Diffusive Model Research Articles

Hybrid control for the prey in a spatial prey-predator model with cooperative hunting and fear effect time lag

In the ecosystem, the chase of the predator with cooperation contributes to fear psychology in the prey, resulting in behavioral changes such as a decrease in the birth rate. We construct a spatially diffusive model with delay to investigate the combined perturbation of these factors. Initially, we establish the existence of positive solutions and examine the stability of steady-state solutions under varying conditions. The bifurcation dynamics of the positive solutions have been analyzed. Turing instability, arising from the random diffusion of the species, generates spatially irregular patterns characterized by patchy distribution of prey and predators in the spatial domain. Hopf bifurcation, resulting from the diffusive rate and delay, contributes to spatially periodic solutions where the number of species will spatially oscillate. The combined influence of diffusion and delay results in the emergence of Turing and Hopf bifurcation phenomena. In this case, the combined effect amplifies the spatially heterogeneous distribution of prey and predator. Our results reveal the heterogeneous behaviors of prey and predator under the coupled influence of cooperation hunting and fear effects. In this paper, we will also study a hybrid control scheme for controlling the generations of Turing patterns and Hopf bifurcation. Our theoretical results and numerical simulations demonstrate that the control scheme can mitigate the negative influence of combined factors and promote the species' stability.

High-temperature-driven degradation analysis and modelling of an industrial gas turbine applicable γ/β NiCoCrAlYRe coating– Part II: Diffusion modelling and experimental validation under isothermal conditions

In a two-part research, the degradation process of a commercially utilised NiCoCrAlYRe coating on an IN738LC substrate was both simulated and experimentally validated. The first part of the study delved into the microstructural characteristics of the overlay coating system and analysed the oxidation and interdiffusion mechanisms. This second part extends the analysis to simulations of the coating degradation at temperatures of 900 °C and 1000 °C.The interdiffusion between the substrate and coating was modelled utilising thermodynamic and kinetic mobility data, while the oxidation aspect was addressed using two different established models from Whittle and Meier et al., along with an adapted approach specifically tailored for MCrAlY overlay coatings devised in this research. The simulation results were validated experimentally for up to 7000 h, with the degradation state evaluated based on the depletion of β-NiAl in the coating.Good agreement was found between simulated and experimental data. The initial coating and substrate microstructures were sufficiently predicted based on thermodynamic data, and the simulations closely matched the observed degradation pattern. The most precise alignment between simulated and experimental β-NiAl depletion was achieved with the newly proposed oxidation modelling approach for MCrAlY systems. While more optimisation is required to accurately predict the precipitation of chromium phases and carbides and to account for interdiffusion-obstructing effects, particularly at 1000 °C, the results demonstrate the potential of thermodynamic-kinetic modelling for estimating the lifespan of MCrAlY systems under diffusion-driven degradation conditions.

The Lambert diffuse reflection model revisited.

The Lambert diffuse reflection model is used widely in computerized prediction of sound in rooms as well as for outdoor scenarios. One seemingly surprising consequence of the model was pointed out by Borish [J. Audio Eng. Soc. 34, 539-545 (1986)]: A diffusely reflecting, non-absorbing wall seems to give a 3 dB stronger reflection than a specularly reflecting wall for a source and receiver along the same plane normal. Similar observations have been made by others, and it is usually commented that the two reflection types distribute the reflected energy in different directions. The aspect of energy conservation does not seem to have been sorted out entirely. It is shown here that the difference between an omnidirectional receiver, like a microphone, and a surface element receiver, which can give the total reflected power, explains the claim. Analytic solutions and numerical evaluations of the well-known integrals for a single infinite wall confirm that energy conservation is indeed maintained and also lead to a spatial distribution of the Lambert reflection strength, which differs substantially from the previously published values. The special case can serve as a useful benchmark test of implementations of diffuse reflections, which follow Lambert's law.

Dynamics of classical solutions of a multi-strain diffusive epidemic model with mass-action transmission mechanism.

We study a diffusive epidemic model and examine the spatial spreading dynamics of a multi-strain infectious disease. In particular, we address the questions of competitive-exclusion or coexistence of the disease's strains. Our results indicate that if one strain has its local reproduction function spatially homogeneous, which either strictly minimizes or maximizes the basic reproduction numbers, then the phenomenon of competitive-exclusion occurs. However, if all the local reproduction functions are spatially heterogeneous, several strains may coexist. In this case, we provide complete information on the large time behavior of classical solutions for the two-strain model when the diffusion rate is uniform within the population and the ratio of the local transmission rates is constant. Particularly, we prove the existence of two critical superimposed functions that serve as threshold values for the ratio of the transmission rates and that of the recovery rates. Furthermore, when the populations' diffusion rates are small, our result on the asymptotic profiles of coexistence endemic equilibria indicate a spatial segregation of infected populations.

Dynamics for a Diffusive Epidemic Model With a Free Boundary: Spreading Speed

ABSTRACTWe study the spreading speed of a diffusive epidemic model proposed by Li et al. [Dynamics for a diffusive epidemic model with a free boundary: spreading‐vanishing dichotomy, Zeitschrift für Angewandte Mathematik und Physik 75 (2024): Article No. 202], where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann condition, respectively. A spreading‐vanishing dichotomy and some sharp criteria were obtained in Li et al. In this paper, when spreading happens, we not only obtain the exact spreading speed of the spreading front described by the right boundary, but derive some sharp estimates on the asymptotical behavior of solution component . Our arguments depend crucially on some detailed understandings for a corresponding semi‐wave problem and a steady‐state problem.

Thermal boundary conductance enhancement of the Si/diamond interface via atomic transition strategy

Developing multi-chip systems introduces significant thermal management challenges, due to dense vertical stacking and interconnections. Specifically, the increased number of interfaces within the heat conduction path of the chips significantly impedes the effective heat transfer. This study utilizes a series of molecular dynamics simulations to explore how the structure and atomic composition at interfaces affect their thermal conduction abilities. This study initially reveals substantial differences in thermal conduction capabilities between Si/Diamond, SiC/Diamond, and Diamond/Diamond interfaces. Further investigations focus on interfaces between different structures of SiC and diamond, clearly identifying the atomic composition and structure at the interface as key factors influencing thermal boundary conductance (TBC). Based on these findings, the study proposes a strategy for atomic transition that involves inserting SiC into the Si/Diamond interface. Under optimal thickness conditions for the SiC transition layer, a significant increase in theoretical TBC is achieved, from 477.1 MW/m²K to 701.1 MW/m²K, which is twice the value predicted by the existing diffusive mismatch model (DMM) for Si/Diamond interfaces. Lastly, through the developed 3D IC model, the study examines the impact of TBC variations on the peak temperature of the entire device, thereby further emphasizing the importance of enhancing interface thermal conduction capabilities. This series provides strategic guidance for thermal management in 3D ICs and offers a theoretical basis for chip design and material selection.

A Diffuse Interface Model for Cavitation, Taking Into Account Capillary Forces

ABSTRACTWe consider the moving least squares method to solve compressible two‐phase water‐water vapor flow with surface tension. A diffuse interface model based on the Navier–Stokes and Korteweg equations is coupled with a suitable system of state equations that allows for a more realistic estimation of the pressure jump across the liquid–vapor interface as a function of temperature. We propose a simple formulation for computing the capillarity coefficient based on the surface tension and the thickness of the diffuse interface. A convergence analysis using pressure jump in the test case of static bubble is conducted to verify our solver. We present several numerical test cases that illustrate the ability of our model to reproduce qualitatively and quantitatively the effects of surface tension on cavitation bubbles in general situations.

Collapse of microbubbles over an elastoplastic wall

The collapse of a vapour bubble over a material surface has been widely studied over the past few decades, but a comprehensive and quantitative analysis of the cavitation dynamics and its effects on solid materials at the mesoscale (nanometre up to micrometre), which would be of particular interest in applications exploiting cavitation power, is still lacking. In this work, we adopt a diffuse interface model to describe the microbubble dynamics, and a dynamic plasticity model for the solid. The former is particularly suited to studying the rich phenomenology characterising bubble collapse at the mesoscale, which comprises transitions to supercritical conditions, emission and propagation of shock waves, generation of liquid microjets and topological transitions, whereas the latter is used to characterise the permanent plastic deformation caused by the bubble collapse, and has been augmented to consider inertial effects, to assess whether or not an interaction between elastic and plastic waves may influence the resulting deformation. Results concerning the collapse of a microbubble at different liquid overpressures and initial standoff ratios are discussed, and the elastoplastic wave propagation in the solid, together with plastic deformation, is studied for different cases, depending on elastic and plastic material parameters.

A diffusive intraguild predation model with variable-carrying capacity proportional to the same biotic resource

A diffusive intraguild predation model with variable-carrying capacity proportional to the same biotic resource

A consistent diffuse-interface model for two-phase flow problems with rapid evaporation

We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several orders of magnitude, leading to high velocity and pressure jumps across the liquid–vapor interface, along with dynamically changing interface topologies. To this end, we integrate an incompressible Navier–Stokes solver combined with a conservative level-set formulation and a regularized, i.e., diffuse, representation of discontinuities into a matrix-free adaptive finite element framework. The achievements are three-fold: First, we propose mathematically consistent definitions for the level-set transport velocity in the diffuse interface region by extrapolating the velocity from the liquid or gas phase. They exhibit superior prediction accuracy for the evaporated mass and the resulting interface dynamics compared to a local velocity evaluation, especially for strongly curved interfaces.Second, we show that accurate prediction of the evaporation-induced pressure jump requires a consistent, namely a reciprocal, density interpolation across the interface, which satisfies local mass conservation. Third, the combination of diffuse interface models for evaporation with standard Stokes-type constitutive relations for viscous flows leads to significant pressure artifacts in the diffuse interface region. To mitigate these, we propose to introduce a correction term for such constitutive model types. Through selected analytical and numerical examples, the aforementioned properties are validated. The presented model promises new insights in simulation-based prediction of melt–vapor interactions in thermal multiphase flows such as in laser-based powder bed fusion of metals.

Temperature‐dependent heat transfer deterioration in ordered graphene/ceramic composites

AbstractBoosting heat transfer of ultrahigh temperature ceramics (UHTCs) with dimensional‐crossover graphene has become an increasing challenge for improving the thermal protective performance of new‐generation spacecraft. Yet its characteristics of anisotropic and high interfacial thermal resistance inevitably cause heat transfer deterioration at high temperatures. Here we develop a few ZrB2/graphene/ZrB2 interface‐dominated diffuse models that are driven by bonding configurations and thermal converger. It has been found that forming stronger bonding configurations by Zr‐C interfacial bonding and designing a preferred thermal converger by ordered graphene are both unarguable ways of suppressing high‐temperature heat transfer deterioration. Each Zr‐C interfacial bonding serves as an independent sluice gate to accelerate heat flow. More high‐frequency phonons are excited at high temperature, which augments the interfacial thermal conductance from 38.5 to 335.4 MW·m−2·K−1 at 700 K. Impressively, a concept of thermal converger inspires us to adopt ordered graphene for changing the diverging behavior in isotropic ZrB2 composites. Its convergent process combines with anisotropic characteristics to transform the isotropic heat flow into the highly ordered graphene. Their thermal conductance can be regulated from minimum (2.5) to maximum (80.8 W·m−1·K−1) by rotating the ordered graphene from 90° to 7.5°. This work paves an optimal way for manipulating the heat transfer of UHTCs.

Drop impact onto wettability-patterned solid surfaces: A phase field approach

Drop impact onto wettability-patterned surfaces is of great significance in industries. Self-propulsion, self-splitting, and directional rebounding can be realized when drops impact on such surfaces. This paper established a diffuse interface/phase field model to delve into drop impact onto wettability-patterned surfaces, with two typical surfaces considered, one having a step change in the contact angle and the other having a smooth change in it. The diffuse interface model used the phase field to track the liquid–gas interface, was discretized on a half-staggered grid, and was run in a parallel manner. The model was validated first against an impact onto a uniform surface and then against an impact onto a hydrophilic surface coated with a superhydrophobic strip. A mesh independence study was conducted for the phase field modeling. Grid independence was achieved while the phase field mobility was kept fixed in meshes of varied resolutions. The major findings are as follows. The spreading of a spherical drop on gradient wettability surfaces resembles that of an ellipsoidal drop on a uniform surface, and axis-switching was observed. On the other hand, directional rebounding on multi-region wettability surfaces is enhanced with increased wettability contrast.

Interdisciplinary insights into the cultural and chronological context of chili pepper (Capsicum annuum var. annuum L.) domestication in Mexico

This study investigates the temporal and spatial factors driving the domestication of Capsicum annuum var. annuum L. in Mexico. This species exhibits the greatest morphological diversity in fruit among Capsicum species-a characteristic that is even more pronounced in contemporary landraces cultivated by indigenous communities. Despite the chili pepper's integral role in regional culinary traditions, its domestication history in this region remains poorly understood, often subject to scholarly interpretations that marginalize or oversimplify archaeological evidence. To address this gap, our interdisciplinary team of archaeologists, botanists, and ecologists combine modern and archaeological Capsicum seed data, diachronic archaeological site locations, and ecological niche modeling to identify potential regions where early human populations and the closest wild ancestors may have coexisted. Our results show spatial correlations between early Capsicum distribution and archaeological site prevalence, suggesting that the beginning of the domestication process occurred in ecologically suitable areas for both wild Capsicum and human settlement. These findings challenge previous hypotheses regarding highland/dry cave domestication regions, as our data indicate that lowland regions-specifically the Yucatán Peninsula and southern coastal Guerrero-were more conducive to early encounters between wild Capsicum and humans. We propose a geographically diffuse and protracted model of chili pepper domestication-driven by a ruderal pathway-which involved at least two asynchronous events across Mexico.

Analysis of a diffusive vector-borne disease model with nonlinear incidence and nonlocal delayed transmission

Analysis of a diffusive vector-borne disease model with nonlinear incidence and nonlocal delayed transmission

Dynamics of a single population model with memory and nonlinear boundary condition

In this paper, a heterogeneous single population model with memory effect and nonlinear boundary condition is investigated. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially nonconstant positive steady state solutions appear from two trivial solutions, respectively. Through the distribution of the eigenvalues and bifurcation analysis, sufficient conditions for the occurrence of the Hopf bifurcation associated with one spatially nonconstant positive steady state are obtained. Results about the stability associated with the other one are also yielded. It is found that with the interaction of memory delay, spatial heterogeneity and nonlinear boundary condition, the Hopf bifurcation will happen in such diffusive model. To be specific, the memory delay could induce a single stability switch from stability to instability. As contrast to the diffusive model only with memory effect, the stability switch is independent of memory delay. The obtained results are applied to some specific models, from which we can find that the theoretical analysis is verified and the results enrich the existing ones.

Diffuse radio sky models using large-scale shapelets

Sky models used in radio interferometric data-processing primarily consist of compact and discrete radio sources. When there is a need to model large-scale diffuse structure such as the Galaxy, specialized source models are sought after for the sake of simplicity and computational efficiency. We propose the use of shapelet basis functions for modeling the large-scale diffuse structure in various radio interferometric data-processing pipelines. The conventional source model construction using shapelet basis functions is restricted to using images of smaller size due to limitations in computational resources such as memory. We propose a novel shapelet decomposition method to lift this restriction, enabling the use of images of millions of pixels (as well as a wide spectral bandwidth) for building models of large-scale diffuse structure. Furthermore, the application of direction-dependent errors onto diffuse sky models is an expensive operation that is often performed as a convolution. We propose using some specific properties of shapelet basis functions to apply these direction-dependent errors as a product of the model coefficients, which avoids the need for convolution. We provide results based on simulations and real observations. In order to measure the efficacy of our proposed method in modeling large-scale diffuse structure, we considered the direction-dependent calibration of simulated as well as real LOFAR observations that have a significant number of diffuse large-scale structure. The results show that by including large-scale shapelet models of the diffuse sky, we are able to overcome a major problem of existing calibration techniques, which do not model this large-scale diffuse structure, that is, the suppression of this large-scale diffuse structure because the model is incomplete.

Complete Dynamics From Ignition to Stabilization of a Lean Hydrogen Flame With Thickened Flame Model

Abstract In recent years, attention has been paid to hydrogen thanks to its carbon-free nature and its interesting characteristics as an energy vector. Despite the large number of numerical analyses regarding hydrocarbon combustion in all the steady and unsteady processes, few papers that cover all those aspects are available in the literature for hydrogen flames. Therefore, a numerical methodology to explore the complete ignition sequence from the spark release to the flame stabilization is validated on a single-sector hydrogen burner. In this context, a preliminary direct numerical simulation (DNS) investigation of laminar spherical expanding flames is performed using different diffusive transport models to isolate their impact. The present work, carried out within the European project HESTIA, investigates the atmospheric test rig installed at the Norwegian University of Science and Technology operating with a lean, perfectly premixed, hydrogen–air flame stabilized on a conical bluff body. Four simulations are performed adopting the thickened flame model with an energy deposition (ED) strategy to assess the impact of preferential and thermal diffusion, as well as grid resolution, on flame dynamics. Three-dimensional (3D) flame structure visualization coupled with detailed particle image velocimetry (PIV)/OH-planar laser induced fluorescence (OH-PLIF) measurements allows the investigation of the key mechanisms involved during the ignition. The dynamic response of the flame through axial fluctuations once the ignition transient is concluded is reconstructed by the numerical strategy employed. Although the overall behavior is almost unchanged by including or not thermal diffusion effects, their local impact on the flame is evident leading to a better agreement with experimental data.

Strategic deployment of hydrogen fuel cell buses and fueling stations: Insights from fleet transition models

Establishing new hydrogen value chains is challenging, requiring economies of scale and balanced supply-demand dynamics. Municipalities can mitigate this risk through government support and deployment strategies. This study analyzes Edmonton's transition to zero-emission buses (ZEBs), focusing on hydrogen fuel cell electric vehicles (HFCEVs) and hydrogen fueling stations (HFSs). Using scenario-based modeling and S-curve models for technology diffusion, we project the adoption of battery electric vehicles (BEVs) and HFCEVs. Deploying over 1000 ZEBs by 2040 is necessary to meet Net-Zero targets, with 310–760 HFCEVs required for the municipal bus inventory. This results in an estimated hydrogen demand of 6.2–14.5 t-H2/day and a reduction of 0.4–1.0 Mt-CO2 in tailpipe emissions by 2050. We use these scenario projections to develop a phased deployment strategy, optimizing fleet operations to reduce HFS costs by 50–60% from 8 to 9 C$/kg-H2 to 3–4 C$/kg-H2. The study underscores the importance of strategic planning and infrastructure investment in realizing net-zero goals, providing a model applicable globally.

The Flattest Infrared Extinction Curve in Four Isolated Dense Molecular Cloud Cores

The extinction curve of interstellar dust in the dense molecular cloud cores is crucial for understanding dust properties, particularly size distribution and composition. We investigate the infrared extinction law in four nearby isolated molecular cloud cores—L429, L483, L673, and L1165—across the 1.2–8.0 μm wavelength range, using deep near-infrared and mid-infrared photometric data from UKIRT Infrared Deep Sky Survey and Spitzer Space Telescope. These observations probe an unprecedented extinction depth, reaching A V ∼ 40–60 mag in these dense cloud cores. We derive color-excess ratios E(K − λ)/E(H − K) by fitting color–color diagrams of (K − λ) versus (H − K), which are subsequently used to calculate the extinction law A λ /A K . Our analysis reveals remarkably similar and exceptionally flat infrared extinction curves for all four cloud cores, exhibiting the most pronounced flattening reported in the literature to date. This flatness is consistent with the presence of large dust grains, suggesting significant grain growth in dense environments. Intriguingly, our findings align closely with the Astrodust model for a diffuse interstellar environment proposed by Hensley and Draine. This agreement between dense core observations and a diffuse medium model highlights the complexity of dust evolution and the need for further investigation into the processes governing dust properties in different interstellar environments.

A diffusive plant-sulphide model: spatio-temporal dynamics contrast between discrete and distributed delay

Abstract This paper studies the spatio-temporal dynamics of a diffusive plant-sulphide model with toxicity delay. More specifically, the effects of discrete delay and distributed delay on the dynamics are explored, respectively. The deep analysis of eigenvalues indicates that both diffusion and delay can induce Hopf bifurcations. The normal form theory is used to set up an exact formula that determines the properties of Hopf bifurcation in a diffusive plant-sulphide model. A sufficiently small discrete delay does not affect the stability and a sufficiently large discrete delay destabilizes the system. Nonetheless, a sufficiently small or large distributed delay does not affect the stability. Both delays cause instability by inducing Hopf bifurcation rather than Turing bifurcation.