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.

Macromolecular crowding has profound effects on the mobility of proteins, with strong implications on the rates of intracellular processes. To describe the dynamics of crowded environments, detailed molecular models are needed, capturing the structures and interactions arising in the crowded system. In this work, we present OPEPv7, which is a coarse-grained force field at amino-acid resolution, suited for rigid-body simulations of the structure and dynamics of crowded solutions formed by globular proteins. Using the OPEP protein model as a starting point, we have refined the intermolecular interactions to match the experimentally observed dynamical slowdown caused by crowding. The resulting force field successfully reproduces the diffusion slowdown in homogeneous and heterogeneous protein solutions at different crowding conditions. Coupled with the lattice Boltzmann technique, it allows the study of dynamical phenomena in protein assemblies and opens the way for the in silico rheology of protein solutions.

Mucociliary clearance is the first defense mechanism of the respiratory tract against inhaled particles. This mechanism is based on the collective beating motion of cilia at the surface of epithelial cells. Impaired clearance, either caused by malfunctioning or absent cilia, or mucus defects, is a symptom of many respiratory diseases. Here, by exploiting the lattice Boltzmann particle dynamics technique, we develop a model to simulate the dynamics of multiciliated cells in a two-layer fluid. First, we tuned our model to reproduce the characteristic length- and time-scales of the cilia beating. We then check for the emergence of the metachronal wave as a consequence of hydrodynamic mediated correlations between beating cilia. Finally, we tune the viscosity of the top fluid layer to simulate the mucus flow upon cilia beating, and evaluate the pushing efficiency of a carpet of cilia. With this work, we build a realistic framework that can be used to explore several important physiological aspects of mucociliary clearance.

Polyelectrolytes can electrophoretically be driven through nanopores in order to be detected. The respective translocation events are often very fast and the process needs to be controlled to promote efficient detection. To this end, we attempt to control the translocation dynamics by coating the inner surface of a nanopore. For this, different charge distributions are chosen that result in substantial variations of the pore–polymer interactions. In addition and in view of the existing detection modalities, experimental settings, and nanopore materials, different types of sensors inside the nanopore have been considered to probe the translocation process and its temporal spread. The respective transport of polyelectrolytes through the coated nanopores is modeled through a multi-physics computational scheme that incorporates a mesoscopic/electrokinetic description for the solvent and particle-based scheme for the polymer. This investigation could underline the interplay between sensing modality, nanopore material, and detection accuracy. The electro-osmotic flow and electrophoretic motion in a pore are analyzed together with the polymeric temporal and spatial fluctuations unraveling their correlations and pathways to optimize the translocation speed and dynamics. Accordingly, this work sketches pathways in order to tune the pore–polymer interactions in order to control the translocation dynamics and, in the long run, errors in their measurements.

In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the Cauchy P.V. integrals on the half line. Moreover, in order to obtain this result they give some new estimates for the distance of the zeros of the Laguerre polynomials that can be useful also in other contests.

In this paper we provide emission estimates due to vehicular traffic via Generic Second OrderModels. We generalize them to model road networks with merge and diverge junctions. Theprocedure consists on solving the Riemann Problem at junction assuming the maximization ofthe flow and a priority rule for the incoming roads. We provide some numerical results for asingle-lane roundabout and we propose an application of the given procedure to estimate theproduction of nitrogen oxides (NOx) emission rates. In particular, we show that the presence ofa traffic lights produces a 28% increase in the NOx emissions with respect to the roundabout.

We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ?. Under the classical Miles-Howard stability condition on the Richardson number, we prove that the system experiences a shear-buoyancy instability: the density variation and velocity undergo an O(t-1/2) inviscid damping while the vorticity and density gradient grow as O(t1/2). The result holds at least until the natural, nonlinear timescale t??-2. Notice that the density behaves very differently from a passive scalar, as can be seen from the inviscid damping and slower gradient growth. The proof relies on several ingredients: (A) a suitable symmetrization that makes the linear terms amenable to energy methods and takes into account the classical Miles-Howard spectral stability condition; (B) a variation of the Fourier time-dependent energy method introduced for the inviscid, homogeneous Couette flow problem developed on a toy model adapted to the Boussinesq equations, i.e. tracking the potential nonlinear echo chains in the symmetrized variables despite the vorticity growth.

We present a simple model describing the chemical aggression undergone by calcium carbonate rocks in presence of acid atmosphere. A large literature is available on the deterioration processes of building stones, in particular in connection with problems concerning historical buildings in the field of Cultural Heritage. It is well known that the greatest aggression is caused by sulfur dioxide and nitrate. In this paper we consider the corrosion caused by sulphur dioxide, which, reacting with calcium carbonate, produces gypsum. The model proposed is obtained by considering both the diffusive and convective effects of propagation and assuming that the porous medium is saturated with a compressible fluid having an assigned polytropic constitutive equation for the pressure. The qualitative behavior of the one dimensional solutions in the fastreaction limit is performed.

WeinvestigatethelinearstabilityofshearsneartheCouetteflowforaclassof2Dincompressible stably stratified fluids. Our main result consists of nearly optimal decay rates for perturbations of stationary states whose velocities are monotone shear flows (U (y), 0) and have an exponential density profile. In the case of the Couette flow U(y) = y, we recover the rates predicted by Hartman in 1975, by adopting an explicit point-wise approach in frequency space. As a by-product, this implies optimal decay rates as well as Lyapunov instability in L2 for the vorticity. For the previously unexplored case of more general shear flows close to Couette, the inviscid damping results follow by a weighted energy estimate. Each outcome concerning the stably stratified regime applies to the Boussinesq equations as well. Remarkably, our results hold under the celebrated Miles-Howard criterion for stratified fluids.

This paper presents a sparse factorization for the delay Vandermonde matrix (DVM) and a faster, exact, radix-2, and completely recursive DVM algorithm to realize millimeter wave beamformers in wireless communication networks. The proposed algorithm will reduce the complexity of $N$-beam wideband beamformers from $\mathcal{O}(N^2)$ to $\mathcal{O}(N {\rm\: log\:} N)$. The scaled DVM algorithm is at least 97$\%$ faster than the brute-force scale DVM by a vector product. The signal flow graphs of the scaled DVM algorithm are shown to elaborate the simplicity of the proposed algorithm. The proposed lower complexity DVM algorithm can be used to design simple signal flow graph and realize in very large scale integrated circuit architecture with the significant reduction of chip area and power consumption. Moreover, the realization of the faster DVM algorithm through analog integrated circuits will be addressed . Finally, the proposed DVM algorithm will be utilized to obtain a low-complexity approximate transform for beamforming