Spreading Dynamics Research Articles

Teatro San Cassiano in Opera History

The study is devoted to the first publicly accessible opera house Teatro San Cassiano (Venice, 1637), the establishment of which became a cardinal factor in the transformation of opera from aristocratic court entertainment to creative industry. The author considers the issues related to the history of the theater’s construction and the actions of its owners, the Venetian nobles, the Tron brothers, aimed at turning opera into a profitable business. The article reveals possible prototypes and reasons for the constructive solutions in the theater, in particular the boxes and the U-shaped audience hall. The author gives the parametric characteristics of the components of the Teatro San Cassiano building — the stage, the audience hall, and the boxes. It is noted that the tiered Theatro San Cassiano became a prototype for other theatres not only in Venice, but also in other cities of Italy and Europe. Thus, among the Venetian theaters of the 17th century, the public theaters, such as SS Giovanni e Paolo (1638), Novissimo (1640), San Moise (1640), and San Giovanni Crisostomo (1678), were inspired by San Cassiano; outside Venice there were Teatro Falcone (Genoa, 1652) and Teatro Tordinona (Rome, 1671). The article emphasizes market competition that was one of the key factors in the dynamic spread of opera and the formation of opera infrastructure in Europe. After the establishment of San Cassiano, the development of opera acquired a clearly defined vector: from elitist entertainment to creative industry.

Mathematical modeling of the infectious spread and outbreak dynamics of avian influenza with seasonality transmission for chicken farms

A compartmental model with a time-varying contact rate, the seasonality effect, and its corresponding nonautonomous model are investigated. The model is developed based on the six compartments: susceptible, latent, infected, asymptomatic, treated, and recovered individuals. We determine the effective reproduction number for this nonautonomous system, and analytic discussion shows that at least one positive periodic solution exists for R0>1. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. From the numerical results, we observe that the degree of seasonality and vaccine efficacy significantly impact the amplitude of the epidemic curve. The latent-infected phase plane shows that periodic solutions exhibit a period-doubling bifurcation as the amplitude of seasonality increases. Finally, the model outcome was compared with the actual field data and found to be consistent.

A universal rescaling law for the maximum spreading factor of non-Newtonian droplets with power-law fluids

The maximum spreading diameter of non-Newtonian fluid droplets impacting on the solid surface is a key concern in a variety of industrial and medical applications. In this work, we focus on the effect of the shear-thinning, one of the most important non-Newtonian properties, on the spreading dynamics of impacting droplets. A finite element scheme combined with a phase field method and dynamic contact angle model has been employed to perform extensive studies on the spreading process of power-law fluid droplets on solid surfaces with various rheological parameters, impact conditions and surface wettability. The simulation results show that on both hydrophilic and hydrophobic surfaces, impacting droplets exhibit two typical morphologies at the maximum spreading state: a spherical cap in the low-Weber-number range (capillary regime) and a thin-film form in the high-Weber-number range (viscous regime). The maximum spreading factor βmax, of droplets with different degrees of shear-thinning converges to the equilibrium spreading state for a droplet with U0=0 at the low-Weber-number limit. Furthermore, a theoretical relationship of βmax∼We1/2 has been derived in the capillary regime. In contrast, the effect of the shear-thinning property becomes significant in the high-Weber-number regime. We discussed the influence of the power-law coefficients K and n on the spreading process and βmax independently. Specifically, as the power-law index n decreases, the morphology of the shear-thinning droplet at the maximum spreading state tends to change from a spherical cap to a thin-film form. Considering the non-uniform distribution of shear rates in the spreading shear-thinning droplet, a new scaling relationship of βmax∼ln(Ren1/(2n+3)) has been proposed based on theoretical derivation and numerical simulations. By introducing an interpolation function on the scaling relationships between the capillary and viscous regimes, we obtained a universal rescaling model that agrees well with numerical and experimental results of non-Newtonian droplets with shear-thinning fluid over a wide range of We numbers, surface wettability and rheological parameters.

Heavy-tailed distributions of confirmed COVID-19 cases and deaths in spatiotemporal space.

This paper conducts a systematic statistical analysis of the characteristics of the geographical empirical distributions for the numbers of both cumulative and daily confirmed COVID-19 cases and deaths at county, city, and state levels over a time span from January 2020 to June 2022. The mathematical heavy-tailed distributions can be used for fitting the empirical distributions observed in different temporal stages and geographical scales. The estimations of the shape parameter of the tail distributions using the Generalized Pareto Distribution also support the observations of the heavy-tailed distributions. According to the characteristics of the heavy-tailed distributions, the evolution course of the geographical empirical distributions can be divided into three distinct phases, namely the power-law phase, the lognormal phase I, and the lognormal phase II. These three phases could serve as an indicator of the severity degree of the COVID-19 pandemic within an area. The empirical results suggest important intrinsic dynamics of a human infectious virus spread in the human interconnected physical complex network. The findings extend previous empirical studies and could provide more strict constraints for current mathematical and physical modeling studies, such as the SIR model and its variants based on the theory of complex networks.

A Novel Method of Modeling Grassland Wildfire Dynamics Based on Cellular Automata: A Case Study in Inner Mongolia, China

Wildfires spread rapidly and cause considerable ecological and socioeconomic losses. Inner Mongolia is among the regions in China that suffer the most from wildfires. A simple, effective model that uses fewer parameters to simulate wildfire spread is crucial for rapid decision-making. This study presents a region-specific technological process that requires a few meteorological parameters and limited grassland vegetation data to predict fire spreading dynamics in Inner Mongolia, based on cellular automata that emphasize the numeric evaluation of both heat sinks and sources. The proposed method considers a case that occurred in 2021 near the East Ujimqin Banner border between China and Mongolia. Three hypothetical grassland wildfires were developed using GIS technology to test and demonstrate the proposed model. The simulation results suggest that the model agrees well with real-world experience and can facilitate real-time decision-making to enhance the effectiveness of firefighting, fire control, and simulation-based training for firefighters.

Coupled lattice Boltzmann method–discrete element method model for gas–liquid–solid interaction problems

In this paper, we propose a numerical model to simulate gas–liquid–solid interaction problems, coupling the lattice Boltzmann method and discrete element method (LBM–DEM). A cascaded LBM is used to simulate the liquid–gas flow field using a pseudopotential interaction model for describing the liquid–gas multiphase behaviour. A classical DEM resorting to fictitious overlaps between the particles is used to simulate the multiple-solid-particle system. A multiphase fluid–solid two-way coupling algorithm between LBM and DEM is constructed. The model is validated by four benchmarks: (i) single disc sedimentation, (ii) single floating particle on a liquid–gas interface, (iii) sinking of a horizontal cylinder and (iv) self-assembly of three particles on a liquid–gas interface. Our simulations agree well with the numerical results reported in the literature. Our proposed model is further applied to simulate droplet impact on deformable granular porous media at pore scale. The dynamic droplet spreading process, the deformation of the porous media (composed of up to 1277 solid particles) as well as the invasion of the liquid into the pores are well captured, within a wide range of impact Weber number. The droplet spreading dynamics on particles is analysed based on the energy budget, which reveals mechanisms at play, showing the evolution of particle energy, surface energy and viscous dissipation energy. A scaling relation based on the impact Weber number is proposed to describe the maximum spreading ratio.

Comparison of Labor Analgesia Efficacy Between Single-orifice and Multiorifice Wire-reinforced Catheters During Programmed Intermittent Epidural Boluses: A Randomized Controlled Clinical Trial

(Reg Anesth Pain Med. 2023;48:61–66) Programmed intermittent epidural bolus (PIEB) has been used since 2006 for labor analgesia. It is theorized that high-flow epidural catheters may be necessary for proper anesthetic spread dynamics within the epidural space. Epidural catheters have varying characteristics that may affect anesthesia administration. Studies show that multiorifice catheters were proven superior when compared with single-orifice catheters; however, due to flow dynamics, single-orifice catheters may be preferred to close-ended multiorifice catheters due to diffusion distance and area coverage. This study aimed to show a comparison between single-orifice and multiorifice catheters when used for intermittent high-rate bolus administration.

Spreading dynamics of an impulsive reaction-diffusion model with shifting environments

This paper focuses on the effects of environmental improvement and worsening on the spread and invasion of populations with birth pulse. We propose an impulsive reaction-diffusion model with a shifting environment to describe the dynamics of species with distinct reproduction stage and dispersal stage. First, the impulsive reaction-diffusion model is reduced to a discrete-time recursive system defined by a discrete map. Next, with the aid of the appropriate test function and comparison principle, we obtain some sufficient conditions on the nonexistence and uniqueness of nontrivial fixed points of the discrete map. This, combined with the abstract theory of spatially non-translation dynamical systems, enables us to establish the existence of traveling wave solutions and the asymptotic propagation properties of the model.

Wolbachia spread dynamics in mosquito populations in cyclic environments

In this paper, we establish a discrete model with periodic parameters to depict the Wolbachia spread dynamics in mosquito populations in cyclic environments. This work modifies the models established in the existing literature that did not take into account the variation of parameters with environmental periodic changes due to seasonality and other factors. When the parameters in our model are constants, it has been extensively studied and widely used. We present a conjecture about the existence of at most two periodic solutions worthy of further study, and show that the conjecture is true for the special case of 2-periodic parameters. Numerical simulations are also provided to illustrate the occurrence of periodic phenomena.

Spreading speeds of a nonlocal diffusion model with free boundaries in the time almost periodic media

In this paper, we mainly investigate the spreading dynamics of a nonlocal diffusion KPP model with free boundaries which is firstly explored in time almost periodic media. As the spreading occurs, the long-run dynamics are obtained. Especially, when the threshold condition for the kernel function is satisfied, applying the novel positive time almost periodic function, we accurately express the unique asymptotic spreading speed of the free boundary problem.

Experimental investigation on the dynamics of a single water droplet impacting wood surface

The dynamic characteristics of water mist droplets hitting the wood surface is one of the important factors affecting the fire extinguishing performance. However, the spreading dynamics between water droplets and wood surfaces during the impacting process have not been adequately characterized in existing literature. This study experimentally investigates the dynamic process of a single water droplet with changing Weber numbers from 66.7 to 1268.5 impacting different solid wood surface from the perspective of fire suppression. Typical impacting phenomena, the phenomena distribution, the droplet spreading dynamics and the maximum spread factor have been analyzed and discussed. Typical phenomena including no splash, transition from no splash to prompt splash, and prompt splash with varying Weber number are observed for the wood surface. The typical phenomena distribution can be distinguished by lgWe and lgRe and the result shows that lgWe < 2.11, 2.11 < lgWe < 2.42, and lgWe > 2.42 correspond to the phenomena of no splash, transition from no splash to prompt splash and prompt splash respectively. The spreading time can be predicted by the expression of ts/(ρRmax3/σ)0.5=6.52∗We-0.92. By analyzing the maximum spreading factor, the model βmax∝(We/Oh)0.198 is found to present good predictions for wood surfaces.

Wetting mechanisms in the mass transfer process of CuSi3 droplets on the TC4 and 304SS multi-metal system controlled by the hybrid shielding gas atmosphere

To explore the synergistic wettability of the Ti-Cu-Fe multi-metal system, the wetting behaviors of CuSi3 droplets on the TC4 and 304SS plates during the cold metal transfer welding process in various gas atmospheres were studied in this work. The effects of Ti, Fe, Si, C, and O on the spreading dynamics of liquid Cu were analyzed in detail. The results reveal that the CO2 + Ar hybrid gas shielding atmosphere significantly affects the interfacial mass transfer. The sufficient interfacial reaction and increased element diffusion promoted the formation of Ti2Cu/TiCu multiphase microstructure at the Cu/Ti interface instead of a continuous Ti2Cu layer, and a thicker and loose Fe (s, s) layer was formed at the Cu/Fe interface. The variations of surface phase composition and the generation of inward flow weakened the wettability of CuSi3/TC4 and CuSi3/304SS systems. The dissolution of Si and surface adsorption of O decreased the σlv of liquid Cu, whereas Ti and Fe had the opposite effect. When the shielding gas changed from pure Ar to CO2 + Ar hybrid gas, the potential spreading model of the CuSi3/TC4 system changed from reaction-limited to diffusion-limited, and the wetting activation energy increased from 46 kJ/mol to 57 kJ/mol. Removing oxide film, forming Ti2Cu and diffusion of Ti controlled the wetting. Whereas for the CuSi3/304SS system, the potential spreading model changed from diffusion-limited to a molecular dynamics model. Removing oxide film, diffusion of Fe and interfacial adsorption were the dominant factors for wetting.

Fractional model of HIV transmission on workplace productivity using real data from Indonesia

A mathematical model approach to control the spread of HIV and AIDS is needed to predict the future effect of HIV and AIDS on work productivity. In this paper, we consider the analysis of fractional-order mathematical models of the spread of HIV with productivity in the workplace. First, we estimate the epidemiological parameters of the HIV/AIDS model using the annual data of AIDS reported in Indonesia from 2006 to 2018. Based on the model analysis, two equilibria are determined, namely the HIV disease-free and endemic equilibrium’s. The disease-free equilibrium of HIV is locally asymptotically stable if the basic reproduction number is less than one, while the endemic equilibrium is globally asymptotically stable if the reproduction number is greater than one. The sensitivity analysis and numerical simulations are then carried out with variations in fractional order values to determine the dynamics of HIV spread with on-site productivity. Based on numerical simulation results, it was found that the transition rate of HIV-productive workers to AIDS sufferers could reduce the labor population of people living with AIDS and increase the workforce population vulnerable to HIV infection.

Fluid Mechanics of Droplet Spreading of Chitosan/PVA-Based Spray Coating Solution on Banana Peels with Different Wettability.

The spreading behavior of a coating solution is an important factor in determining the effectiveness of spraying applications. It determines how evenly the droplets spread on the substrate surface and how quickly they form a uniform film. Fluid mechanics principles govern it, including surface tension, viscosity, and the interaction between the liquid and the solid surface. In our previous work, chitosan (CS) film properties were successfully modified by blending with polyvinyl alcohol (PVA). It was shown that the mechanical strength of the composite film was significantly improved compared to the virgin CS. Here we propose to study the spreading behavior of CS/PVA solution on fresh bananas. The events upon droplet impact were captured using a high-speed camera, allowing the identification of outcomes as a function of velocity at different surface wettabilities (wetting and non-wetting) on the banana peels. The mathematical model to predict the maximum spreading factor, βmax, was governed by scaling law analysis using fitting experimental data to identify patterns, trends, and relationships between βmax and the independent variables, Weber (We) numbers, and Reynolds (Re) numbers. The results indicate that liquid viscosity and surface properties affect the droplet's impact and spreading behavior. The Ohnesorge (Oh) numbers significantly influenced the spreading dynamics, while the banana's surface wettability minimally influenced spreading. The prediction model reasonably agrees with all the data in the literature since the R2 = 0.958 is a powerful goodness-of-fit indicator for predicting the spreading factor. It scaled with βmax=a+0.04We.Re1/3, where the "a" constants depend on Oh numbers.

An Integrated GIS-Based Reinforcement Learning Approach for Efficient Prediction of Disease Transmission in Aquaculture

This study explores the design and capabilities of a Geographic Information System (GIS) incorporated with an expert knowledge system, tailored for tracking and monitoring the spread of dangerous diseases across a collection of fish farms. Specifically targeting the aquacultural regions of Greece, the system captures geographical and climatic data pertinent to these farms. A feature of this system is its ability to calculate disease transmission intervals between individual cages and broader fish farm entities, providing crucial insights into the spread dynamics. These data then act as an entry point to our expert system. To enhance the predictive precision, we employed various machine learning strategies, ultimately focusing on a reinforcement learning (RL) environment. This RL framework, enhanced by the Multi-Armed Bandit (MAB) technique, stands out as a powerful mechanism for effectively managing the flow of virus transmissions within farms. Empirical tests highlight the efficiency of the MAB approach, which, in direct comparisons, consistently outperformed other algorithmic options, achieving an impressive accuracy rate of 96%. Looking ahead to future work, we plan to integrate buffer techniques and delve deeper into advanced RL models to enhance our current system. The results set the stage for future research in predictive modeling within aquaculture health management, and we aim to extend our research even further.

Photovoltaic Energy Generation in Hungary: Potentials of Green Hydrogen Production by PEM Technology

The dynamic spread of photovoltaic power plants in the global energy industry facilitates cost-effective and clean electricity generation. However, the intermittent nature of solar energy poses an increasing challenge from a system management point of view due to the fast-growing capacities. As a consequence, energy storage systems are increasingly important in this area, as they allow the efficient and flexible storage of excess electricity generated in the electricity system. Among various energy storage systems, the power-to-gas technology is becoming more and more important in the integration of weather-dependent renewable energy sources, as it can now provide an effective solution for increasing grid stability and scheduling efficiency, as well as enabling wide variety of application possibilities in the economy, for example in transport, industry or heating systems. The aim of the present research was to determine the potential amount of green hydrogen that can be produced by using the proton-exchange membrane technology, taking into account the climatic conditions in Hungary and the energy production potentials of photovoltaic power plants of given capacities. This is not only novel but also of practical use, as it provides important information about the integration of photovoltaic power plants and the power-to-gas technology to the actors of energy systems and the energy market and the decision-makers concerned. In addition to the vital economic aspects of the research, supporting the decisions of potential investors, it also contains important insights for market-related technological developments.

Insight into the invasion process and immune-protective evaluation of Tp0971, a membrane lipoprotein from Treponema pallidum.

Treponema pallidum (T. pallidum), the pathogen of syphilis, can invade organisms through mucous membranes or broken skin and proliferate in the host. It spreads rapidly and causes chronic systemic multi-organ damage. Currently, the invasion and pathogenesis of T. pallidum remain a mystery. In this study, we established a T. pallidum infection model in New Zealand rabbits, and the T. pallidum burden in various tissues and organs was detected to investigate the dynamic spread of T. pallidum in different organs. Our results indicated that the T. pallidum burden in rabbits was in a cyclic and repeated dynamic process of decreasing and increasing after infection. In addition, the localization of lipoprotein Tp0971 was confirmed by using the gel microdroplet method. We found that Tp0971 might be a membrane lipoprotein that exists in the inner and outer membranes of T. pallidum. The immune-protective effect of the T. pallidum infection-dependent antigen Tp0971 was evaluated. Tp0971/CpG can induce high levels of Tp0971-specific antibodies, delay skin damage, and promote healing at the infected sites of T. pallidum in New Zealand rabbits. This indicated that Tp0971 may serve as a vaccine antigen candidate. Our results provide new ideas for future research on the proliferation, spread mechanism, and vaccine development of T. pallidum. IMPORTANCE The past two decades have seen a worldwide resurgence in infections caused by Treponema pallidum (T. pallidum) subsp. pallidum, the syphilis spirochete. The well-recognized capacity of the syphilis spirochete for early dissemination and immune evasion has earned it the designation "the stealth pathogen." There are many hurdles to studying syphilis pathogenesis, most notably the difficulty of culturing and genetically manipulating T. pallidum, as well as the absence of an effective vaccine for T. pallidum prevention. T. pallidum infection in humans is a complex and lengthy process. In this study, we investigated the invasion process and the function of the infection-dependent antigen Tp0971 as an immunogen to inhibit the dissemination of T. pallidum in an animal infection model. This enables a better understanding of the specific pathogenic mechanism of this pathogen, syphilis pathogenesis, and vaccine research.

Enhancement of flame spread and droplet dynamics behavior of biodiesel constituents with ethanol and MWCNT-OH additions

The interactive droplet combustion between three adjacent droplets of biodiesel constituents was investigated to obtain flame spread and droplet dynamics behavior enhancement with ethanol and hydroxyl-functionalized multi-walled carbon nanotubes (MWCNT-OH) additives. The experiment was conducted at atmospheric pressure and under normal gravity using spatial and temporal tracking. This study found that ethanol effectively increases flame spread velocity and shortens droplet heating time at a close droplet distance. Meanwhile, MWCNT-OH shortens flame spread induction time at a large droplet distance when thermal conduction time mainly controls the flame spread. Both additives improve the volatility and thermal conductivity of fuel blends, extending the flame spread limit distance with strong reciprocal interaction between droplets and accelerating combustion with a higher burning rate. Different flame spread mechanisms were observed and determined by the fuel additives. Child droplet ejection and microburst flame encourage rapid ignition and flame spread to the next unburned droplet. The puffing and microexplosion mechanisms of the fuel blends were determined by the nucleation type preceding the child droplet ejection. Combining ethanol and MWCNT-OH as fuel additives is the most effective way to improve combustion and flame spread performance because ethanol induces nanoparticle burns at the earlier combustion stage.

Sharp asymptotic profile of the solution to a West Nile virus model with free boundary

AbstractWe consider the long-time behaviour of a West Nile virus (WNv) model consisting of a reaction–diffusion system with free boundaries. Such a model describes the spreading of WNv with the free boundary representing the expanding front of the infected region, which is a time-dependent interval $[g(t), h(t)]$ in the model (Lin and Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary. J. Math. Biol. 75, 1381–1409, 2017). The asymptotic spreading speed of the front has been determined in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019) by making use of the associated semi-wave solution, namely $\lim _{t\to \infty } h(t)/t=\lim _{t\to \infty }[\!-g(t)/t]=c_\nu$ , with $c_\nu$ the speed of the semi-wave solution. In this paper, by employing new techniques, we significantly improve the estimate in Wang et al. (Spreading speed for a West Nile virus model with free boundary. J. Math. Biol. 79, 433–466, 2019): we show that $h(t)-c_\nu t$ and $g(t)+c_\nu t$ converge to some constants as $t\to \infty$ , and the solution of the model converges to the semi-wave solution. The results also apply to a wide class of analogous Ross–MacDonold epidemic models.

OTFS-IM Modulation Based on Four-Dimensional Spherical Code in Air-to-Ground Communication

Unmanned aerial vehicles (UAVs) have been widely utilized for their various advantages. However, UAVs exhibit high mobility and energy storage restrictions in some applications, which can compromise the quality and reliability of communication links. This is a challenge that future aircraft and low-orbit aircraft will inevitably encounter. To effectively address the issue of dynamic Doppler spread in air-to-ground communication, this paper creatively introduces four-dimensional spherical code modulation into the orthogonal time–frequency space with an index modulation (OTFS-IM) system. The fundamental concept of the four-dimensional spherical code is elaborated in detail. Multiple resource symbols can be jointly used to increase the modulation dimension, thereby achieving a larger minimum Euclidean distance between constellation points. Furthermore, detailed analysis is conducted on the bit error rate (BER) and the peak-to-average-power ratio (PAPR) expressions of the proposed system to evaluate its performance and provide theoretical guidance. The proposed scheme not only adapts well to high-speed scenarios but also achieves better power consumption efficiency. The simulation results demonstrate that our proposed scheme outperforms conventional methods. Its robustness and generalization ability are also validated.