Inhomogeneous Diffusion Research Articles

Impact of inhomogeneous diffusion on secondary cosmic ray and antiproton local spectra

Recent γ-ray and neutrino observations seem to favor the consideration of non-uniform diffusion of cosmic rays (CRs) throughout the Galaxy.In this study, we investigate the consequences of spatially-dependent inhomogeneous propagation of CRs on the fluxes of secondary CRs and antiprotons detected at Earth. A comparison is made among different scenarios in search of potential features that may guide us toward favoring one over another in the near future. We also examine both the influence of inhomogeneous propagation in the production of secondary CRs from interactions with the gas, and the effects of this scenario on the local fluxes of antiprotons and light antinuclei produced as final products of dark matter annihilation. Our results indicate that the consideration of an inhomogeneous diffusion model could improve the compatibility of the predicted local antiproton flux with that of B, Be and Li, assuming only secondary origin of these particles. In addition, our model predicts a slightly harder local antiproton spectrum, making it more compatible with the high energy measurements of AMS-02.Finally, no significant changes are expected in the predicted local flux of antiprotons and antinuclei produced from dark matter among the different considered propagation scenarios.

Meridional circulation streamlined

Time-dependent meridional circulation and differential rotation in radiative zones are central open issues in stellar evolution theory. We streamline this challenging problem using the “downward control principle” of atmospheric science, under a geostrophic f-plane approximation. We recover the known stellar physics result that the steady-state meridional circulation decays on the length scale proportional to N / f × Pr , assuming molecular viscosity is the dominant drag mechanism. Prior to steady-state, the meridional circulation and the zonal wind (= differential rotation) spread together via radiative diffusion, under thermal wind balance. The corresponding (fourth-order) hyperdiffusion process is reasonably well approximated by regular (second-order) diffusion on scales of order a pressure scale-height. We derive an inhomogeneous diffusion (equiv. advection-diffusion) equation for the zonal flow which admits closed-form time-dependent solutions in a finite depth domain, allowing for rapid prototyping of differential rotation profiles. In the weak drag limit, we find that the time to rotational steady-state can be longer than the Eddington-Sweet time and be instead determined by the longer drag time. Unless strong enough drag operates, the internal rotation of main-sequence stars may thus never reach a steady-state. Streamlined meridional circulation solutions provide leading-order internal rotation profiles for studying the role of fluid/MHD instabilities (or waves) in redistributing angular momentum in the radiative zones of stars. Despite clear geometrical limitations and simplifying assumptions, one might expect our thin-layer geostrophic approach to offer qualitatively useful results to understand deep meridional circulation in stars.

Macroscopic limit for stochastic chemical reactions involving diffusion and spatial heterogeneity

To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction–diffusion master equations or deterministic, macroscopic reaction–diffusion system. The connection between these two models is not only theoretically important but also plays an essential role in applications. This paper considers the macroscopic limits of the chemical reaction–diffusion master equation for first-order chemical reaction systems in highly heterogeneous environments. More precisely, the diffusion coefficients as well as the reaction rates are spatially inhomogeneous and the reaction rates may also be discontinuous. By carefully discretizing these heterogeneities within a reaction–diffusion master equation model, we show that in the limit we recover the macroscopic reaction–diffusion system with inhomogeneous diffusion and reaction rates.

Diffusive lensing as a mechanism of intracellular transport and compartmentalization.

While inhomogeneous diffusivity has been identified as a ubiquitous feature of the cellular interior, its implications for particle mobility and concentration at different length scales remain largely unexplored. In this work, we use agent-based simulations of diffusion to investigate how heterogeneous diffusivity affects the movement and concentration of diffusing particles. We propose that a nonequilibrium mode of membrane-less compartmentalization arising from the convergence of diffusive trajectories into low-diffusive sinks, which we call 'diffusive lensing,' is relevant for living systems. Our work highlights the phenomenon of diffusive lensing as a potentially key driver of mesoscale dynamics in the cytoplasm, with possible far-reaching implications for biochemical processes.

Diffusive lensing as a mechanism of intracellular transport and compartmentalization

While inhomogeneous diffusivity has been identified as a ubiquitous feature of the cellular interior, its implications for particle mobility and concentration at different length scales remain largely unexplored. In this work, we use agent-based simulations of diffusion to investigate how heterogeneous diffusivity affects the movement and concentration of diffusing particles. We propose that a nonequilibrium mode of membrane-less compartmentalization arising from the convergence of diffusive trajectories into low-diffusive sinks, which we call ‘diffusive lensing,’ is relevant for living systems. Our work highlights the phenomenon of diffusive lensing as a potentially key driver of mesoscale dynamics in the cytoplasm, with possible far-reaching implications for biochemical processes.

TbCu7-type Sm-Fe(-N) powder synthesized by low-temperature reduction-diffusion process using the Li–Ca reductant

It was predicted that TbCu7-type Sm-Fe powder prepared by the low-temperature reduction-diffusion (LTRD) process using a Li-Ca reductant would contain no residual ɑ-Fe because this reductant would not produce the absorbed water that hinders the reaction between Sm and Fe by forming oxychlorides when molten salt is used as the reductant. Contrary to this expectation, a detailed microstructure analysis revealed that a residual phase of unreacted ɑ-Fe existed in some TbCu7-type Sm-Fe particles rather than as separate Fe particles. This residual ɑ-Fe phase was not located in the center of the Sm-Fe particles and was not detected in some Sm-Fe particles, suggesting that the reason for the residual ɑ-Fe phase is inhomogeneous diffusion of Sm into the Fe due to slow diffusion at low temperatures. Although this TbCu7-type Sm-Fe powder contained a small amount of unreacted ɑ-Fe phase, the magnetic properties of the nitride TbCu7-type Sm-Fe were also estimated.

T-wave inversion through inhomogeneous voltage diffusion within the FK3V cardiac model.

The heart beats are due to the synchronized contraction of cardiomyocytes triggered by a periodic sequence of electrical signals called action potentials, which originate in the sinoatrial node and spread through the heart's electrical system. A large body of work is devoted to modeling the propagation of the action potential and to reproducing reliably its shape and duration. Connection of computational modeling of cells to macroscopic phenomenological curves such as the electrocardiogram has been also intense, due to its clinical importance in analyzing cardiovascular diseases. In this work, we simulate the dynamics of action potential propagation using the three-variable Fenton-Karma model that can account for both normal and damaged cells through a the spatially inhomogeneous voltage diffusion coefficient. We monitor the action potential propagation in the cardiac tissue and calculate the pseudo-electrocardiogram that reproduces the R and T waves. The R-wave amplitude varies according to a double exponential law as a function of the (spatially homogeneous, for an isotropic tissue) diffusion coefficient. The addition of spatial inhomogeneity in the diffusion coefficient by means of a defected region representing damaged cardiac cells may result in T-wave inversion in the calculated pseudo-electrocardiogram. The transition from positive to negative polarity of the T-wave is analyzed as a function of the length and the depth of the defected region.

Studying the Effect of the Instantaneous and Continuous Pollutants Sources on the Advection-diffusion Equation and Its Applications

This study investigates instantaneous and continuous sources as point, line, and area sources. Gaussian concentration in the case of the puff model with an instantaneous point source inhomogeneous longitudinal diffusion is investigated. The concentration is calculated using different dispersion parameters to get the proposed normalized concentration of the puff model at ground level around the centerline, which is compared with observed data by the Copenhagen experiment and previous work [1]. Also, the continuous point source is used to get the Gaussian plume model in three dimensions using dispersion parameters to compare with the observed concentration data measured by the Egyptian Atomic Energy Authority for Iodine-135 (I135) in an unstable condition.

Approximation of nonlocal dispersal problem with inhomogeneous kernel

In this paper, we study the Neumann problem for a class of nonlocal dispersal models with inhomogeneous kernel function. We investigate the existence, uniqueness, and limit of solutions when the inhomogeneous diffusion kernel is rescaled. Our result exhibits that the inhomogeneous nonlocal dispersal equation is analogous to local problem without convection in the limit case.

Impact of the Unstirred Water Layer on the Permeation of Small-Molecule Drugs.

Over the last two decades, numerous molecular dynamics (MD) simulation-based investigations have attempted to predict the membrane permeability to small-molecule drugs as indicators of their bioavailability, a majority of which utilize the inhomogeneous solubility diffusion (ISD) model. However, MD-based membrane permeability is routinely 3-4 orders of magnitude larger than the values measured with the intestinal perfusion technique. There have been contentious discussions on the sources of the large discrepancies, and the two indisputable, potentially dominant ones are the fixed protonation state of the permeant and the neglect of the unstirred water layer (UWL). Employing six small-molecule drugs of different biopharmaceutical classification system classes, the current MD study relies on the ISD model but introduces the (de)protonation of the permeant by characterizing the permeation free energy of both neutral and charged states. In addition, the role of the UWL as a potential resistance against permeation is explored. The new MD protocol closely mimics the nature of small-molecule permeation and yields estimates that agree well with in vivo intestinal permeability.

Inhomogeneous Diffusion-Induced Network for Multiview Semi-Supervised Classification.

The challenges posed by heterogeneous data in practical applications have made multiview semi-supervised classification a focus of attention for researchers. While several graph-based approaches have been suggested for this task, they tend to use homogeneous feature propagation, leading to even diffusion of node information to their neighbors. However, this diffusion strategy results in nodes acquiring information of equal proportion from dissimilar samples. In this article, we propose a solution to address these issues by introducing a graph diffusion-induced network for multiview semi-supervised classification. By formulating a discretized partial differential equation on a manifold, we derive a nonlinear and inhomogeneous diffusion equation to govern information propagation on the graph. Then, we investigate the impact of various nonlinear activation functions on random switching edge directions and their suppressive effects on information diffusion between different nodes. In addition, the cross-view consistency under the semi-supervised scenarios is defined and guaranteed for better information fusion. The comprehensive experimental results demonstrate the superiority of the proposed method compared with state-of-the-art approaches. The effectiveness of the proposed approach in handling diverse and heterogeneous data showcases its potential for advancing multiview semi-supervised classification techniques.

Understanding the Influences of Laser Perforation on Thick Electrodes for Lithium Ion Batteries Via 3D Microstructure Simulations

Laser perforation is a precise technique to decrease ionic diffusion limitations by selectively removing material with spatial precisions of tenth of micrometres. It is mainly applied in thick electrodes to improve foremost rate capability, as well as cycle stability, Li plating detention and wetting efficiency.[1] [2]Mostly, holes are created in the batteries through-direction leading to a material removal of about 5%-10% of the initial load. This removal creates inhomogeneous diffusion channels especially into layers close to the current collector, as opposed to a homogeneous increase in porosity.It is of interest to find an optimal trade-off between the competing factors of capacity loss and increase in ion conductivity due to material ablation. Optimization of structuring parameters requires intimate knowledge of electrode and material properties. However, there is a lack of an adequate description of the inhomogeneous structure and its influence on the electrochemical performance. [1]In our presentation we show a detailed 3D microstructure resolved simulation study, examining the influencing parameters for laser perforation. The data suggests, that perforating holes with small diameter at a short distance, which results in an ablation of ca. 8% gives generally desirable improvements for the rate capability. Laser perforation is distinctively favourable in contrast to a raise in homogenous porosity.Moreover, the microstructure resolved simulation also allows for a detailed analysis of different hole shapes and hole misalignment in electrodes after stacking. We evaluate the impact of different configurations on the electro chemical performance. [3]

Effect of thermal exposure on microstructure, orientation relationship, residual stress and failure mechanism of ultrasonic-assisted Kovar/SnSb10/Kovar joints

Thermal exposure is often accompanied by the accumulation of inhomogeneous element diffusion, continued solid-state phase transformation, and occurrence of residual stress, causing the failure of the joint directly. In this work, we focused on the orientation relationship (OR) alternation, residual stress distribution, and failure mechanism of the reflow/ultrasonic-assisted Kovar/SnSb10/Kovar joint after thermal exposure. Especially, the role of Ni element during thermal exposure was analyzed in detail. It was noticed that the thickness of interfacial intermetallic was merely lower than 4 μm, even after thermal exposure for 45 d. The interfacial ORs of IMC/Kovar, whether ultrasound was applied or not, changed to an incoherent state. However, it did not deteriorate the ultimate shear strength, which reached over 50 MPa even after thermal exposure at 160 °C for 45 d. Compared to the reflow process after thermal exposure, the joints with ultrasonic improves the strength by about 10%. However, it dramatically decreased to only 20 MPa after thermal exposure at 200 °C for 45 d. The rationale was that ultrasonic-induced supersaturated Ni elements in solder and the Ni elements from the Kovar alloy diffused into the IMC region simultaneously, forming the (Fe, Ni)Sn2 IMC layer with relatively high residual stress and acting as the fracture origin region. The current findings demonstrated that the Kovar/SnSb10 interface proposed outstanding microstructure stability and mechanical reliability and was a promising alternative for a more extensive range of high-temperature applications.

Diffusion in media with membranes and some nonlocal parabolic problems

UDC 519.21 We establish the classical solvability of a certain conjugation problem for one-dimensional (with respect to a spatial variable) Kolmogorov backward equation with discontinuous coefficients and some variants of the general nonlocal Feller–Wentzell boundary condition given on nonsmooth boundaries of considered curvilinear domains. In addition, we prove, that the two-parameter Feller semigroup defined by the solution of this problem describes some inhomogeneous diffusion process with moving membranes on the given region of the real line. We also show the relationship between the constructed process and the generalized diffusion in the sense of M. I. Portenko.

Tuning the growth of intermetallic compounds at Sn-0.7Cu solder/Cu substrate interface by adding small amounts of indium

The void defect in intermetallic compounds (IMCs) layer at the joints caused by inhomogeneous atomic diffusion is one of the most important factors limiting the further development of Sn-based solders. In this work, the thermodynamic stability of IMCs (high-temperature η-Cu6Sn5 and o-Cu3Sn phases) was improved by adding small amounts of indium (In), and the IMCs layers with moderate thickness, low defect concentrations and stable interface bonding were successfully obtained. The formation order of compounds and the interfacial orientation relationships in IMCs layers, the atomic diffusion mechanism, and the growth tuning mechanism of In on η-Cu6Sn5 and Cu3Sn, after In adding, were discussed comprehensively by combining calculations and experiments. It is the first time that the classic heterogeneous nucleation theory and CALPHAD data were used to obtain the critical nucleus radius of η-Cu6Sn5 and Cu3Sn, and to explain in detail the main factors affecting the formation order and location of IMCs at joints during the welding process. A novel and systematic growth model about IMCs layers in the case of doping with alloying elements was proposed. The growth tuning mechanism of In doping on η-Cu6Sn5 and Cu3Sn was further clarified based on the proposed model using first-principles calculations. The growth model used in this study can provide insights into the development and design of multielement Sn-based solders.

Pattern formation in a one-dimensional MARCKS protein cyclic model with spatially inhomogeneous diffusion coefficients

Pattern formation in a one-dimensional MARCKS protein cyclic model with spatially inhomogeneous diffusion coefficients

Advances in Computational Approaches for Estimating Passive Permeability in Drug Discovery.

Passive permeation of cellular membranes is a key feature of many therapeutics. The relevance of passive permeability spans all biological systems as they all employ biomembranes for compartmentalization. A variety of computational techniques are currently utilized and under active development to facilitate the characterization of passive permeability. These methods include lipophilicity relations, molecular dynamics simulations, and machine learning, which vary in accuracy, complexity, and computational cost. This review briefly introduces the underlying theories, such as the prominent inhomogeneous solubility diffusion model, and covers a number of recent applications. Various machine-learning applications, which have demonstrated good potential for high-volume, data-driven permeability predictions, are also discussed. Due to the confluence of novel computational methods and next-generation exascale computers, we anticipate an exciting future for computationally driven permeability predictions.

Passive permeability controls synthesis for the allelochemical sorgoleone in sorghum root exudate

Competition for soil nutrients and water with other plants foster competition within the biosphere for access to these limited resources. The roots for the common grain sorghum produce multiple small molecules that are released via root exudates into the soil to compete with other plants. Sorgoleone is one such compound, which suppresses weed growth near sorghum by acting as a quinone analog and interferes with photosynthesis. Since sorghum also grows photosynthetically, and may be susceptible to sorgoleone action if present in tissues above ground, it is essential to exude sorgoleone efficiently. However, since the P450 enzymes that synthesize sorgoleone are intracellular, the release mechanism for sorgoleone remain unclear. In this study, we conducted an in silico assessment for sorgoleone and its precursors to passively permeate biological membranes. To facilitate accurate simulation, CHARMM parameters were newly optimized for sorgoleone and its precursors. These parameters were used to conduct 1 μs of unbiased molecular dynamics simulations to compare the permeability of sorgoleone with its precursors molecules. We find that interleaflet transfer is maximized for sorgoleone, suggesting that the precursor molecules may remain in the same leaflet for access by biosynthetic P450 enzymes. Since no sorgoleone was extracted during unbiased simulations, we compute a permeability coefficient using the inhomogeneous solubility diffusion model. The requisite free energy and diffusivity profiles for sorgoleone through a sorghum membrane model were determined through Replica Exchange Umbrella Sampling (REUS) simulations. The REUS calculations highlight that any soluble sorgoleone would quickly insert into a lipid bilayer, and would readily transit. When sorgoleone forms aggregates in root exudate as indicated by our equilibrium simulations, aggregate formation would lower the effective concentration in aqueous solution, creating a concentration gradient that would facilitate passive transport. This suggests that sorgoleone synthesis occurs within sorghum root cells and that sorgoleone is exuded by permeating through the cell membrane without the need for a transport protein once the extracellular sorgoleone aggregate is formed.

Effects of Thermal-Strain-Induced Atomic Intermixing on the Interfacial and Photoluminescence Properties of InGaAs/AlGaAs Multiple Quantum Wells.

Quantum-well intermixing (QWI) technology is commonly considered as an effective methodology to tune the post-growth bandgap energy of semiconductor composites for electronic applications in diode lasers and photonic integrated devices. However, the specific influencing mechanism of the interfacial strain introduced by the dielectric-layer-modulated multiple quantum well (MQW) structures on the photoluminescence (PL) property and interfacial quality still remains unclear. Therefore, in the present study, different thicknesses of SiO2-layer samples were coated and then annealed under high temperature to introduce interfacial strain and enhance atomic interdiffusion at the barrier-well interfaces. Based on the optical and microstructural experimental test results, it was found that the SiO2 capping thickness played a positive role in driving the blueshift of the PL peak, leading to a widely tunable PL emission for post-growth MQWs. After annealing, the blueshift in the InGaAs/AlGaAs MQW structures was found to increase with increased thickness of the SiO2 layer, and the largest blueshift of 30 eV was obtained in the sample covered with a 600 nm thick SiO2 layer that was annealed at 850 °C for 180 s. Additionally, significant well-width fluctuations were observed at the MQW interface after intermixing, due to the interfacial strain introduced by the thermal mismatch between SiO2 and GaAs, which enhanced the inhomogeneous diffusion rate of interfacial atoms. Thus, it can be demonstrated that the introduction of appropriate interfacial strain in the QWI process is of great significance for the regulation of MQW band structure as well as the control of interfacial quality.

Visualizing spatially inhomogeneous hydrogen isotope diffusion by hydrogenography

Visualizing spatially inhomogeneous hydrogen isotope diffusion by hydrogenography