Dimensionality reduction is a hot research topic in data analysis today. Thanks to the advances in high performance computing technologies and in the engineering field, we entered in the so-called big-data era and an enormous quantity of data is available in every scientific area, ranging from social networking, economy and politics to e-health and life sciences. However, much of the data is highly redundant and can be efficiently brought down to a much smaller number of variables without a significant loss of information using different strategies.

In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods, encompassing non-standard finite difference schemes, direct quadrature techniques and predictor- corrector approaches. The proposed discretizations guarantee the positivity, monotonicity and boundedness of the solution regardless of the temporal, spatial and frequency stepsizes. Comprehensive numerical experiments confirm the theoretical findings and demonstrate the efficacy of the proposed methods in simulating realistic photochemical phenomena.

We explicitly demonstrate the universality of critical dynamics through unprecedented large-scale Graphics Processing Units (GPU)-based simulations of two out-of-equilibrium processes, comparing the behavior of spin-1/2 Ising and spin-1 Blume-Capel models on a square lattice. In the first protocol, a completely disordered system is instantaneously brought into contact with a thermal bath at the critical temperature, allowing it to evolve until the coherence length exceeds 103 lattice spacings. Finite-size effects are negligible due to the mesoscopic scale of the lattice sizes studied, with linear dimensions up to L=222 and 219 for the Ising and Blume-Capel models, respectively. Our numerical data, and the subsequent analysis, demonstrate a strong dynamic universality between the two models and provide the most precise estimate to date of the dynamic critical exponent for this universality class, z=2.1676⁢(1). In the second protocol, we corroborate the role of the universal ratio of dynamic and static length scales in achieving an exponential acceleration in the approach to equilibrium just above the critical temperature, through a time-dependent variation of the thermal bath temperature. The results presented in this work leverage our Compute Unified Device Architecture (CUDA)-based numerical code, breaking the world record for the simulation speed of the Ising model.

We present high-performance implementations of the two-dimensional Ising and Blume-Capel models for large-scale, multi-GPU simulations. Our approach takes full advantage of the NVIDIA GB200 NVL72 system, which features up to 72 GPUs interconnected via high-bandwidth NVLink, enabling direct GPU-to-GPU memory access across multiple nodes. By utilizing Fabric Memory and an optimized Monte Carlo kernel for the Ising model, our implementation supports simulations of systems with linear sizes up to L=223, corresponding to approximately 70 trillion spins. This allows for a peak processing rate of nearly 1.15×105 lattice updates per nanosecond—setting a new performance benchmark for Ising model simulations. Additionally, we introduce a custom protocol for computing correlation functions, which strikes an optimal balance between computational efficiency and statistical accuracy. This protocol enables large-scale simulations without incurring prohibitive runtime costs. Benchmark results show near-perfect strong and weak scaling up to 64 GPUs, demonstrating the effectiveness of our approach for large-scale statistical physics simulations. Program summary: Program title: cuIsing (optimized) CPC Library link to program files: https://doi.org/10.17632/ppkwwmcpwg.1 Licensing provisions: MIT license Programming languages: CUDA C Nature of problem: Comparative studies of the critical dynamics of the Ising and Blume-Capel models are essential for gaining deeper insights into phase transitions, enhancing computational methods, and developing more accurate models for complex physical systems. To minimize finite-size effects and optimize the statistical quality of simulations, large-scale simulations over extended time scales are necessary. To support this, we provide two high-performance codes capable of running simulations with up to 70 trillion spins. Solution method: We present updated versions of our multi-GPU code for Monte Carlo simulations, implementing both the Ising and Blume-Capel models. These codes take full advantage of multi-node NVLink systems, such as the NVIDIA GB200 NVL72, enabling scaling across GPUs connected across different nodes within the same NVLink domain. Communication between GPUs is handled seamlessly via Fabric Memory–a novel memory allocation technique that facilitates direct memory access between GPUs within the same domain, eliminating the need for explicit data transfers. By employing highly optimized CUDA kernels for the Metropolis algorithm and a custom protocol that reduces the computational overhead of the correlation function, our implementation achieves the highest recorded performance to date.

In this work we present three classes of unconditionally positive numerical methods for a photochemical model governed by non-local integro-differential equations. Specifically, we design and compare dynamically-consistent approximation schemes based on non-standard finite differences discretizations, predictor-corrector approaches and direct quadrature integrators. A rigorous analysis is performed to establish the preservation of key physical properties, i.e. positivity, monotonicity and boundedness, regardless of the temporal, spatial and frequency stepsizes. Furthermore, theoretical results are provided to establish the high-order consistency and convergence of the methods. Comprehensive numerical experiments confirm the theoretical findings and allow for a detailed comparison of the performance and computational efficiency of the proposed discretizations. Applications to two case studies of interest, photoactivation of serotonin in left-right brain patterning and photodegradation of cadmium pigments in historical paintings, demonstrate the practical relevance of the proposed model and simulation techniques in addressing complex phenomena in photochemistry.

A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms' decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction-diffusion system of PDEs generalizing a nonlinear triopoly model describing a master-slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations.

Morphological Characterization of figs leaves

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 the 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≃t2/3 (t: time) to a late-time regime L≃gt5/3 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.

This paper broaches the peridynamic inverse problem of determining the horizon size of the kernel function in a one-dimensional model of a linear microelastic material. We explore different kernel functions, including V-shaped, distributed, and tent kernels. The paper presents numerical experiments using PINNs to learn the horizon parameter for problems in one and two spatial dimensions. The results demonstrate the effectiveness of PINNs in solving the peridynamic inverse problem, even in the presence of challenging kernel functions. We observe and prove a one-sided convergence behavior of the Stochastic Gradient Descent method towards a global minimum of the loss function, suggesting that the true value of the horizon parameter is an unstable equilibrium point for the PINN's gradient flow dynamics.

Most vaccines require multiple doses, the first to induce recognition and antibody production and subsequent doses to boost the primary response and achieve optimal protection. We show that properly prioritizing the administration of first and second doses can shift the epidemic threshold, separating the disease-free from the endemic state and potentially preventing widespread outbreaks. Assuming homogeneous mixing, we prove that at a low vaccination rate, the best strategy is to give absolute priority to first doses. In contrast, for high vaccination rates, we propose a scheduling that outperforms a first-come first-served approach. We identify the threshold that separates these two scenarios and derive the optimal prioritization scheme and interdose interval. Agent-based simulations on real and synthetic contact networks validate our findings. We provide specific guidelines for effective resource allocation, showing that adjusting the timing between the primer and booster significantly impacts epidemic outcomes and can determine whether the disease persists or disappears.

Far-infrared Outgoing Radiation Understanding and Monitoring (FORUM) was selected in 2019 as the ninth Earth Explorer mission by the European Space Agency. Its primary objective is to collect interferometric measurements in the far-infrared (FIR) spectral range, which accounts for 50% of Earth's outgoing longwave radiation emitted into space, and will be observed from space for the first time. Accurate measurements of the FIR at the top of the atmosphere are crucial for improving climate models. Current instruments are insufficient, necessitating the development of advanced computational techniques. FORUM will provide unprecedented insights into key atmospheric parameters, such as surface emissivity, water vapor, and ice cloud properties, through the use of a Fourier transform spectrometer. To ensure the quality of the mission's data, an end-to-end simulator was developed to simulate the measurement process and evaluate the effects of instrument characteristics and environmental factors. The core challenge of the mission is solving the retrieval problem, which involves estimating atmospheric properties from the radiance spectra observed by the satellite. This problem is ill-posed and regularization techniques are necessary to stabilize the solution. In this work, we present a data-driven approach to approximate the inverse mapping in the retrieval problem, aiming to achieve a solution that is both computationally efficient and accurate. In the first phase, we generate an initial approximation of the inverse mapping using only simulated FORUM data. In the second phase, we improve this approximation by introducing climatological data as a priori information and using a neural network to estimate the optimal regularization parameters during the retrieval process. While our approach does not match the precision of full-physics retrieval methods, its key advantage is the ability to deliver results almost instantaneously, making it highly suitable for real-time applications. Furthermore, the proposed method can provide more accurate a priori estimates for full-physics methods, thereby improving the overall accuracy of the retrieved atmospheric profiles.

In this work, we present accLB, a high-performance Fortran-based lattice Boltzmann (LB) solver tailored to multiphase turbulent flows on multi-GPU architectures. The code couples a conservative phase-field formulation of the Allen–Cahn equation with a thread-safe, regularized LB method to capture complex interface dynamics. Designed from the ground up for HPC environments, accLB employs MPI for distributed memory parallelism and OpenACC for GPU acceleration, achieving excellent portability and scalability on leading pre-exascale systems such as Leonardo and LUMI. Benchmark tests demonstrate strong and weak scaling efficiencies on multiple GPUs. Physical validation includes direct numerical simulations of homogeneous isotropic turbulence (HIT). Further, we examine bubble-laden HIT and observe a transition to a -3 energy scaling, as in experiments and theoretical predictions, due to bubble-induced dissipation, along with enhanced small-scale intermittency. These results highlight accLB as a robust and scalable platform for the simulation of multiphase turbulence in extreme computational regimes.

We introduce a regularized fluctuating lattice Boltzmann model (Reg-FLBM) for the D3Q27 lattice, which incorporates thermal fluctuations through Hermite-based projections to ensure compliance with the fluctuation-dissipation theorem. By leveraging the recursive regularization framework, the model achieves thermodynamic consistency for both hydrodynamic and ghost modes. Compared to the conventional single-relaxation-time BGK-FLBM, the Reg-FLBM provides improved stability and a more accurate description of thermal fluctuations. The implementation is optimized for large-scale parallel simulations on graphics processing unit-accelerated architectures, enabling systematic investigation of fluctuation-driven phenomena in mesoscale and nanoscale fluid systems.

This study presents a high-order, thread-safe version of the lattice Boltzmann method, incorporating an interface-capturing equation, based on the conservative Allen-Cahn equation, to simulate incompressible two-component systems with high-density and viscosity contrasts. The method utilizes a recently proposed thread-safe implementation optimized for shared-memory architectures, and it is employed to reproduce the dynamics of droplets and bubbles in several test cases with results in agreement with experiments and other numerical simulations from the literature. The proposed approach offers promising opportunities for high-performance computing simulations of realistic fluid systems with high-density and viscosity contrasts for advanced applications in environmental, atmospheric, and meteorological flows, all the way down to microfluidic and biological systems, particularly on graphic processing unit-based architectures.

Accurate prediction of rarefied gas dynamics is crucial for optimizing flows through microelectromechanical systems, air filtration devices, and shale gas extraction. Traditional methods, such as discrete velocity and direct simulation Monte Carlo (DSMC), demand intensive memory and computation, especially for microflows in non-convex domains. Recently, physics-informed neural networks (PINNs) emerged as a meshless and adaptable alternative for solving non-linear partial differential equations. We trained a PINN using a limited number of DSMC-generated rarefied gas microflows in the transition regime (0.1<3), incorporating continuity and Cauchy momentum exchange equations in the loss function. The PINN achieved under 2 % error on these residuals and effectively filtered DSMC's intrinsic statistical noise. Predictions remained strong for a tested flow field with Kn=0.7, and showed limited extrapolation performance on a flow field with Kn=5 with a local overshoot of about 20 %, while maintaining physical consistency. Notably, each DSMC field required ∼20 hours on 4 graphics processing units (GPU), while the PINN training took <2 hours on one GPU, with evaluations under 2 seconds.

Recent experiments of fluid transport in nano-channels have shown evidence of a coupling between charge-fluctuations in polar fluids and electronic excitations in graphene solids, which may lead to a significant reduction of friction a phenomenon dubbed “negative quantum friction.” In this paper, we present a semi-classical mesoscale Boltzmann-Wigner lattice kinetic model of quantum-nanoscale transport and perform a numerical study of the effects of the quantum interactions on the evolution of a one-dimensional nano-fluid subject to a periodic external potential. It is shown that the effects of quantum fluctuations become visible once the quantum length scale (Fermi wavelength) of the quasiparticles becomes comparable to the lengthscale of the external potential. Under such conditions, quantum fluctuations are mostly felt on the odd kinetic moments, while the even ones remain nearly unaffected because they are “protected” by thermal fluctuations. It is hoped that the present Boltzmann-Wigner lattice model and extensions thereof may offer a useful tool for the computer simulation of quantum-nanofluidic transport phenomena at scales of engineering relevance.

We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the reactivity of the non-spatial and spatial dynamics, stability analyses, and numerical continuation to uncover detailed aspects of this system’s pattern-forming potential. In addition to patterning in Turing unstable parameter regimes, reactivity of the spatial system can itself lead to a range of parameters where a spatially uniform state is asymptotically stable, but exhibits transient growth that can induce pattern formation. We show that this occurs in the bistable region of a subcritical Turing bifurcation. Intriguingly, such bistable regions appear in two spatial dimensions, but not in a one-dimensional domain, suggesting important interplays between geometry, transient growth, and the emergence of multistable patterns. We discuss the implications of our analysis for the bacterial soil organic carbon system, as well as for reaction-transport modeling more generally.

In this work we propose a bi-objective variant of the well-known 0/1 Knapsack Problem, that finds application in cases in which some item pairs may be seen as mutually conflicting. Previous variants considered in this scenario proposed to either avoid all conflicts, or to deal with them by considering the payment of appropriate penalty costs. We propose a different approach where the maximization of the profit and the minimization of the accepted conflicts are considered two different objective functions. We aim at identifying all Pareto-optimal solutions, so that a decision maker may choose a posteriori the optimal trade-off. We propose an exact resolution method based on the epsilon-constraint approach. Computational results on a wide set of instances show that our approach can be used in practice to identify and analyze their Pareto front.

We report a numerical study addressing the dynamics of compound vesicles confined in a channel under shear flow. The system comprises a smaller vesicle embedded within a larger one and can be used to mimic, for example, leukocytes or nucleate cells. A two-dimensional model, which combines molecular dynamics and mesoscopic hydrodynamics including thermal fluctuations, is adopted to perform an extended investigation. We are able to vary independently the swelling degree and the relative size of vesicles, the viscosities of fluids internal and external to vesicles, and the Capillary number, so to observe a rich dynamical phenomenology which goes well beyond what observed for single vesicles, matching quantitatively with experimental findings. Tank-treading, tumbling, and trembling motions are enriched by dynamical states where inner and outer vesicles can perform different motions. We show that thermal fluctuations are crucial during trembling and swinging dynamics, as observed in experiments. Undulating motion of the external vesicle, characterized by periodic oscillation of the inclination and buckling of the membrane, is observed at high filling fractions. This latter state exhibits features that are shown to depend on the relative size, the swelling degree of both vesicles as well as on thermal noise lacking in previous analytical and numerical studies.

Scaling properties of active ring polymers