The nonequilibrium structural and dynamical properties of semiflexible active polar polymers subject to linear flow are studied using numerical simulations. Filaments are confined in two dimensions and immersed in a fluid described by the Brownian multiparticle collision dynamics approach. The applied shear flow causes conformational changes in a polymer, aligns it along the flow direction, and induces a tumbling motion at high flow rates. In an intermediate, activity-dependent shear-rate regime, a characteristic scaling exponent for the mean-square end-to-end distance along the gradient direction is observed. This exponent appears to be determined by the semiflexibility of the polymer. The tumbling dynamics exhibits a characteristic time, with a stronger dependence on the Weissenberg number than that of flexible active or passive polymers. Activity strongly impacts the rheological properties of semiflexible polymers and even implies a negative viscosity for weak flows. At very large values of the shear rate, shear dominates over activity, and passive-polymer behavior is assumed.

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.

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<

In this paper, we derive a new method to compute the nodes and weights of simultaneous n-point Gaussian quadrature rules. The method is based on the eigendecomposition of the banded lower Hessenberg matrix that contains the coefficients of the recurrence relations for the corresponding multiple orthogonal polynomials. The novelty of the approach is that it uses the property of total nonnegativity of this matrix associated with the particular considered multiple orthogonal polynomials, in order to compute its eigenvalues and eigenvectors in a numerically stable manner. The overall complexity of the computation of all the nodes and weights is O(n^2).

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.

On the half line, we introduce a new sequence of near-best uniform approximation polynomials, easily computable by the values of the approximated function at a truncated number of Laguerre zeros. Such approximation polynomials come from a discretization of filtered Fourier–Laguerre partial sums, which are filtered using a de la Vallée Poussin (VP) filter. They have the peculiarity of depending on two parameters: a truncation parameter that determines how many of the n Laguerre zeros are considered, and a localization parameter, which determines the range of action of the VP filter we will apply. As n→∞, under simple assumptions on such parameters and the Laguerre exponents of the involved weights, we prove that the new VP filtered approximation polynomials have uniformly bounded Lebesgue constants and uniformly convergence at a near–best approximation rate, for any locally continuous function on the semiaxis. The numerical experiments have validated the theoretical results. In particular, they show a better performance of the proposed VP filtered approximation versus the truncated Lagrange interpolation at the same nodes, especially for functions a.e. very smooth with isolated singularities. In such cases, we see a more localized approximation and a satisfactory reduction of the Gibbs phenomenon.

Intraguild predation, representing a true combination of predation and competition between two species that rely on a common resource, is of foremost importance in many natural communities. We investigate a spatial model of three species interaction, characterized by a Holling type II functional response and linear cross-diffusion. For this model we report necessary and sufficient conditions ensuring the insurgence of Turing instability for the coexistence equilibrium; we also obtain conditions characterizing the different patterns by multiple scale analysis. Numerical experiments confirm the occurrence of different scenarios of Turing instability, also including Turing–Hopf patterns.

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weights denominators to achieve it.

Droplet microfluidics has emerged as highly relevant technology in diverse fields such as nanomaterials synthesis, photonics, drug delivery, regenerative medicine, food science, cosmetics, and agriculture. While significant progress has been made in understanding the fundamental mechanisms underlying droplet generation in microchannels and in fabricating devices to produce droplets with varied functionality and high throughput, challenges persist along two important directions. On one side, the generalization of numerical results obtained by computational fluid dynamics would be important to deepen the comprehension of complex physical phenomena in droplet microfluidics, as well as the capability of predicting the device behavior. Conversely, truly three-dimensional architectures would enhance microfluidic platforms in terms of tailoring and enhancing droplet and flow properties. Recent advancements in artificial intelligence (AI) and additive manufacturing (AM) promise unequaled opportunities for simulating fluid behavior, precisely tracking individual droplets, and exploring innovative device designs. This review provides a comprehensive overview of recent progress in applying AI and AM to droplet microfluidics. The basic physical properties of multiphase flows and mechanisms for droplet production are discussed, and the current fabrication methods of related devices are introduced, together with their applications. Delving into the use of AI and AM technologies in droplet microfluidics, topics covered include AI-assisted simulations of droplet behavior, real-time tracking of droplets within microfluidic systems, and AM-fabrication of three-dimensional systems. The synergistic combination of AI and AM is expected to deepen the understanding of complex fluid dynamics and active matter behavior, expediting the transition toward fully digital microfluidic systems.

We establish the existence of quasi-periodic traveling wave solutions forthe β-plane equation on T2 with a large quasi-periodic traveling wave external force.These solutions exhibit large sizes, which depend on the frequency of oscillations of theexternal force. Due to the presence of small divisors, the proof relies on a nonlinear Nash-Moser scheme tailored to construct nonlinear waves of large size. To our knowledge,this is the first instance of constructing quasi-periodic solutions for a quasilinear PDEin dimensions greater than one, with a 1-smoothing dispersion relation that is highlydegenerate - indicating an infinite-dimensional kernel for the linear principal operator.This degeneracy challenge is overcome by preserving the traveling-wave structure, theconservation of momentum and by implementing normal form methods for the linearizedsystem with sublinear dispersion relation in higher space dimension.

Introduction Practicing physical activity (PA) on a regular basis is an important support for people with type 1 diabetes (T1D). However, exercise may induce in them hypoglycaemic events during or after it. One major consequence of this is that, to limit this risk, many people with T1D tend to avoid performing PA. The availability of modern continuous glucose-monitoring (CGM) devices is potentially a great asset for reducing the chances of hypoglycaemia (HP) due to PA. Several algorithms have already been proposed to predict HP in subjects with T1D. However, not many of them are specifically focused on HP induced by exercise. Among those, many involve a large number of covariates making the applicability more difficult, and none uses CGM values available during the training session. Objectives We study the problem of predicting hypoglycaemia events in subjects with T1D during PA. The final aim is to produce algorithms enabling a person with T1D to perform a planned PA session without experiencing HP. Method One of the two algorithms we developed uses the CGM data in an initial part of a PA session. A parametric model is fitted to the data and then used to predict a possible HP during the remaining part of the session. Our second algorithm uses the CGM value at the start of a session. It also relies on statistical information about the average rate of decrease of the aforementioned model, as derived from a previously measured CGM data during PA. Then, the algorithm estimates the probability of HP during the planned PA session. Both algorithms have a very simple structure and therefore are of wide applicability. Results The application of the two algorithms to a very large dataset shows their very good ability to predict HP during PA in people with T1D.

Wetlands are essential for global biogeochemical cycles and ecosystem services, with the dynamics of soil organic carbon (SOC) serving as the critical regulatory mechanism for these processes. However, accurately modeling carbon dynamics in wetlands presents challenges due to their complexity. Traditional approaches often fail to capture spatial variations, long-range transport, and periodical flooding dynamics, leading to uncertainties in carbon flux predictions. To tackle these challenges, we introduce a novel extension of the fractional RothC model, integrating temporal fractional-order derivatives into spatial dimensions. This enhancement allows for the creation of a more adaptive tool for analyzing SOC dynamics. Our differential model incorporates Richardson–Richard's equation for moisture fluxes, a diffusion–advection–reaction equation for fractional-order dynamics of SOC compounds, and a temperature transport equation. We examine the influence of diffusive movement and sediment moisture content on model solutions, as well as the impact of including advection terms. Finally, we validated the model on a restored wetland scenario at the Ebro Delta site, aiming to evaluate the effectiveness of flooding strategies in enhancing carbon sequestration and ecosystem resilience.

The driving mechanisms at the base of the clearance of biological wastes in the brain interstitial space (ISS) are still poorly understood and an actively debated subject. A complete comprehension of the processes that lead to the aggregation of amyloid proteins in such environment, hallmark of the onset and progression of Alzheimer’s disease, is of crucial relevance. Here we employ combined computational fluid dynamics and molecular dynamics techniques to uncover the role of fluid flow and proteins transport in the brain ISS. Our work identifies diffusion as the principal mechanism for amyloid-β proteins clearance, whereas fluid advection may lead transport for larger molecular bodies, like amyloid-β aggregates or extracellular vesicles. We also clearly quantify the impact of large nascent prefibrils on the fluid flowing and shearing. Finally, we show that, even in the irregular brain interstitial space (ISS), hydrodynamic interactions enhance amyloid-β aggregation at all stages of the aggregation pathway. Our results are key to understand the role of fluid flow and solvent-solute interplay on therapeutics like antibodies acting in the brain ISS.

Forecasting functional time series (FTS) has arguably achieved tremendous success in recent years. Time series of curves, or functional time series, exist in many disciplines. Among the numerous existing contributions for forecasting time series, one-step-ahead functional time series forecasting, that is one-step-ahead prediction of a curve-valued time series, has been studied in several practical studies. Predominantly most traditional functional time series studies use functional (Hilbertian) autoregressive models for one-step-ahead forecast, but their application in real-world data remains a pertinent challenge due to a non-stationary behavior. Opposed to such models, several nonparametric approaches have been proposed in the recent literature for forecasting time series of curves. An analysis of the forecasting performances of such nonparametric approaches, validated empirically with a set of real experiments, is presented in this paper. While a complete understanding of these approaches remains elusive, we hope that our perspectives, discussions, and comparisons serve as a stimulus for new statistical research.

Retrieving LST from infrared spectral observations is challenging because it needs separation from emissivity in surface radiation emission, which is feasible only when the state of the surface-atmosphere system is known. Thanks to its high spectral resolution, the Infrared Atmospheric Sounding Interferometer (IASI) instrument onboard Metop polar-orbiting satellites is the only sensor that can simultaneously retrieve LST, the emissivity spectrum, and atmospheric composition. Still, it cannot penetrate thick cloud layers, making observations blind to surface emissions under cloudy conditions, with surface and atmospheric parameters being flagged as voids. The present paper aims to discuss a downscaling-fusion methodology to retrieve LST missing values on a spatial field retrieved from spatially scattered IASI observations to yield level 3, regularly gridded data, using as proxy data LST from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) flying on Meteosat Second Generation (MSG) platform, a geostationary instrument, and from the Advanced Very High-Resolution Radiometer (AVHRR) onboard Metop polar-orbiting satellites. We address this problem by using machine learning techniques, i.e., Gradient Boosting, Random Forest, Gaussian Process Regression, Neural Network, and Stacked Regression. We applied the methodology over the Po Valley region, a very heterogeneous area that allows addressing the trained models' robustness. Overall, the methods significantly enhanced spatial sampling, keeping errors in terms of Root Mean Square Error (RMSE) and bias (Mean Absolute Error, MAE) very low. Although we demonstrate and assess the results primarily using IASI data, the paper is also intended for applications to the IASI follow-on, that is, IASI Next Generation (IASI-NG), and much more to the Infrared Sounder (IRS), which is planned to fly this year, 2025, on the Meteosat Third Generation platform (MTG).

Literature confirms the crucial influence on glacier and rock glacier flow of non-viscous deformations together with temperature impact. This observation suggests numerical glaciologists ought to reconsider the established mathematical modeling based on the representation of ice as a power-law viscous fluid and the Glen's law. Along this line, we propose the numerical solution of a two-dimensional rock-glacier flow model, based on a constitutive law of second grade of complexity two, as just published for a one-dimensional set-up by two of the authors. With the representation of the composition of the rocky ice as a mixture of ice and rock and sand grains, and the inclusion of the local impact of pressure and of thermal effects, this model has allowed the reproduction of borehole measurement data from alpine glacier internal sliding motion via a similarity solution of the flow governing equations. Here, the adopted numerical procedure uses a second order finite difference scheme and imposes the incompressibility constrain up to computer accuracy via the pressure method, that we have extended from Newtonian computational fluid dynamics. This method solves the governing equations for the flow in primitive variables with the advantage that no pre-/post-processing is required; in addition, it avoids splitted solution of the Poisson equation for pressure which might be source of undesired numerical mass unbalancing. The results of a numerical test on the Murtel-Corvatsch alpine glacier flow, reporting satisfactory matching with published on-field observations, are presented.