cosmological models featuring dynamical dark energy (DE), based on the idea that the creation of its constituents arises from the gravitational field of the expanding universe, whose non-equilibrium physics is described by a non-zero bulk viscosity coefficient. We consider the complete scenario, in which both matter creation and bulk viscosity are present, together with its two limiting cases, in which only one of the two effects is retained. Once each model is constrained by requiring its present-day deceleration parameter q0 to match specific values, the complete scenario introduces up to two additional free parameters with respect to the Lambda CDM model, one of which is the equation of state parameter w of the created dark energy. We consider two choices for q0: the value predicted by the Lambda CDM model, and one obtained from a background analysis of Fazzari et al. (2025). To perform the analysis, we construct the effective running Hubble constant, i.e. a theoretical function corresponding to the ratio between the Hubble parameter of our models and the Lambda CDM expansion rate. The theoretical predictions for the effective running Hubble constant of the three models are tested against the Master binned sample of Type Ia Supernovae (SNe Ia), through a Markov Chain Monte Carlo procedure with up to four free parameters. The most important result emerging from this analysis is that, when using the cosmographic q0, all three models exhibit a quintessence-to-phantom transition in the effective equation of state parameter of the dark energy; on the contrary, when using the q0 coming from the Lambda CDM limit, the transition cannot happen, and the effective equation of state parameter is entirely of phantom nature across the considered redshift range.
We study the spectral theory of mixed local and nonlocal operators with lower-order terms in the right-hand side of the equation. This kind of problems is motivated by the analysis of superposition operators of mixed order and with the "wrong sign" of the lower-order terms with respect to the classical elliptic theory. Our results include: -convergence to classical cases when the right-hand side of the eigenvalye equations "localizes", recovering the simplicity and sign-definiteness of eigenfunctions in the limit; -a detailed analysis of disconnected domains, showing that, unlike the classical case, any eigenfunction associated with the first eigenvalue must change sign, and that the first eigenvalue of a union of disconnected domains is strictly smaller than that of its individual components; -examples in which the first eigenvalue is either simple or non-simple in disconnected domains; -a regularity theory that underpins these results.
We discuss a free boundary model for tumor invasion that describes a cloud of cells that diffuse and, at the same time, are drifted along the vector field of the chemotactic direction. The model captures the evolution of a solid tumor, including the process of angiogenesis, which consists in the formation of new blood vessels that supply the tumor with oxygen and other nutrients, thereby promoting its spread and growth. We prove that, once formed, the tumor survives through time, maintaining strictly positive thickness. An explicit expression in terms of the initial data is derived. Moreover, we distinguish two regimes depending on the ratio κ between the spreading of tumor cells and the growth of the tumor mass. If κ is sufficiently large, then the tumor grows exponentially in time and invades the entire host tissue. In contrast, if κ is small enough, then either the tumor remains bounded in size over time or may experience a fast contraction.
Shell-based spinodal architectures have recently attracted significant attention as mechanical metamaterials due to their highly tuneable effective properties. In this work, the suitability of shell-based spinodal metamaterials as core materials for lightweight sandwich structures is investigated. For this purpose, a multiscale computational framework supported by experimental validation is developed.At the small-scale, a computational homogenization approach is employed to evaluate the effective elastic properties of periodic spinodal-shell unit cells, including the effective Young’s and shear moduli along the principal material directions. The adopted homogenization framework evolves from its application on solid-based topologies towards a dedicated framework specifically refined for shell-based architectures. Experimental validation of the homogenized elastic properties is provided through compression tests performed on additively manufactured spinodal-shell unit-cell specimens.At the structural scale, the homogenized properties are integrated into finite element models of sandwich beams to investigate their flexural response under three-point bending. The sandwich specimens, consisting of two face sheets bonded to a core made of an array of shell-based spinodal cells, are manufactured and tested for selected span lengths. The experimental bending results provide quantitative validation of the numerical predictions, enabling a consistent comparison between numerical and experimental flexural stiffness and confirming the capability of the proposed modelling framework to capture the dominant deformation mechanisms governing the bending response.The combined numerical and experimental results demonstrate that shell-based spinodal architectures represent a valid class of sandwich cores, offering favourable stiffness-to-weight performance and design flexibility.
Objectives: To investigate the incidence, timing, and neurophysiological characteristics of focal upper limb peripheral nerve injury (PNI) related to positional brachial plexus involvement after prone positioning in patients with acute respiratory distress syndrome (ARDS). Methods: Prospective single-centre observational cohort study conducted in the ICU of an academic tertiary-level hospital in Milan (Italy), between April 2022 and September 2025. All adult patients with ARDS requiring invasive mechanical ventilation and treated with prone positioning were screened. Patients underwent predefined longitudinal neurophysiological assessments at baseline, after each prone positioning cycle and before ICU discharge, whenever feasible. Focal upper limb PNI was defined using specific electrodiagnostic criteria. Cumulative incidence analyses accounted for ICU death as a competing event. Results: Overall, 128 prone positioning cycles were performed in 54 patients. Focal upper limb PNI occurred in 11 patients (20.4%; 95% CI 10.6-33.5), after a median of 2 prone positioning cycles (IQR 1-3) and 36 h (IQR 21-50) of cumulative prone exposure. By day 28, the estimated cumulative incidence was 29.1% (95% CI 11.6-46.7), rising to 42.7% (95% CI 17.6-67.9) in patients exposed to at least one uninterrupted prone cycle lasting >= 24 h, compared with 8.6% (95% CI 0-20.4) in patients with shorter exposure (p = 0.047). Among prone positioningrelated complications, pressure ulcers were the most frequent, occurring in 40.7% (22/54) of patients and predominantly involving the facial region, whereas no vascular access loss or accidental endotracheal tube displacement were recorded. Conclusions: Focal upper limb PNI was a frequent, clinically relevant, and potentially under-recognised complication of prolonged prone positioning in patients with ARDS. Implications for clinical practice: A prone positioning bundle should include systematic upper limb surveillance, repeated reassessment of limb, head and shoulder alignment, and early detection of focal asymmetric upper limb weakness, particularly during uninterrupted prone cycles lasting 24 h or longer.
