Employing numerical simulations, we provide an accurate insight into the heat transfer mechanism in the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets. We focus on the unsteady dynamics characterizing the thermal convection of these complex fluids close to the transition from conductive to convective states, where the heat transfer phenomenon, expressed in terms of the Nusselt number Nu, is characterized by pronounced fluctuations triggered by collective droplet motion [F. Pelusi et al., Soft Matter, 2021, 17(13), 3709-3721]. By systematically increasing the droplet concentration, we show how these fluctuations emerge along with the segregation of “extreme events” in the boundary layers, causing intermittent bursts in the heat flux fluctuations. Furthermore, we quantify the extension S and the duration of the coherent droplet motion accompanying these extreme events via a suitable statistical analysis involving the droplet displacements. We show how the increase in droplet concentration results in a power-law behaviour of the probability distribution function of S and and how this outcome is robust at changing the analysis protocol. Our work offers a comprehensive picture, linking macroscopic heat transfer fluctuations with the statistics of droplets at the mesoscale.

Since long time THz-TDS techniques have been seen as a good option for the measurements of plasma parameters [1]. This becomes a particularly interesting option for nuclear fusion experiments where Far Infrared and microwave diagnostics, in the frequency range 0.1-4000 THz, are one of the most important measurement tool [2] [3]. The application of THz-TDS techniques can potentially provide important plasma parameters, such as density, temperature and fluctuations, by using a multi-functional device with relatively small access requirements [4].

Wood is a hygroscopic material that is subject to phenomena of water exchange with the external environment. These exchanges can cause dimensional variations and cracks to appear on a macroscopic level. In recent years, the use of terahertz technologies in the field of diagnostics applied to cultural heritage has increased considerably. One of the most important characteristics of terahertz radiation is its sensitivity to water content; this polar liquid strongly absorbs and reflects this radiation. The subject of this study will be the detection of moisture in pine wood samples using a 97 GHz terahertz imaging system.

In Deuterium Plasmas differences were detected in JET between electron temperature measurements (Te) made by Electron Cyclotron Emission - Te_ECE - and Thomson Scattering diagnostics systems (Te_TS) [1]. Similar behaviour was found in TFTR [2]. Plasmas heated by ECRH (Electron Cyclotron Heating) in Deuterium on FTU showed T_ECE < T_TS for 8 KeV ≤ Te ≤ 14 keV [3]. These differences can be due to the non-Maxwellian nature of the Electron velocity Distribution Function (EDF) [5,6]. The radiation temperature (Trad) measured by ECE is equal to the Te only for a Maxwellian plasma: being Trad dependent on the derivative of the EDF with respect to perpendicular velocity [5]. This paper describes differences of Te measured by ECE (ECE_MP, Martin-Puplett interferometer) and High-Resolution Thomson Scattering (HRTS) diagnostic. HRTS gives independent information on these differences, having shorter space resolution (2 cm), and faster repetition rate (20 Hz) on a different line of sight (16 cm from the magnetic centre): HRTS measurements confirm the trends observed using LIDAR TS [4,5]. Comparison between HRTS and ECE radiometer measurements is also reported (see sec.3).

In this paper, we introduce peridynamic theory and its application to Richards’ equation with a piecewise smooth initial condition. Peridynamic theory is a non-local continuum theory that models the deformation and failure of materials. Richards’ equation describes the unsaturated flow of water through porous media, and it plays an essential role in many applications, such as groundwater management, soil science, and environmental engineering. We develop a peridynamic formulation of Richards’ equation that includes the effect of peridynamic forces and a piecewise smooth initial condition, further introducing a non-standard symmetric influence function to describe such peridynamic interactions, which turns out to provide beneficial effects from a numerical point of view. Moreover, we implement a numerical scheme based on Chebyshev polynomials and symmetric Gauss–Lobatto nodes, providing a powerful spectral method able to capture singularities and critical issues of Richards’ equation with piecewise smooth initial conditions. We also present numerical simulations that illustrate the performance of the proposed approach. In particular, we perform a computational investigation into the spatial order of convergence, showing that, despite the discontinuity in the initial condition, the order of convergence is retained.

The aim of this chapter is to device a computationally effective procedure for numerically solving fractional-time-space differential equations with the spectral fractional Laplacian. A truncated spectral representation of the solution in terms of the eigenfunctions of the usual integer-order Laplacian is considered. Time-dependent coefficients in this representation, which are solutions to some linear fractional differential equations, are evaluated by means of a generalized exponential time-differencing method, with some advantages in terms of accuracy and computational effectiveness. Rigorous a priori error estimates are derived, and they are verified by means of some numerical experiments.

Membrane viscosity is known to play a central role in the transient dynamics of isolated viscoelastic capsules by decreasing their deformation, inducing shape oscillations and reducing the loading time, that is, the time required to reach the steady-state deformation. However, for dense suspensions of capsules, our understanding of the influence of the membrane viscosity is minimal. In this work, we perform a systematic numerical investigation based on coupled immersed boundary-lattice Boltzmann (IB-LB) simulations of viscoelastic spherical capsule suspensions in the non-inertial regime. We show the effect of the membrane viscosity on the transient dynamics as a function of volume fraction and capillary number. Our results indicate that the influence of membrane viscosity on both deformation and loading time strongly depends on the volume fraction in a non-trivial manner: dense suspensions with large surface viscosity are more resistant to deformation but attain loading times that are characteristic of capsules with no surface viscosity, thus opening the possibility to obtain richer combinations of mechanical features.

Let 1 < p < ∞, ε0 ∈]0, p − 1], Ω ⊂ Rn be a Lebesgue measurable set of positive, finite measure, and let δ : (0, p − 1] → (0, ∞) be such that δb(·):= δ(·) p−·1 is nondecreasing and bounded. We show that the linear set of functions 5 f Lebesgue measurable on Ω: 0<ε sup ≤ε0(δ(ε) k − |f(x)|p−εdx ) p−1 ε < ∞ 5 Ω does not depend on small values of ε0 if and only if δb ∈ ∆2(0+) (i.e., δb(2ε) ≤ cδb(ε) for ε small, for some c > 1), which is equivalent to say that δ ∈ ∆2(0+). This means that in the case δb ∈/ ∆2(0+), the parameter ε0 plays a crucial role in the definition of a generalized grand Lebesgue space, namely, different values of ε0 define different Banach function spaces.

Some recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type inequalities, and criteria for compact embeddings. The limits of these spaces when the smoothness parameter s ∈ (0, 1) tends to either of the endpoints of its range are also discussed. This note is based on recent papers of ours, where additional material and proofs can be found.

A necessary and sufficient condition for fractional Orlicz–Sobolev spaces to be continuously embedded into L∞(Rn) is exhibited. Under the same assumption, any function from the relevant fractional-order spaces is shown to be continuous. Improvements of this result are also offered. They provide the optimal Orlicz target space, and the optimal rearrangement-invariant target space in the embedding in question. These results complement those already available in the subcritical case, where the embedding into L∞(Rn) fails. They also augment a classical embedding theorem for standard fractional Sobolev spaces.

The wetting dynamics of liquid particles, from coated droplets to soft capsules, holds significant technological interest. Motivated by the need to simulate liquid metal droplets with an oxidized surface layer, in this work, we introduce a computational scheme that allows us to simulate droplet dynamics with general surface properties and model different levels of interface stiffness, also describing cases that are intermediate between pure droplets and capsules. Our approach is based on a combination of the immersed boundary and the lattice Boltzmann methods. Here, we validate our approach against the theoretical predictions in the context of shear flow and static wetting properties, and we show its effectiveness in accessing the wetting dynamics, exploring the ability of the scheme to address a broad phenomenology.

Dysregulated inflammation underlies various diseases. Specialized pro-resolving mediators (SPMs) like Resolvin D1 (RvD1) have been shown to resolve inflammation and halt disease progression. Macrophages, key immune cells that drive inflammation, respond to the presence of RvD1 by polarizing to an anti-inflammatory type (M2). However, RvD1's mechanisms, roles, and utility are not fully understood. This paper introduces a gene-regulatory network (GRN) model that contains pathways for RvD1 and other SPMs and proinflammatory molecules like lipopolysaccharides. We couple this GRN model to a partial differential equation–agent-based hybrid model using a multiscale framework to simulate an acute inflammatory response with and without the presence of RvD1. We calibrate and validate the model using experimental data from two animal models. The model reproduces the dynamics of key immune components and the effects of RvD1 during acute inflammation. Our results suggest RvD1 can drive macrophage polarization through the G protein-coupled receptor 32 (GRP32) pathway. The presence of RvD1 leads to an earlier and increased M2 polarization, reduced neutrophil recruitment, and faster apoptotic neutrophil clearance. These results support a body of literature that suggests that RvD1 is a promising candidate for promoting the resolution of acute inflammation. We conclude that once calibrated and validated on human data, the model can identify critical sources of uncertainty, which could be further elucidated in biological experiments and assessed for clinical use.

Introduction: Mathematical modeling has emerged as a crucial component in understanding the epidemiology of infectious diseases. In fact, contemporary surveillance efforts for epidemic or endemic infections heavily rely on mathematical and computational methods. This study presents a novel agent-based multi-level model that depicts the transmission dynamics of gonorrhea, a sexually transmitted infection (STI) caused by the bacterium Neisseria gonorrhoeae. This infection poses a significant public health challenge as it is endemic in numerous countries, and each year sees millions of new cases, including a concerning number of drug-resistant cases commonly referred to as gonorrhea superbugs or super gonorrhea. These drug-resistant strains exhibit a high level of resistance to recommended antibiotic treatments.MethodsThe proposed model incorporates a multi-layer network of agents' interaction representing the dynamics of sexual partnerships. It also encompasses a transmission model, which quantifies the probability of infection during sexual intercourse, and a within-host model, which captures the immune activation following gonorrhea infection in an individual. It is a combination of agent-based modeling, which effectively captures interactions among various risk groups, and probabilistic modeling, which enables a theoretical exploration of sexual network characteristics and contagion dynamics.ResultsNumerical simulations of the dynamics of gonorrhea infection using the complete agent-based model are carried out. In particular, some examples of possible epidemic evolution are presented together with an application to a real case study. The goal was to construct a virtual population that closely resembles the target population of interest.DiscussionThe uniqueness of this research lies in its objective to accurately depict the influence of distinct sexual risk groups and their interaction on the prevalence of gonorrhea. The proposed model, having interpretable and measurable parameters from epidemiological data, facilitates a more comprehensive understanding of the disease evolution.

Fluid dynamics turbulence refers to the chaotic and unpredictable dynamics of flows. Despite the fact that the equations governing the motion of fluids are known since more than two centuries, a comprehensive theory of turbulence is still a challenge for the scientific community. Rather recently a number of important breakthroughs have clarified many relevant, fascinating, and largely unexpected, statistical features of turbulent fluctuations. In these lectures, we discuss recent advances in the field with the aim of highlighting the physical meaning and implication of these new ideas and their role in contributing to disentangling different parts of our understanding of the turbulence problem. The lectures aim at introducing non-experts to the subject and no previous knowledge of the field is required.

Understanding the behavior of human crowds is a key step toward a safer society and more livable cities. Despite the individual variability and will of single individuals, human crowds, from dilute to dense, invariably display a remarkable set of universal features and statistically reproducible behaviors. Here, we review ideas and recent progress in employing the language and tools from physics to develop a deeper understanding about the dynamics of pedestrians.

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature Tr=T/Tg=0.95, where Tg is the spin-glass condensation temperature. For H>10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ζ(t,tw;H). Here, t is the time after H changes, and tw is the time from the quench for T>Tg to the working temperature T until H changes. We connect the growth of ζ(t,tw;H) to the barrier heights Δ(tw) that set the dynamics. The effect of H on the magnitude of Δ(tw) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ(tw). Superposition is preserved if Δ(tw) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap qEA and the overlap q[Δ(tw)]). However, superposition is violated if Δ(tw) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(tw) do increase more rapidly than linearly with Hd through the observation that the growth of ζ(t,tw;H) slows down as ζ(t,tw;H) increases. In this paper, we display the difference between the zero-field-cooled ζZFC(t,tw;H) and the thermoremanent magnetization ζTRM(t,tw;H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

Memory and rejuvenation effects in the magnetic response of off-equilibrium spin glasses have been widely regarded as the doorway into the experimental exploration of ultrametricity and temperature chaos. Unfortunately, despite more than twenty years of theoretical efforts following the experimental discovery of memory and rejuvenation, these effects have, thus far, been impossible to reliably simulate. Yet, three recent developments convinced us to accept this challenge: first, the custom-built Janus II supercomputer makes it possible to carry out simulations in which the very same quantities that can be measured in single crystals of CuMn are computed from the simulation, allowing for a parallel analysis of the simulation and experimental data. Second, Janus II simulations have taught us how numerical and experimental length scales should be compared. Third, we have recently understood how temperature chaos materializes in aging dynamics. All these three aspects have proved crucial for reliably reproducing rejuvenation and memory effects on the computer. Our analysis shows that at least three different length scales play a key role in aging dynamics, whereas essentially all the theoretical analyses of the aging dynamics emphasize the presence and crucial role of a single glassy correlation length.

Controlling and planning the removal of invasive species are topics of outmost importance in management of natural resources because of the severe ecological damages and economic losses caused by non-native alien species. Optimal management strategies often rely on coupling population dynamics models with optimization procedures to achieve an effective allocation of limited resources for removing invasive species from hosting ecosystems. We analyse a parabolic optimal control model to simulate the best spatiotemporal strategy for the removal of the species when a budget constraint is applied. The model also predicts the species spread under the control action. We improve the capability of the model to reproduce realistic scenarios by introducing an advection term in the state equation. That allows to model the action of external forces, like currents or winds, which might bias dispersal in certain directions. The analytical properties of the model are discussed under suitable boundary conditions. As a further original contribution, we introduce a novel numerical procedure for approximating the solution reducing the computational costs in view of its implementation as a support decision tool. Then we test the approach by simulating the spread and the control of a hypothetical invasive plant in the territory of the Italian Sardinia island. To reproduce the anisotropy of the diffusion we include the effect of the altitude in the habitat suitability of the species.

We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction-diffusion PDE (RD-PDE) systems. We show that solutions of surrogate models built by classical Proper Orthogonal Decomposition (POD) exhibit an unstable error behaviour over the dimension of the reduced space. To overcome this drawback, first of all, we propose a POD-DEIM technique with a correction term that includes missing information in the reduced models. To improve the computational efficiency, we propose an adaptive version of this algorithm in time that accounts for the peculiar dynamics of the RD-PDE in presence of Turing instability. We show the effectiveness of the proposed methods in terms of accuracy and computational cost for a selection of RD systems, i.e., FitzHugh-Nagumo, Schnakenberg and the morphochemical DIB models, with increasing degree of nonlinearity and more structured patterns.

In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of ordinary differential equations for any step size. A stability investigation for these methods, which are outside the class of general linear methods, is challenging since the iterates are always generated by a nonlinear map even for linear problems. Recently, a stability theorem was derived presenting criteria for understanding such schemes. For the analysis, the schemes are applied to general linear equations and proven to be generated by C1-maps with locally Lipschitz continuous first derivatives. As a result, the above mentioned stability theorem can be applied to investigate the Lyapunov stability of non-hyperbolic fixed points of the numerical method by analyzing the spectrum of the corresponding Jacobian of the generating map. In addition, if a fixed point is proven to be stable, the theorem guarantees the local convergence of the iterates towards it. In the case of first and second order gBBKS schemes the stability domain coincides with that of the underlying Runge–Kutta method. Furthermore, while the first order GeCo scheme converts steady states to stable fixed points for all step sizes and all linear test problems of finite size, the second order GeCo scheme has a bounded stability region for the considered test problems. Finally, all theoretical predictions from the stability analysis are validated numerically.