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At least 433 records · Page 24

A Mathematical Model of Diffusion-Limited Gas Bubble Dynamics in Tissue with Varying Diffusion Region Thickness

A three-region mathematical model of gas bubble dynamics has been shown suitable for describing diffusion-limited dynamics of more than one bubble in a given volume of extravascular tissue. The model is based on the dynamics of gas exchange between a bubble and a well-stirred tissue region through an intervening unperfused diffusion region previously assumed to have constant thickness and uniform gas diffusivity. As a result, the gas content of the diffusion region remains constant as the volume of the region increases with bubble growth, causing dissolved gas in the region to violate Henry's law. Earlier work also neglected the relationship between the varying diffusion region volume and the fixed total tissue volume, because only cases in which the diffusion region volume is a small fraction of the overall tissue volume were considered. We herein extend the three-region model to correct these theoretical inconsistencies by allowing both the thickness and gas content of the diffusion region to vary during bubble evolution. A postulated difference in gas diffusivity between an infinitesimally thin layer at the bubble surface and the remainder of the diffusion region leads to variation in diffusion region gas content and thickness during bubble growth and resolution. This variable thickness, differential diffusivity (VTDD) model can yield bubble lifetimes considerably longer than those yielded by earlier three-region models for given model and decompression parameters, and meets a need for theoretically consistent but relatively simple bubble dynamics models for use in studies of decompression sickness (DCS) in human subjects, Keywords: decompression sickness, gas diffusion in tissue, diffusivity

Srinivasan, R. Srini↗

Model for radon diffusion through the lunar regolith.

Description of a model for radon diffusion through the lunar regolith in which the atom migrates by random walk. The regolith is represented by a system of randomly oriented baffles in which the mean distance which the atom travels between two collisions takes on the role of a mean free path. The effective mean time between two collisions depends on two entities: the actual mean time-of-flight and the mean sticking time on grain surfaces for one collision. The latter depends strongly on the temperature and the heat of adsorption of radon on regolith materials. Both the mean free path as well as the heat of adsorption are either poorly known or unknown for the lunar regolith; hence these quantities are treated as free parameters. Because of the greatly different mean lifetimes against radioactive decay of Rn219, Rn220, and Rn222, the regolith acts as a powerful 'filter' for these species. Rn222 escape is significant (32%) even for a mean free path of 1 micron, a heat of adsorption of 7.0 kcal/mole and a regolith depth of 4 m. Calculations of radon escape from a 4 m thick regolith, using mean free paths of 1, 10, and 80 microns and heats of adsorption of 4.0, 5.2, and 7.0 kcal/mole show that the Rn222/Rn220 escape ratio can be as small as 7.7 and as large as, or larger than 47. The small value of 7.7 is of particular interest, because it is nearly equal to the escape ratio inferred by Turkevich et al. (1970) from their Surveyor 5 results.

Friesen, L. J.↗

THE ROLE OF COSMIC-RAY PRESSURE IN ACCELERATING GALACTIC OUTFLOWS

We study the formation of galactic outflows from supernova (SN) explosions with the moving-mesh code AREPO in a stratified column of gas with a surface density similar to the Milky Way disk at the solar circle. We compare different simulation models for SN placement and energy feedback, including cosmic rays (CRs), and find that models that place SNe in dense gas and account for CR diffusion are able to drive outflows with similar mass loading as obtained from a random placement of SNe with no CRs. Despite this similarity, CR-driven outflows differ in several other key properties including their overall clumpiness and velocity. Moreover, the forces driving these outflows originate in different sources of pressure, with the CR diffusion model relying on non-thermal pressure gradients to create an outflow driven by internal pressure and the random-placement model depending on kinetic pressure gradients to propel a ballistic outflow. CRs therefore appear to be non-negligible physics in the formation of outflows from the interstellar medium.

79 ASTRONOMY AND ASTROPHYSICS↗

A semi-automated algorithm for designing stellarator divertor and limiter plates and application to HSX

We present a semi-automated algorithm for designing three-dimensional divertor or limiter plates targeting low heat loads. The algorithm designs the plates in two stages: firstly, the parallel heat flux distribution is caught on vertically-inclined plates at one or several toroidal locations. Secondly, the power per unit area is reduced by stretching, tilting and bending the plates toroidally. Heat transport is modelled using the EMC3-Lite code, which uses an anisotropic diffusion model. We apply this scheme to HSX, a medium-sized stellarator located at the University of Wisconsin–Madison. Starting from the current machine with an extended vessel wall, we construct plates which are able to effectively catch and spread the heat for three different magnetic configurations. The scheme has a computational cost in the order of tens of CPU-minutes, making it a powerful tool for semi-automated plasma-facing component design in three-dimensional environments.

anisotropic diffusion↗

A new dynamic zOnal model with air-diffuser (DOMA) - Application to thermal comfort prediction

A new Dynamic zOnal Model with Air-diffuser (DOMA) was developed. Several case studies were investigated and tested to evaluate and validate this program using measurement data. This new model was integrated into a TRaNsient SYstems Simulation program library and coupled with the multi-zone thermal model. The DOMA/TRNSYS coupled model was then used to predict room temperature distribution over an entire day of a single-zone building. The results show that increasing the heating outputs of the electric floor system, for example, from 75 to 200 W/m 2 , would not effectively improve the indoor thermal comfort, since the thermostat will reach the set point first and then turn off the system before the room gets enough heat and reach a comfortable level. This indicates the importance of selecting an appropriate location and set point for the thermostat when using a floor heating system. This potential thermal comfort issue can only be identified through the two-node model with a dynamic zonal model rather than the conventional PMV model, which thus suggests that for optimizing indoor thermal comfort of a building equipped with a time-sensitive control strategy and/or HVAC system, the TSENS results obtained from the two-node model integrated with DOMA are more appropriate than PMVs.

Construction & Building Technology↗

Analysis of redox additive-based overcharge protection for rechargeable lithium batteries

The overcharge condition in secondary lithium batteries employing redox additives for overcharge protection, has been theoretically analyzed in terms of a finite linear diffusion model. The analysis leads to expressions relating the steady-state overcharge current density and cell voltage to the concentration, diffusion coefficient, standard reduction potential of the redox couple, and interelectrode distance. The model permits the estimation of the maximum permissible overcharge rate for any chosen set of system conditions. Digital simulation of the overcharge experiment leads to numerical representation of the potential transients, and estimate of the influence of diffusion coefficient and interelectrode distance on the transient attainment of the steady state during overcharge. The model has been experimentally verified using 1,1-prime-dimethyl ferrocene as a redox additive. The analysis of the experimental results in terms of the theory allows the calculation of the diffusion coefficient and the formal potential of the redox couple. The model and the theoretical results may be exploited in the design and optimization of overcharge protection by the redox additive approach.

Narayanan, S. R.↗

Kinetic and Mechanistic Evaluation of Inorganic Arsenic Species Adsorption onto Humic Acid Grafted Magnetite Nanoparticles

In this study, humic acid coated magnetic iron oxide nanoparticles (HA-MNP) were synthesized, characterized, and studied for the removal of toxic inorganic arsenic species from aqueous media. The adsorption of As(III) and As(V) followed pseudo-second order kinetics and the observed data were accurately modeled employing Freundlich adsorption isotherm. Application of the Weber and Morris intraparticle diffusion model to the observed kinetic data suggest that the adsorption occurs in three distinct stages, fast, intermediate, and slow steps. We propose the initial stage is governed by surface association, followed by intraparticle diffusion of arsenic through the HA matrix and finally, chemical reaction or bonding between the arsenic species and HA functionality. The HAMNP nano-adsorbent absorbs > 95% of the inorganic arsenic species with an absorption capacity of 12.2-12.6 mg/g from aqueous media and is effective under a variety of conditions. Post arsenic adsorption characterization of the nanoparticles suggests that As(III) binds with the carboxylate group of HA through a proposed ester type linkage while electrophilic reactions can occur between the nucleophilic functional groups present in HA and the electrophilic arsenic atom in As(V). Finally, the results obtained demonstrated that HA-MNP are robust and have promise for effective As (III) and As(V) remediation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

The AEOLUS Center is dedicated to developing a unified optimization-under-uncertainty framework for (1) learning predictive models from data and (2) optimizing experiments, processes, and designs governed by these models, all driven by complex, uncertain energy systems. AEOLUS addressed the critical need for principled, rigorous, scalable, and structure-exploiting capabilities for exploring parameter and decision spaces of complex forward simulation models---the so-called outer loop. This report summarizes the work done under DE-SC0021077 on (1) nonlocal models for solidification problems, (2) a multifidelity method for a nonlocal diffusion model, and (3) multifidelity Monte Carlo methods.

97 MATHEMATICS AND COMPUTING↗

Electron transport and the magnetic field in the Crab Nebula

Observational data obtained at radio, optical, and X-ray frequencies on the size of the emission region in the Crab Nebula are used to examine various energy-transport models. It is shown that the data cannot be fitted by diffusion models, even when the energy-injection region is extended. A more favorable comparison is made with an extended source model in which bulk motion is the transport mechanism. Assuming a point source of electrons and a uniform nebular magnetic field, a perpendicular magnetic-field component of less than 0.0008 gauss is determined. Combining this with the lower limit obtained from gamma-ray observations, a perpendicular field component of between 0.0005 and 0.0008 gauss is obtained. A break in the size dependence is predicted at about 12 microns and 45 keV. Above 45 keV, the size should decrease as the inverse square root of proton energy.

Wolff, R. S.↗

Improving Ocean Reanalyses and ENSO Forecasts By Assimilation of Rain Corrected Satellite Sea Surface Salinity Using the GMAO S2S Forecast System

During the past years, we have seen that the La Nina to El Nino transition has had a significant global socio-economic impact and so has been the key focus for improving coupled ocean-atmosphere forecasts. Assimilation of satellite altimetry and subsurface temperature and salinity from (mostly) Argo help to improve the initialization of the thermocline, while satellite Sea Surface Temperature (SST) aids in constraining surface heat-fluxes, leading to improved subseasonal to seasonal forecasts of the coupled system. However, few studies have focused on improving the fresh-water flux and near-surface density and mixing through assimilation of satellite sea surface salinity (SSS). For expediency, the few ocean models that do assimilate SSS bias-correct the satellite SSS data to normalize towards the near-surface Argo data. However, in rainy regions, where buoyant water sits as a fresh lens at the surface, this assumption is likely inadequate. In previous work, we have shown that adjusting SSS data to bulk salinity (Sb) using the Rain Impact Model (RIM) of Santos-Garcia et al., 2014 has improved the near-surface density and mixed layer depth, leading to deeper thermocline and improved the NINO3.4 SST forecasts. Now we utilize the Soil Moisture/Ocean Salinity, Rain Corrected (SMOS_RC) SSS product provided by the Centre Aval de Traitement des données SMOS (CATDS CPDC) to represent the Sb more accurately at first model layer (in our case 5 m). Rather than using a diffusivity model as with RIM, SMOS_RC relies on an observed relationship between the spatial heterogeneity of SMOS SSS and instantaneous rain rate (RR) (Supply et al., 2020). In order to test the impact of SMOS_RC versus SMOS, we compare two reanalyses over the period 2014 to 2021. For both reanalysis experiments, all available along-track absolute dynamic topography and in situ observations are assimilated using the LETKF scheme (Penny et al., 2013). One reanalysis additionally assimilates SMOS SSS data as is (i.e., with the fresh bias), and a separate reanalysis is performed assimilating the SMOS_RC data. We assess the impact for near-surface and subsurface dynamics within ocean reanalyses by validating against observations and explore how SSS assimilation (SMOS versus SMOS_RC) impacts dynamical ENSO forecasts using the NASA GMAO Sub-seasonal to Seasonal coupled forecast system (GEOS S2S-3, Molod et al., 2020, Hackert et al., 2023). We will show that improved SSS estimates and near-surface density and mixing led to more accurate coupled air/sea interaction and better ENSO forecasts.

Eric Hackert↗

Modeling the Dynamics of Energetic Protons in Earth's Inner Magnetosphere

Recently, Van Allen Probes data have revealed the interesting energy-dependent dynamics of energetic protons in Earth's inner magnetosphere. To quantify the role of radial diffusion and charge exchange to the observed energy-dependent dynamics of ring current protons, a 1D radial diffusion model with charge exchange loss is implemented. The observed proton flux over the long-term period of November 2012 to September 2013 is first converted to phase space densities, which are then simulated by our model driven by an outer boundary condition at L* = 5.5 derived from the data. The simulation results show that our model generally captures the transport and acceleration of energetic protons at μ = 30, 50, and 80 MeV/G and K = 0.11 G 1/2 R E , suggesting that radial diffusion is the dominant source mechanism for >75 keV protons at L* = 3.5–5.5. Additionally, the observed fast decay of protons at lower μ and slow decay at higher μ are well captured by the model, demonstrating the dominant role of charge exchange in explaining the observed energy-dependent proton decay. For higher μ protons, prompt losses of protons on the time scale of hours are observed over a wide range of L*, which is too fast to be explained by charge exchange. Some of the prompt losses at high L* regions are reproduced by the model with outward radial diffusion to the outer boundary. However, many prompt losses observed at lower L* regions are not captured by the model, which could be due to other loss mechanisms including electromagnetic ion cyclotron wave scattering and field line curvature scattering.

79 ASTRONOMY AND ASTROPHYSICS↗

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares.

97 MATHEMATICS AND COMPUTING↗

Moisture ingress into electronics enclosures under isothermal conditions

The number of electronics used in outdoor environment is constantly growing. The humidity causes about 19 % of all electronics failures and, especially, moisture increases these problems due to the ongoing process of miniaturization and lower power consumption of electronic components. Moisture loads are still not understood well by design engineers, therefore this field has become one of the bottlenecks in the electronics system design. The objective of this paper is to model moisture ingress into an electronics enclosure under isothermal conditions. The moisture diffusion model is based on a 1D quasi-steady state (QSS) approximation for Fick’s second law. This QSS approach is also described with an electrical analogy which gives a fast tool in modelling of the moisture response. The same QSS method is applied to ambient water vapour variations. The obtained results are compared to an analytical solution and very good agreement is found.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A two component model of the diurnal variations in the thermospheric composition

A self-consistent, two-dimensional, two-component diffusion model is presented to describe the diurnal component of thermosphere dynamics. In the regions where oxygen and helium are the minor constituents, diffusion is shown to increase the amplitudes of these constituents and to advance the times of their diurnal maxima by several hours with respect to the gas temperature and the major species. Both effects are in basic agreement with satellite observations. The diffusion process is relatively insignificant for temperature, total mass density, and wind fields. The magnitude of the temperature-density phase delay is discussed with respect to its dependence on the electron density distribution.

Mayr, H. G.↗

Equilibrium, kinetic, and thermodynamic studies on the sorption of some heavy metal ions by the phosphorus-containing polymer sorbent

The sorption of Cu+{sup 2}, Ni+{sup 2}, Co+{sup 2}, and Zn+{sup 2} ions onto the phosphorus-containing sorbent were studied as a function of the contact time, temperature, and concentration of the initial metal ions. The equilibrium studies are presented by the Langmuir, Freundlich, and Temkin isotherm models. The sorption data are well described by the Langmuir isotherm model, and they also can be simulated by the Freundlich isotherm model. The pseudo-first-order, pseudo-second-order, and intraparticle diffusion models were applied to test the experimental data of the kinetic studies. The pseudo-second-order kinetic model provided the best correlation of the experimental data compared to the other kinetic models. The sorption capacity of the metal ions increased with temperature increasing. The positive value of enthalpy (ΔH°) and the negative value of Gibbs free energy (ΔG°) indicated that the sorption process was endothermic and spontaneous.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data on the comprehensive first-principles diffusion study of the aluminum-magnesium system

First-principles calculation of diffusion coefficients between Mg and Al is investigated comprehensively using density functional theory (DFT). The effect of different uncertainty sources arising from first principles calculations has been investigated systematically. These sources include the diffusion model, energetic, entropic and attempt frequency calculations. Variation in self and impurity diffusion coefficients of Mg and Al in stable phases are quantified using different DFT settings and compared with the experiments. Using the optimal DFT settings, diffusion coefficients in metastable phases of Al and Mg are predicted. The dataset refers to “An integrated experimental and computational study of diffusion and atomic mobility of the aluminum-magnesium system” [1].

36 MATERIALS SCIENCE↗