Diffusive Model Research Articles

The effect of anxiety and its interplay with social cues when perceiving aggressive behaviours.

Contextual cues and emotional states carry expectations and biases that are used to attribute meaning to what we see. In addition, emotional states, such as anxiety, shape our visual systems, increasing overall, and particularly threat-related, sensitivity. It remains unclear, however, how anxiety interacts with additional cues when categorising sensory input. This is especially important in social scenarios where ambiguous gestures are commonplace, thus requiring the integration of cues for a proper interpretation. To this end, we decided to assess how states of anxiety might bias the perception of potentially aggressive social interactions, and how external cues are incorporated in this process. Participants (N = 71) were tasked with signalling the presence of aggression in ambiguous social interactions. Simultaneously, an observer (facial expression) reacted (by showing an emotional expression) to this interaction. Importantly, participants performed this task under safety and threat of shock conditions. Decision measures and eye-tracking data were collected. Our results showed that threat of shock did not affect sensitivity nor criterion when detecting aggressive interactions. The same pattern was observed for response times. Drift diffusion modelling analysis, however, suggested quicker evidence accumulation when under threat. Finally, dwell times over the observer were higher when under threat, indicating a possible association between anxiety states and a bias towards potentially threat-related indicators. Future probing into this topic remains a necessity to better explain the current findings.

Electronic interfacial thermal conductance between metal nano-films in sub-picosecond non-equilibrium transport process

Interfaces play a critical role in nanoscale thermal transport, and understanding thermal transport mechanisms across metal/metal interfaces at the non-equilibrium states is urgently needed for highly integrated electronic structures or devices. In this work, the electronic interfacial thermal conductance hee of two metal interfaces, Au/Pt and Au/Al, was measured by time domain thermoreflectance (TDTR) at the non-equilibrium states and an extended two-temperature model was applied to well describe the interactions of electrons between the metal films. For the Au/Pt structure, the measured hee is 4.4 ± 1.8 GWm−2K−1, which is consistent with the predicted value by the electronic diffuse mismatch model (DMM). While for the Au/Al structure, the measured hee (0.13±0.05 GWm−2K−1) is an order of magnitude smaller than that of Au/Pt and the predicted value of the electronic DMM. The results indicate that even the extremely thin oxide layer at the Au/Al interface can significantly hinder the electron thermal transport across the metal interface. Overall, our findings contribute to revealing the non-equilibrium interfacial thermal transport mechanisms and pave the way for designing the highly integrated electronic devices.

Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow

Abstract The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative entropy methods, which have recently proven to be a powerful tool in interface evolution problems. With the same relative entropy, we prove a weak–strong uniqueness result, which relies on the construction of gradient flow calibrations for our anisotropic energy functionals.

Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model

Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model

Analysis of a diffusive two-strain malaria model with the carrying capacity of the environment for mosquitoes

We propose a malaria model involving the sensitive and resistant strains, which is described by reaction-diffusion equations. The model reflects the scenario that the vector and host populations disperse with distinct diffusion rates, susceptible individuals or vectors cannot be infected by both strains simultaneously, and the vector population satisfies the logistic growth. Our main purpose is to get a threshold type result on the model, especially the interaction effect of the two strains in the presence of spatial structure. To solve this issue, the basic reproduction number (BRN) R0i and invasion reproduction number (IRN) Rˆ0i of each strain (i = 1 and 2 are for the sensitive and resistant strains, respectively) are defined. Furthermore, we investigate the influence of the diffusion rates of populations and vectors on BRNs and IRNs.

Physics-informed neural network for diffusive wave model

The diffusive wave model (DWM), a nonlinear second-order simplified form of the shallow water equation, has been widely used in hydraulic, hydrologic and irrigation engineering. Solution of the forward problem of the DWM can be utilized to predict evolution in water levels and discharge. Solution of its inverse problem allows for the identification of crucial parameters (such as Manning coefficient, rainfall intensity, etc.) based on observations. This paper applied the physics-informed neural network (PINN) with novel improvements to solve the DWM for both forward and inverse problems. In the forward problem, compared to traditional numerical methods, PINN was able to predict the evolution at any location. In the inverse problem, PINN provided a simple and efficient solution process. In order to overcome the gradient explosion in the training process caused by the characteristics of the DWM, the stop-gradient technique was adopted to train the neural network. To improve the estimation of DWM parameters, the concept of time division was developed, and a new network structure was proposed. To verify the effectiveness of PINN and its improved algorithm for DWM, seven examples were simulated. The PINN solutions for forward problems were compared with the results obtained by classical numerical methods, while the correct rainfall pattern was identified for the inverse problem.

A diffuse interface model of tumour evolution under a finite elastic confinement

Diffuse interface models have gained a growing interest in cancer research for their ability to investigate the mechano-biological features during tumour progression and to provide simulation tools for personalised anti-cancer strategies at an affordable computational cost. Here we propose a diffuse interface model for tumour evolution which accounts for an interfacial structure mimicking a finite elastic confinement at the tumour boundary, possibly due either to a localised elastic stress induced by host tissue displacements, or collagen remodelling in the peritumoural area. This model consists of a partial differential equation of the Cahn–Hilliard type, with degenerate mobility, single-well potential, and an elastic non-local term acting as the effect of a membrane confinement in the chemical potential. Using mixture theory, we derive the corresponding governing equations from thermodynamic principles based on realistic physical and biological assumptions. First, we introduce a suitable regularised problem in order to deal with the degeneracy set of the mobility and the singularity of the potential. For this problem we find a weak solution and provide a regularity result. Then, we establish suitable a priori estimates which are uniform with respect to the regularisation parameters. Passing to the limit in the regularised problem, we prove existence results for different classes of weak solutions to the original problem. Finally, we propose a continuous Galerkin Finite-Element discretisation of the problem, where the positivity of the discrete solution is enforced through a variational inequality. Numerical simulations in a two-dimensional domain are also discussed in three test cases for illustrative purposes.

A risk-induced dispersal strategy of the infected population for a disease-free state in the SIS epidemic model

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy.

Equation-of-state-based lattice Boltzmann model of multicomponent adsorption onto fluid–fluid interfaces

In diffuse interface models, such as the lattice Boltzmann method (LBM), interfacial physics plays an important role. An example of an important interfacial phenomenon is adsorption onto a fluid–fluid interface. In the context of LBM, adsorption studies have traditionally only focused on adsorption onto a solid surface. The studies on adsorption onto fluid–fluid interfaces have been qualitative in nature, suffer from restrictions on the number of components, or are based on simple thermodynamic models designed for fully immiscible phases. Our recently published fugacity-based LBM model introduces a platform for the accurate modeling of multiphase fluids unrestricted by the number of components, and governed through accurate equations of state (Soomro and Ayala, 2023). In this study, we utilize the fugacity-based LBM to capture interfacial adsorption. This paper begins by simulating adsorption in a binary system with a flat interface, and shows that the amount of adsorption, quantified by relative adsorption measures, is in exact agreement with Gibbs theory. Next, the analysis is continued for a ternary system with two species adsorbing onto the interface. The binary and ternary simulations are then repeated for the case of a droplet and finally a five component case is presented. The study shows that the fugacity-based LBM can capture adsorption in full agreement with Gibbs adsorption theory. This provides a path for a generalized LBM model for adsorption, based on robust thermodynamic models for the fluids and unrestricted by the number of components, marking a significant contribution to the LBM literature.

Petrologically controlled oxygen isotopic classification of cogenetic magmatic and metamorphic sapphire from Quaternary volcanic fields in the Eifel, Germany

Gem sapphire is commonly retrieved from primary and secondary deposits associated with alkali basaltic fields, but its source rocks are rarely preserved. The Eifel (Rhenish Massif, western Germany), although not producing gem sapphire, shares many petrologic and geochemical similarities with such fields worldwide. Due to the young age of volcanic deposits and active quarrying, sapphire-bearing rocks are readily accessible, along with detrital sapphire from modern sediments. Here, oxygen isotope and trace element compositions are reported for 223 sapphire grains, and rutile and zircon inclusions in sapphire were dated indicating crystallization synchronous with Paleogene–Quaternary volcanism. Endmembers in δ18O range are sapphires from syenites representing mantle-derived differentiated melts with minor crustal contamination (~4–6‰) and contact metamorphic mica schists (>10‰) as purely crustal source rocks. Intermediate values between ~6 and 10‰ require variable degrees of mantle-crust hybridization. Lower crustal granulite sources are dismissed based on their oxygen isotopic compositions being lower than most sapphire crystals. Diffusion modelling of sharp oxygen isotopic zonation in compositionally zoned crystals precludes crystal residence at >900 °C over the lifetime of evolved magma reservoirs in the Eifel (c. 50 ka). This argues against direct mantle or lower crustal sapphire origins. Instead, low temperature residence is consistent with sharp δ18O gradients, coexisting andalusite, and fluid inclusion barometry. Hence, Eifel sapphire crystallization is attributed to contact metamorphic aureoles around upper crustal (5–7 km) magma bodies where phonolite, trachyte, and carbonatite melts differentiated from mafic parental magmas, and reacted with metasedimentary wall rocks.

A one-dimensional diffusive transport model to evaluate H2S generation in salt caverns hydrogen storage sites

Salt caverns are considered a potential hydrogen storage site given the ductility, tightness, and chemical inertness of halite. In addition, unlike porous media, salt caverns require less cushion gas and allow more cycles of injection and production within a year. However, hydrogen is an electron donor for many hydrogenotrophic microorganisms including halophilic sulfate-reducing microbes (SRM) and hydrogen sulfide (H2S) can be generated in a cavern once sulfate and hydrogen become available in the aqueous phase. As salt deposits are often associated with large amounts of impurities such as anhydrite and gypsum, their dissolution during the leaching phase can release the required sulfate ions for SRMs to produce H2S once hydrogen diffuses and dissolves in the brine at the bottom of the cavern. In this study, a one-dimensional diffusive transport model was developed using PHREEQC to simulate sulfate reduction and H2S generation in a cavern at the gas-brine interface. The solution of Fick's diffusion equation was used to calculate the hydrogen concentration at each level of the 1D model while the kinetic rates of reactions were derived from reported experimental and field site observations of brine samples taken from salt caverns. The results obtained indicated that hydrogen consumption at the gas-brine interface can trigger H2S and methane formations. This is followed by a reduction in sulfate and carbonate concentration and a slight increase in pH due to the reduction of protons in the solution. It was also observed that the presence of Fe2+ ions can reduce the amount of the hydrogen sulfide production while Ca2+ ions slightly favour sulfate reduction due to the production of methane. Although the kinetic reaction rate of the reactions in the model is subject to a certain degree of uncertainty, the workflow and results this study can serve as a guide for the future storage of hydrogen in salt caverns.

Effect of crustal stress state on magmatic stalling and ascent: case study from Puyehue-Cordón Caulle, Chile

The Southern Volcanic Zone (SVZ) in Chile is an active continental arc with a complex history of volcanism, where a range of magmatic compositions have been erupted in a variety of styles. In the Central SVZ, both monogenetic and polygenetic volcanoes exist, in close proximity to the Liquiñe-Ofqui Fault System (LOFS), but with variable local stress states. Previous studies have inferred varying crustal storage timescales, controlled by the orientation of volcanic centres relative to the N-S striking LOFS and σHMax in this region. To assess the relationship between volcanism and crustal stress states affected by large-scale tectonic structures and edifice controls, we present whole rock geochemical data, to ensure consistency in source dynamics and crustal processing, mineral-specific compositional data, thermobarometry, and Fe–Mg diffusion modelling in olivine crystals from mafic lavas, to assess ascent timescales, from the stratovolcanic edifice of Puyehue-Cordón Caulle and proximal small eruptive centres. Textural observations highlight differences in crystal maturation timescales between centres in inferred compression, transpression, and extension, yet source melting dynamics remain constant. Only samples from the stratovolcanic edifice (in regional compression) preserve extensive zonation in olivine macrocrysts; these textures are generally absent from proximal small eruptive centres in transtension or extension. The zonation in olivines from stratovolcanic lavas yields timescales on the order of a few days to a few weeks, suggesting that even in environments which inhibit ascent, timescales between unrest and eruption of mafic magmas may be short. Significantly, high-resolution compositional profiles from olivine grains in the studied samples record evidence for post-eruptive growth and diffusion, highlighting the importance of careful interpretation of diffusion timescales from zoned minerals in more slowly cooled lavas when compared with tephra samples.

Impact of temperature variations on BISON predictions of Ag release in AGR-1 and AGR-2 experiments

Understanding and quantifying the release of fission products like silver (Ag) from TRistructural ISOtropic (TRISO) fuel particles is important to assess the safe operation of advanced high temperature reactors. Although the silicon carbide (SiC) layer of TRISO particles is effective as the main fission product barrier, Ag can be released from intact TRISO particles. A mechanistic model for the effective Ag diffusivity, Deff, was previously developed as a function of temperature and microstructure variables informed by atomistic modeling of Ag diffusivity. In this study, we use this model to explore how experimental temperature uncertainties impact the overall predicted Ag release. This analysis indicates that calculated temperature uncertainties have a significant impact on the overall Ag release predictions. Furthermore, we show that the time average volume average (TAVA) temperature is not an appropriate proxy for the detailed temperature histories to predict fission product release due to the Arrhenius dependence of Ag diffusivity with respect to temperature. The detailed temperature histories, therefore, provide the most accurate results and are of most importance for modeling efforts. Overall, this work shows the importance of considering the experimental uncertainty of the temperature on computational predictions of fission product transport and release and the need for more accurate temperature histories from future experiments.

Optimal distributed control for a Cahn-Hilliard-Darcy system with mass sources, unmatched viscosities and singular potential

We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the averaged velocity u as well as homogeneous Neumann boundary conditions for the phase function ϕ and the chemical potential µ. The source term in the convective Cahn-Hilliard equation contains a control R that can be thought as a drug or a nutrient in applications. Our goal is to study a distributed optimal control problem in the two-dimensional setting with a cost functional of tracking-type. In the physically relevant case with unmatched viscosities for the binary fluid mixtures and a singular potential, we first prove the existence and uniqueness of a global strong solution with ϕ being strictly separated from the pure phases ±1. This well-posedness result enables us to characterize the control-to-state mapping S: R→ϕ. Then we obtain the existence of an optimal control, the Frechet differentiability of S and first-order necessary optimality conditions expressed through a suitable variational inequality for the adjoint variables. Finally, we prove the differentiability of the control-to-costate operator and establish a second-order sufficient condition for the strict local optimality.

On how structures convey non-diffusive turbulence spreading

We report on comprehensive experimental studies of turbulence spreading in edge plasmas. These studies demonstrate the relation of turbulence spreading and entrainment to intermittent convective density fluctuation events or bursts (i.e. blobs and holes). The non-diffusive character of turbulence spreading is thus elucidated. The turbulence spreading velocity (or mean jet velocity) manifests a linear correlation with the skewness of density fluctuations, and increases with the auto-correlation time of density fluctuations. Turbulence spreading by positive density fluctuations is outward, while spreading by negative density fluctuations is inward. The degree of symmetry breaking between outward propagating blobs and inward propagating holes increases with the amplitude of density fluctuations. Thus, blob-hole asymmetry emerges as crucial to turbulence spreading. These results highlight the important role of intermittent convective events in conveying the spreading of turbulence, and constitute a fundamental challenge to existing diffusive models of spreading.

Visual Impairment in Pre-Clinical Models of Mild Traumatic Brain Injury.

Impairment in visual function is common after traumatic brain injury (TBI) in the clinical setting, a phenomenon that translates to pre-clinical animal models as well. In Morris et al. (2021), we reported histological changes following weight-drop-induced TBI in a rodent model including retinal ganglion cell (RGC) loss, decreased electroretinogram (ERG) evoked potential, optic nerve diameter reduction, induced inflammation and gliosis, and loss of myelin accompanied by markedly impaired visual acuity. In this review, we will describe several pre-clinical TBI models that result in injuries to the visual system, indicating that visual function may be impaired following brain injury induced by a number of different injury modalities. This underscores the importance of understanding the role of the visual system and the potential detrimental sequelae to this sensory modality post-TBI. Given that most commonly employed behavioral tests such as the Elevated Plus Maze and Morris Water Maze rely on an intact visual system, interpretation of functional deficits in diffuse models may be confounded by off- target effects on the visual system.

Experimental study on moisture diffusivity, activation energy, and mathematical modeling of drying kohlrabi under different solar drying methods

AbstractThe assessment and enhancement of any drying system for optimal drying processes relies on critical parameters, namely moisture diffusivity and activation energy. In this study, medicinally beneficial kohlrabi of 40‐mm diameter and 6‐mm thickness samples were dried under three different drying methods, namely open sun drying (OSD), natural air‐circulation mode (NACM) single slope direct solar dryer (SSDSD), and forced air‐circulation mode (FACM) SSDSD. The experimental results showed that the drying chamber operating temperature and air velocity played significant roles in the moisture diffusion process and activation energy required to dry the kohlrabi sample. The FACM exhibited the highest average moisture diffusivity values at 7.29 × 10−10 m2/s, surpassing both NACM (5.65 × 10−10 m2/s) and OSD (3.28 × 10−10 m2/s). The activation energy needed for the drying process was the lowest in FACM at 27.44 kJ/mol, followed by NACM at 31.37 kJ/mol and OSD at 35.29 kJ/mol. This is due to the uniform temperature distribution and high airflow rate in the case of FACM. Additionally, 10 thin‐layer models were tested for all three experimental conditions. The statistical analysis showed that for OSD and NACM, the Midilli et al. model, and for FACM, the Page model was best suited for representing drying kinetics with lowest χ2 and root mean square error and highest R2 values. Furthermore, the energy and exergy assessment guaranteed an evaluation of the solar drying system's efficiency.Practical applicationsThis research provides valuable insights into optimizing solar drying methods for kohlrabi preservation. Understanding how temperature and air velocity influence moisture diffusivity and activation energy allows practitioners to enhance drying efficiency. Forced air‐circulation mode (FACM) single slope direct solar dryer (SSDSD) emerges superior, with higher moisture diffusivity and lower activation energy. The study also identifies appropriate drying kinetics models for each method, aiding the accurate prediction of drying behavior. Emphasizing efficiency, the research highlights FACM's superior thermal efficiency and natural air‐circulation mode's higher exergetic efficiency. These insights empower practitioners to make informed decisions, potentially improving agricultural product preservation, reducing energy consumption, and promoting sustainability. Moreover, the research's findings hold significant implications for industrial food processing and preservation applications, suggesting the direct implementation of optimized solar drying techniques in large‐scale settings for kohlrabi and similar agricultural products.

Research on the fiber intensity modulation model of superconducting magnetic levitation rotor.

The measurement of the pole axis deviation angle of superconducting magnetic levitation rotors plays a crucial role in the field of high-precision navigation. This article conducts theoretical analysis and experimental research on the diffuse reflection intensity modulation principle of optical fiber sensors and the ideal diffuse reflection modulation model under ideal conditions. First, the structural distribution of optical fiber sensors is presented, and the principle of measuring the polar deviation angle of superconducting magnetic levitation rotors is analyzed. Then, based on the diffuse reflection intensity modulation principle, an optical fiber intensity modulation model for ideal superconducting magnetic levitation rotors is established. The correctness of this model was verified through simulation and calibration experiments, and the error between the simulation and experimental results was less than 8%.

A unified two-scale gas–liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales

In this contribution, we derive a gas–liquid two-scale multi-fluid model with capillarity effects to enable a novel interface regularization approach for multi-fluid models. As this unified modelling is capable of switching from the interface representation of a separated to a disperse regime it lays a new way of modelling regime transitions as it occurs in atomization processes. Above a preset length threshold at large scale, a multi-fluid diffuse interface model resolves the dynamics of the interface while, at small-scale, a set of geometric variables is used to characterize the interface geometry. These variables result from a reduced-order modelling of the small-scale kinetic equation that describes a collection of liquid inclusions. The flow model can be viewed as a two-phase two-scale mixture, and the equations of motion are obtained thanks to the Hamilton’s Stationary Action Principle, which requires to specify the kinetic and potential energies at play. We particularly focus on modelling the effects of capillarity on the mixture’s energy by including dependencies on additional variables accounting for the interface’s geometry at both scales. The regularization of the large-scale interface is then introduced as a local and dissipative process. The local curvature is limited via a relaxation towards a modified Laplace equilibrium such that an inter-scale mass transfer is triggered when the mean curvature is too high. We propose an original numerical method and assess the properties and potential of the modelling strategy on the relevant test-case of a two-dimensional liquid column in a compressible gas flow.

A robust multiplicity result in a generalized diffusive predator-prey model

A robust multiplicity result in a generalized diffusive predator-prey model