Diffusive Model Research Articles

The impulsive vaccination in an SVIS diffusive model

This paper examines a reaction-diffusion problem with impulses, which presents a susceptible-vaccinated-infected-susceptible (SVIS) epidemic model with impulsive vaccination. First, the existence and uniqueness of the global solution and the disease-free periodic solution have been established. Second, by considering the principal eigenvalue, the asymptotic behavior of the disease-free periodic solution and the sufficient condition for the persistence of diseases are given, in addition, the mono-tonicity of the principal eigenvalue is investigated. Third, the periodic state of the endemic disease has been explored when vaccination is not completely effective. Finally, the numerical simulations presented reveal the impacts of the infection rate and impulses, and demonstrate that effective vaccination is a reliable way to control the spread of diseases.

Decision cost hypersensitivity underlies Huntington's disease apathy.

The neuropsychiatric syndrome of apathy is now recognized to be a common and disabling condition in Huntington's disease (HD). However, the mechanisms underlying it are poorly understood. One way to investigate apathy is to utilise a theoretical framework of normal motivated behaviour, to determine where breakdown has occurred in people with this behavioural disruption. A fundamental computation underlying motivated, goal-directed behaviour across species is weighing up the costs and rewards associated with actions. Here, we asked whether people with apathy are more sensitive to costs of actions (physical effort and time delay), less sensitive to rewarding outcomes, or both. Based on the unique anatomical substrates associated with HD pathology, we hypothesised that a general hypersensitivity to costs would underpin HD apathy. Genetically confirmed carriers of the expanded Huntingtin gene (premanifest to mild motor manifest disease (n=53) were compared to healthy controls (n = 38). Participants performed a physical effort-based decision-making task (Apple Gathering Task) and a delay discounting task (Money Choice Questionnaire). Choice data was analysed using linear regression and drift diffusion models that also accounted for the time taken to make decisions. Apathetic people with HD accepted fewer offers overall on the Apple Gathering Task, specifically driven by increased sensitivity to physical effort costs, and not explained by motor severity, mood, cognition, or medication. Drift diffusion modelling provided further evidence of effort hypersensitivity, with apathy associated with a faster drift rate towards rejecting offers as a function of varying effort. Increased delay sensitivity was also associated with apathy, both when analysing raw choice and also drift rate, where there was moderate evidence of HD apathy drifting faster towards the immediately available (low cost) option. Furthermore, the effort and delay sensitivity parameters from these tasks were positively correlated. The results demonstrate a clear mechanism for apathy in HD, cost hypersensitivity, which manifests in both the effort and time costs associated with actions towards rewarding goals. This suggests that HD pathology may cause a domain-general disruption of cost processing, which is distinct to apathy occurrence in other brain disorders, and may require different therapeutic approaches.

Bifurcation analysis of a diffusive radio-dependent model with spatial memory

The cognitive abilities of animals, such as memory, have a significant impact on their movement in space. In this paper, we consider a radio-dependent model with memory-based diffusion under the conditions of Neumann boundary. The stability of a positive equilibrium and the existence of the Turing–Hopf bifurcation induced by memory diffusion and memory delay are carried out in details. Notably, our findings indicate that with a relatively short average memory period, the large memory diffusion can stabilize an otherwise unstable equilibrium. In addition, the third-order truncated normal form for the Turing–Hopf bifurcation restricted to the central manifold is derived, which can reveal the generation of some steady-state and time-periodic solutions with spatial heterogeneity. The coefficients within the normal form are systematically determined through matrix operations, and these results can also be applied to other models with memory diffusion. Ultimately, leveraging the theoretical findings, we elucidated the intricate spatial-temporal dynamics and their associated parameter scopes caused by Turing–Hopf bifurcation through numerical simulations.

Dynamics for a nonlocal diffusive SIR epidemic model with double free boundaries

In this paper, we study an SIR epidemic model with nonlocal diffusion and double free boundaries, which can be used to describe a class of biological phenomena: the depletion of native resources by all individuals, the infected individuals do not lose their fertility completely, the recovered individuals are immune and no longer infected, the infected and recovered individuals spread along the same free boundary. We first investigate the existence and uniqueness of global solution, long time behaviors and some sufficient conditions for spreading and vanishing. Then we estimate the spreading speed and derive that accelerated spreading could happen when the kernel function does not satisfy a threshold condition.

Significant effect of salinity on zinc adsorption on tropical coastal and floodplain soils

AbstractRising sea levels due to climate change are causing increased salinisation of low‐lying coastal and floodplain soils, and the impact of this process on the bioavailability of plant nutrients needs to be understood as mitigation strategies are adapted. Zinc (Zn) is an element of particular importance due to its function as a micronutrient for plants including rice and other staple foods. In the current study, our aim was to investigate the effects of salinisation on zinc adsorption onto soils representing at‐risk coastal and floodplain environments, addressing in particular our knowledge gap concerning the roles that solution chemistry and soil composition play. To this end, we conducted batch adsorption experiments in the laboratory and ran geochemical models in saline solutions up to 0.7 mol L−1 ion strength incorporating both (i) a multi surface model (MSM) for surface reactions containing three phases, that is iron hydroxides, organic matter and phyllosilicate clays, and (ii) aqueous‐phase complexation to dissolved organic and inorganic ligands. Surface reactions were modelled using the diffuse double layer model, the NICA–Donnan model and an ion exchange model using the Gaines–Thomas convention. We combined the experimentally determined mass composition of surface phases with generic modelling parameters taken from the literature. We first show that increasing salinity enhances the formation of aqueous Zn‐chloride complexes in the presence of dissolved organic matter and bicarbonate, thereby decreasing the availability of free Zn2+ and supressing the partitioning of zinc to the adsorbed phase. We demonstrate using batch adsorption experiments with a calcareous hydraquent and a tropaquept, that salinity decreases zinc adsorption strongly in the pH range between 3 and 6. Satisfactory agreement between experiments and model calculations was achieved with root‐mean‐square errors ranging for different salinities between 2.88% and 2.92% for the hydraquent and between 4.59% and 2.74% for the tropaquept soil. Model predictions of adsorption were slightly inferior at low salinity for the hydraquent soil and at high salinity for the tropaquept soil, pointing possibly to an incomplete geochemical model or to a need to parametrise surface adsorption models at higher ionic strengths. Present surface models have been largely parametrised at lower ionic strength. We lastly apply the MSM to examine zinc adsorption in five endoaquepts soils, representing soil series from Bangladesh. We show that increasing salinity decreases zinc adsorption to the soil organic matter and the clay fractions. We conclude from our findings that increased soil salinity due to rising sea levels and climate change will have a significant impact on zinc cycling and possibly other micronutrients in areas where coastal soils and floodplain soils overlap, such as deltas and estuaries. In particular, we predict a decrease in zinc adsorption in acidic to neutral soils. The availability of zinc for biouptake through the roots of crop plants including rice will be significantly disturbed following salinisation, most likely affecting crop production. Our study demonstrates the potential that geochemical modelling combined with experimental data has to improve our capability to assess the effects of salinity due to rising seawater levels in vulnerable regions of the world.

Multiphase modeling of pressure-dependent hydrogen diffusivity in fractal porous structures of acrylonitrile butadiene rubber-carbon black composites with different fillers

The hydrogen diffusivities of acrylonitrile butadiene rubber (NBR) composites with different types and contents of carbon black (CB) fillers were investigated in the exposure pressure range of 0.5–10 MPa using a volumetric analysis system. These measured diffusivities exhibited distinct pressure-dependent behavior. The diffusivities of unfilled NBR and NBR composites containing medium-thermal CB filler decreased from 39.7 × 10−11 m2/s to 9.4 × 10−11 m2/s as the pressure increased. On the other hand, the pressure-dependent diffusivities of NBR composites containing high-abrasion furnace, fast-extrusion furnace and semireinforcing furnace CB fillers revealed left-biased unimodal shaped curves, with peak values ranging from 19.7 × 10−11 m2/s to 5.6 × 10−11 m2/s. To model this observed behavior, the diffusion resistance theory with a heterogeneous NBR–CB composite and a fractal porous structure for H2 was introduced. The theoretical parallel diffusion resistance model was found to coexist independently as the surface, Knudsen, and bulk diffusion phases. This theoretical multiphase modeling was applied to the measured diffusivities, determining diffusion resistance parameters for each phase. The obtained individual parametric characteristics for each diffusion were interpreted by considering the CB filler content and volume fraction of the filler. As a result, the diffusivities calculated by multiphase diffusion modeling were in quite agreement with the measured diffusivities for all investigated specimens, where the determined squared correlation coefficient (R2) by fitting process was in the range from 0.69 to 0.97.

Applicability of calibrated diffuse reflectance spectroscopy models across spatial and temporal boundaries

Diffuse reflectance spectroscopy (DRS) is an emerging soil testing approach. Although several studies have validated the DRS approach, limited efforts are made to assess the applicability of calibrated DRS models on new samples collected at different locations and/or time. To test such spatio-temporal applicability of calibrated DRS models, we collected surface soil samples from 1,112 smallholder farms during 2018 (T2018) and 607 farms during 2021 (T2021) covering seven districts of the Bundelkhand region of central India. The T2018 samples covered 7 development blocks; the T2021 samples were also collected from these blocks but from different sampling locations. Additionally, a new sampling site (Jhansi-Bamour block) was added during 2021 to create an independent test dataset. Collected samples were analysed for 17 soil parameters (basic soil properties, macronutrients, and micronutrients) and spectral reflectance over the visible to near-infrared region. Corresponding soil test crop response (STCR) ratings were also estimated. The Cubist model was calibrated in the T2018 dataset and tested against the T2021 dataset using the coefficient of determination (R2), root-mean-squared error (RMSE), and percentage relative error deviation (PRED) at 30% error threshold as performance statistics. Model applicability was assessed at each block level (site-specific), by dividing the study site into their two geology-specific regions, and by treating the entire dataset as a regional-scale spectral library. Results showed that DRS models calibrated on a finer scale (site-specific) are less efficient in estimating soil parameters in broader scale (geology-specific and regional-scale) test T2021 samples although their STCR ratings may safely be estimated at local scales. When site-specific data were aggregated to broader scales and T2018 dataset was spiked with 20% samples from the T2021 dataset, model performance improved for critical soil parameters such as soil organic carbon (SOC) contents and several plant nutrients and their ratings; application of such large-scale models also improved the estimation accuracy when applied to site-specific datasets. Exchangeable Ca and Mg, clay and SOC contents were frequently well-estimated with R2 values ranging from 0.54 to 0.93. Fine sand was the next best estimated soil property with R2 values in the range of 0.40–0.75. The STCR ratings estimated in the DRS approach matched the wet chemistry-based STCR ratings to the tune of 43 to 100%. Overall, as many as 60% of all new samples could be estimated with more than 70% accuracy for 8 out of 17 parameters. With the DRS approach tested on both spatially- and temporally-independent test datasets and, specifically, with high estimation accuracy of STCR ratings, our results suggest that the DRS approach may safely be used as a viable alternative to conventional soil testing in smallholder farms.

Existence of weak solutions to a Cahn–Hilliard–Biot system

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot’s equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic regularization of Kelvin–Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems.

Improved accuracy of continuum surface flux models for metal additive manufacturing melt pool simulations

Computational modeling of the melt pool dynamics in laser-based powder bed fusion metal additive manufacturing (PBF-LB/M) promises to shed light on fundamental mechanisms of defect generation. These processes are accompanied by rapid evaporation so that the evaporation-induced recoil pressure and cooling arise as major driving forces for fluid dynamics and temperature evolution. The magnitude of these interface fluxes depends exponentially on the melt pool surface temperature, which, therefore, has to be predicted with high accuracy. The present work utilizes a diffuse interface finite element model based on a continuum surface flux (CSF) description of interface fluxes to study dimensionally reduced thermal two-phase problems representative for PBF-LB/M in a finite element framework. It is demonstrated that the extreme temperature gradients combined with the high ratios of material properties between metal and ambient gas lead to significant errors in the interface temperatures and fluxes when classical CSF approaches, along with typical interface thicknesses and discretizations, are applied. It is expected that this finding is also relevant for other types of diffuse interface PBF-LB/M melt pool models. A novel parameter-scaled CSF approach is proposed, which is constructed to yield a smoother temperature field in the diffuse interface region, significantly increasing the solution accuracy. The interface thickness required to predict the temperature field with a given level of accuracy is less restrictive by at least one order of magnitude for the proposed parameter-scaled approach compared to classical CSF, drastically reducing computational costs. Finally, we showcase the general applicability of the parameter-scaled CSF to a 3D simulation of stationary laser melting of PBF-LB/M considering the fully coupled thermo-hydrodynamic multi-phase problem, including phase change.

Olivine Time-Capsules Constrain the Pre-Eruptive History of Holocene Basalts, Mount Meager Volcanic Complex, British Columbia, Canada

Abstract The Canadian segment of the Cascade Volcanic Arc (i.e. the Garibaldi Volcanic Belt) comprises more than 100 eruptive centres, spanning the entire Quaternary period (Pleistocene to Holocene in age), and with deposits ranging in composition from alkaline basalt to rhyolite. At least one of the volcanoes is currently active; Mount Meager / Q̓welq̓welústen erupted explosively 2360 years BP and has ongoing fumarolic activity. Long-term forecasting of eruption frequency and style depends on reconstruction of the history and timescales of magmatic processes preceding previous volcanic eruptions. Utilising diffusion chronometry, we investigate the Mount Meager Volcanic Complex focusing on Holocene olivine-phyric basalts (Lillooet Glacier basalts) exposed by the retreat of the Lillooet Glacier. We identify two distinct olivine populations in samples of quenched, glassy basalt lavas that record different magmatic processes and histories. Glomerocrysts of Fo83 olivine phenocrysts, entrained and transported by a hot mafic input, form Population 1. These exhibit resorption and normally zoned outermost rim compositions of Fo76–78; a third of them also show interior reverse compositional zoning. A second population of skeletal microphenocrysts have the same composition as the phenocryst rims (i.e. Fo76–78) and are in equilibrium with the adjacent matrix glass. We estimate the pre-eruptive temperature-fO2 conditions in a shallow reservoir (100 MPa; ~3 km) for a melt with H2O content of 0.5 to 1 wt % as ~1097°C to 1106°C (± 30°C), and NNO + 0.5 (±1.1), respectively. Using these input parameters, we report Fe-Mg diffusion chronometry results for 234 normally zoned profiles from 81 olivine phenocrysts. Diffusion modelling of compositional profiles in oriented crystals indicates pre-eruptive magmatic residence times of 1 to 3 months. These remarkably short residence times in shallow reservoirs prior to eruption suggest very short periods of unrest may precede future eruptions.

Differential diffusion modelling for LES of premixed and partially premixed flames with presumed FDF

Large eddy simulations (LES) with flamelet and presumed filtered density function closure are used to simulate turbulent premixed and partially premixed hydrogen flames. Different approaches to model differential diffusion are investigated and compared. In particular, two existing models are extended to the LES framework to correct the resolved diffusive flux of the controlling variables due to differential diffusion. A lean premixed turbulent hydrogen flame in a slotted burner configuration is simulated first to compare the capability of the considered models in capturing local mixture fraction redistribution, super-adiabatic temperatures and thermo-diffusive instabilities. Results show that both models describe the formation of cellular burning structures. Next, a partially premixed lifted hydrogen flame in vitiated hot coflow is simulated to gain insight on the relevance of differential diffusion modelling at a higher turbulence level, a different combustion mode and in the presence of a complex stabilisation mechanism. Good predictions of the turbulent mixing and temperature fields are observed. Moreover, results show that the flame lift-off height has an appreciable sensitivity to the differential diffusion model. When differential diffusion is included only in the thermochemistry database, only mild effects on the predicted temperature fields, mixing and flame height are observed. On the contrary, a considerable shift of the flame base is observed when corrections are applied in the LES at the resolved level, depending on what controlling variables are considered. Further analyses reveal how the corrections of diffusive fluxes in the thermochemistry and at the LES level affect differently the flame burning mode, whose details are given throughout the paper.

Error analysis of fully decoupled SAV scheme for two phase magnetohydrodynamic diffuse interface model

Error analysis of fully decoupled SAV scheme for two phase magnetohydrodynamic diffuse interface model

Combination of locoregional radiotherapy with a TIM-3 aptamer improves survival in diffuse midline glioma models.

Pediatric diffuse midline gliomas (DMG) with altered H3-K27M are aggressive brain tumors that arise during childhood. Despite advances in genomic knowledge and the significant number of clinical trials testing new targeted therapies, patient outcomes are still poor. Immune checkpoint blockades with small molecules, such as aptamers, are opening new therapeutic options that represent hope for this orphan disease. Here, we demonstrated that a TIM-3 aptamer (TIM-3 Apt) as monotherapy increased the immune infiltration and elicited a strong specific immune response with a tendency to improve the overall survival of treated DMG-bearing mice. Importantly, combining TIM-3 Apt with radiotherapy increased the overall median survival and led to long-term survivor mice in 2 pediatric DMG orthotopic murine models. Interestingly, TIM-3 Apt administration increased the number of myeloid populations and the proinflammatory CD8-to-Tregs ratios in the tumor microenvironment as compared with nontreated groups after radiotherapy. Importantly, the depletion of T cells led to a major loss of the therapeutic effect achieved by the combination. This work uncovers TIM-3 targeting as an immunotherapy approach to improve the radiotherapy outcome in DMGs and offers a strong foundation for propelling a phase I clinical trial using radiotherapy and TIM-3 blockade combination as a treatment for these tumors.

Stability criterion of a nonautonomous 3-species ratio-dependent diffusive predator-prey model

The global stability of a nonautonomous 3-species ratio-dependent diffusive predator-prey model is studied in this paper. Firstly, some easily verifiable sufficient conditions which guarantee the existence of the strictly positive space homogenous periodic solution (SHPS) of the ratio- dependent predator-prey model (RDPPM) with diffusive and variable coefficient are achieved by using a comparison theorem of differential equation and fixed point theorem. At the same time, some new analysis techniques are developed as a byproduct. Secondly, some sufficient conditions ensuring the globally asymptotically stability of the strictly positive SHPS of the diffusive nonautonomous predator-prey model are given by using the method of upper and lower solutions (UALS) for the parabolic partial differential equations and Lyapunov stability theory. In addition, two numerical examples are given to validate the theoretical results obtained in this paper.

Nitrate and silicate fluxes at the sediment–water interface of the deep North Pacific Ocean illuminated by 226Ra/230Th disequilibria

By taking advantage of recent analytical advances, we herein develop the 226Ra/230Th isotope systematics as a novel tool for quantifying nitrate and dissolved silicate fluxes across the sediment–water interface of the deep-ocean floor. Sediment cores were retrieved from the seabed between 4927 m and 5951 m in the North Pacific Ocean. Downcore profiles of 230Th and both dissolved and total 226Ra were measured using a high-sensitivity inductively coupled plasma mass spectrometer. At all study sites, a marked deficit of total 226Ra with respect to 230Th was observed between 0 and 20 cm, indicating active migration of soluble 226Ra from the sediment into the overlying seawater. By constructing the mass balance of 226Ra in the sediment column, the flux of dissolved 226Ra across the sediment–water interface was estimated to range from 461 to 1320 dpm m−2 yr−1. When coupled to a diffusive transport model as developed by early investigators, these flux values of 226Ra enabled us to calculate the flux of any dissolved constituent of interest by measuring their bottom water concentrations and pore water “saturation” concentrations. Based on the 226Ra/230Th disequilibrium approach, the derived fluxes vary between 4.1 and 10.5 mmol m−2 yr−1 for nitrate and between 11 and 49 mmol m−2 yr−1 for dissolved silicate. A compilation of nitrate and silicate fluxes from the seabed in the deep Pacific Ocean shows that these values are consistent with historical flux measurements based on the conventional core incubation method in the same study region. In addition, both nitrate and silicate fluxes exhibit a clear depth-dependent trend. Overall, our results suggest that sedimentary diagenetic alterations at the North Pacific Ocean floor below ∼ 5000 m are efficient so that only < 2 % of the particulate organic carbon and < 12 % of the biogenic opal raining to the seafloor are ultimately preserved in the sediment.

Global particle buildup simulations with gas puff scan: application to WEST discharge

This paper deals with the distribution of sources, transport, and exhaust of particles in a tokamak. Knowledge and understanding of all the physical phenomena involved in the global particle buildup are necessary to study and predict density regimes and subsequently to develop optimized scenarios for tokamak operation in order to control heat and particle exhaust. Neutral particles and their interactions with plasma are central in this perspective. This paper discusses the impact of varying the intensity of particle fueling in 2D transport simulations of a WEST discharge. Simulations are performed with an updated version of SOLEDGE-HDG that allows a more realistic transport of neutrals using a self-consistent diffusive model based on charge exchange and ionization processes. New code capabilities allow the entire WEST poloidal cross section to be simulated in a realistic configuration for both geometry and the range of control parameters. A gas puff scan illustrates the main features of the sheath-limited, high-recycling, and detached regimes, such as the buildup of the temperature gradient and the pressure drop in the scrape-off layer (SOL), the target temperature falling to 1 eV, and the ionization source moving away from the targets, as well as the particle flux rollover. A crude estimate of wall erosion is also provided, showing the respective role of each plasma wall component in each of these regimes.

Primary murine high-grade glioma cells derived from RCAS/tv-a diffuse glioma model reprogram naive T cells into immunosuppressive regulatory T lymphocytes

High-grade gliomas (HGGs) and glioblastomas (GBMs) are the most aggressive and lethal brain tumors. The current standard of care (SOC) includes gross safe surgical resection followed by chemoradiotherapy. The main chemotherapeutic agents are the DNA-alkylating agent temozolomide (TMZ) and adjuvants. Due to the outdated therapeutic protocols and lack of specific treatments, there is an urgent and rising need to improve ourunderstanding of tumor biology and design more effective therapeutic strategies. Invitro models are essential for investigating glioma biology and testing novel therapeutic approaches. While using commercially available and patient-derived glioma cell lines for invitro studies is common practice, they exhibit several limitations, including failing to maintain the genetic and phenotypic diversity of primary tumors, undergo genetic drift over time, and often lacking the invasive and stem-like characteristics of patient tumors. These limitations can lead to inconsistent and non-reproducible results, hampering translational research progress. In this study, we established a novel primary murine HGG cell line, isolated from an immunocompetent HGG-bearing RCAS/T-va mouse. We characterized the transcriptome and phenotype to ensure that this cell line resembles the nature of HGGs and retains the ability to reprogram primary murine T lymphocytes.

Low Mach number limit of a diffuse interface model for two‐phase flows of compressible viscous fluids

AbstractIn this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding system for incompressible fluids in the case of well‐prepared initial data and same densities in the limit.

Mixture theory for diffuse interface models of two-phase flows

Mixture theory for diffuse interface models of two-phase flows

Direct serotonin release in humans shapes aversive learning and inhibition

The role of serotonin in human behaviour is informed by approaches which allow in vivo modification of synaptic serotonin. However, characterising the effects of increased serotonin signalling in human models of behaviour is challenging given the limitations of available experimental probes, notably selective serotonin reuptake inhibitors. Here we use a now-accessible approach to directly increase synaptic serotonin in humans (a selective serotonin releasing agent) and examine its influence on domains of behaviour historically considered core functions of serotonin. Computational techniques, including reinforcement learning and drift diffusion modelling, explain participant behaviour at baseline and after week-long intervention. Reinforcement learning models reveal that increasing synaptic serotonin reduces sensitivity for outcomes in aversive contexts. Furthermore, increasing synaptic serotonin enhances behavioural inhibition, and shifts bias towards impulse control during exposure to aversive emotional probes. These effects are seen in the context of overall improvements in memory for neutral verbal information. Our findings highlight the direct effects of increasing synaptic serotonin on human behaviour, underlining its role in guiding decision-making within aversive and more neutral contexts, and offering implications for longstanding theories of central serotonin function.