Effects of Different Cosmic Ray Transport Models on Galaxy Formation

Cosmic rays (CRs) with ∼ GeV energies can contribute significantly to the energy and pressure budget in the interstellar, circumgalactic, and intergalactic medium (ISM, CGM, IGM). Recent cosmological simulations have begun to explore these effects, but almost all studies have been restricted to simplified models with constant CR diffusivity and/or streaming speeds. Physical models of CR propagation/scattering via extrinsic turbulence and self-excited waves predict transport coefficients which are complicated functions of local plasma properties. In a companion paper, we consider a wide range of observational constraints to identify proposed physically-motivated cosmic-ray propagation scalings which satisfy both detailed Milky Way (MW) and extra-galactic γ-ray constraints. Here, we compare the effects of these models relative to simpler “diffusion+streaming” models on galaxy and CGM properties at dwarf through MW mass scales. The physical models predict large local variations in CR diffusivity, with median diffusivity increasing with galacto-centric radii and decreasing with galaxy mass and redshift. These effects lead to a more rapid dropoff of CR energy density in the CGM (compared to simpler models), in turn producing weaker effects of CRs on galaxy star formation rates (SFRs), CGM absorption profiles and galactic outflows. The predictions of the more physical CR models tend to lie “in between” models which ignore CRs entirely and models which treat CRs with constant diffusivity.

Turbulent Mixing in the benthic biolayer of streams with bedforms

<p>The importance of the benthic biolayer (the first few centimeters in the shallow part of the streambed) comes from the active biogeochemical reactions that happen within this thin layer. Currently, many studies use the simplified approach of using the constant profile to represent the diffusivity in the sedimented; however, other studies claim that the exponential profile is a better representation due to the turbulence penetration into the sediment bed. In this work, we are using an analytical model to simulate the temporal variation of solute concentration in water column in bedform morphology type by adopting two diffusivity profile; constant diffusivity profile, and exponential diffusivity profile. This rigorous analytical framework was built by Grant et al. 2019 (not published yet),  and is based on Duhamel’s Theorem. The model is used to fit a set of laboratory data that were performed on streams with dunes type bedforms, where temporal concentration variation is measured in the water column. Based on Root Mean Square Error (RMSE), coefficient of determination (R<sup>2</sup>), and modified Akaike Information Criterion (AICc), the exponential profile is superior over the whole range of Permeability Reynolds Number, and it can be considered as the best fit for the laboratory data compared to the constant diffusivity.  Additionally, the influence of sediment bed depth on the effective diffusivity, and therefore, on the benthic biolayer characteristics is investigated here by running the model with constant diffusivity profile in Infinite and finite sediment bed cases. An indicator () to determine whether the sediment bed depth influences the diffusivity within the sediment domain or not, is introduced here. when this indicator is larger than 1, the sediment bed depth will likely influence the diffusivity within the sediment. Based on our results, our analytical framework can be a predictive tool for the solute transfer into the benthic layer in bedform morphology type.</p><p><img 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alt=""></p><p> </p>

Experimental characterization and computational modeling of hydrogel cross-linking for bioprinting applications

Alginate-based hydrogels are extensively used to create bioinks for bioprinting, due to their biocompatibility, low toxicity, low costs, and slight gelling. Modeling of bioprinting process can boost experimental design reducing trial-and-error tests. To this aim, the cross-linking kinetics for the chemical gelation of sodium alginate hydrogels via calcium chloride diffusion is analyzed. Experimental measurements on the absorbed volume of calcium chloride in the hydrogel are obtained at different times. Moreover, a reaction-diffusion model is developed, accounting for the dependence of diffusive properties on the gelation degree. The coupled chemical system is solved using finite element discretizations which include the inhomogeneous evolution of hydrogel state in time and space. Experimental results are fitted within the proposed modeling framework, which is thereby calibrated and validated. Moreover, the importance of accounting for cross-linking-dependent diffusive properties is highlighted, showing that, if a constant diffusivity property is employed, the model does not properly capture the experimental evidence. Since the analyzed mechanisms highly affect the evolution of the front of the solidified gel in the final bioprinted structure, the present study is a step towards the development of reliable computational tools for the in silico optimization of protocols and post-printing treatments for bioprinting applications.

Diffusivity-Factor Approximation for Spectral Outgoing Longwave Radiation

Accurate integration of directional radiance shows that the conventional diffusivity-factor approximation with a constant diffusivity angle results in an overestimation of the outgoing longwave radiation (OLR) in the window band and an underestimation in the absorption band. We propose an analytical estimation of a spectrally dependent diffusivity angle for clear-sky spectral OLR, considering actual atmospheric conditions and realistic optical path geometry. Beginning with the plane-parallel geometry, we present a new, physical explanation of the conventional diffusivity angle that applies to the gas absorption bands and derives an alternative solution for the window bands. Then a correction scheme is developed to account for the impact of the spherical Earth geometry on the diffusivity angle. The proposed method achieves higher accuracy, reducing biases to generally less than 2% in all spectral regions.

Diffusivity of Gas Into Bitumen: Part II—Data Set and Correlation

Summary The oil-production rate of in-situ heavy-oil-recovery processes involving the injection of gaseous hydrocarbons partly depends on the diffusivity of the gas in the bitumen. Data for gas diffusivities, particularly above ambient temperature, are relatively scarce because they are time consuming to measure. In this study, the diffusion and solubilities of gaseous methane, ethane, propane, and n-butane in a Western Canadian bitumen were measured from 40 to 90°C and pressures from 300 to 2300 kPa, using a pressure-decay method. The diffusivities were determined from a numerical model of the experiments that accounted for the swelling of the oil. In Part I of this study (Richardson et al. 2019), it was found that both constant and viscosity-dependent diffusivities could be used to model the mass of gas diffused and the gas-concentration profile in the bitumen; however, the constant diffusivity was different for each experiment and mainly depended on the oil viscosity. In this study, a correlation for the constant diffusivity to the oil viscosity is developed as a tool to quickly estimate the gas diffusivity. A correlation of diffusivity to the mixture viscosity is also developed for use in more-rigorous diffusion models. The maximum deviations in the mass diffused over time predicted with the constant and viscosity-dependent (mixture viscosity) correlations at each condition are on average 7.4 and 8.7%, respectively.

Diffusivity of Gas Into Bitumen: Part I—Analysis of Pressure-Decay Data With Swelling

Summary The oil-production rate of in-situ heavy-oil-recovery processes involving the injection of gaseous hydrocarbons partly depends on the diffusivity of the gas in the bitumen. The gas diffusivities required to model these processes are determined indirectly from models of mass-transfer experiments. However, the data in the literature are scattered partly because different methods and model assumptions are used in each case. In this work, the pressure-decay method is examined with a focus on accounting for swelling and the dependence of the diffusivity on the solvent content. To assess these issues, the diffusion of gaseous propane into bitumen is measured at conditions where significant swelling occurs. A numerical model is developed for the pressure-decay experiment that accounts for swelling (including excess volumes of mixing) and variable diffusivity. For gases, such as propane, with a relatively high solubility in bitumen, the error in the calculated diffusivity reached 25% when swelling was not included in the model. The error in the height of the gas/oil interface reached 15%. Nonideal mixing had no effect on the calculated diffusivity and only a small effect on the height of the interface. It was found that the diffusion data from a single experiment could be modeled equally well with a constant or a solvent-concentration-dependent (or viscosity-dependent) diffusivity. However, the apparent constant diffusivities for each experiment were different, confirming their dependence on the solvent content. The constant diffusivity approximately correlated to the viscosity of the oil. A larger data set is required to fully develop and test a correlation, and this work will be presented in Part II of this study (Richardson et al. 2019).

STATISTICAL MODEL OF INTERNAL MOISTURE TRANSFER FOR DRYING OF POTATO IN CIRCULATING FLUIDIZED BED

Исследованы параметры процесса сушки картофельных цилиндров в циркуляционном кипящем слое при различных температурных режимах. Эксперименты выполнены при температурах сушильного агента 30, 35, 40, 45°С и фиктивной скорости ожижающего воздуха 8,0 м/с. Начальное влагосодержание материала составило 4,15 кг/кг, влагосодержание в конце обработки (0,20 ± 0,05) кг/кг. Предлагаемая статистическая модель основана на аналогии между главным членом численного решения уравнения диффузии методом Кранка-Николсон и уравнением регрессии для относительного влагосодержания материала. Коэффициент эффективной диффузии получен в диапазоне 7,402 · 10–9 м2/с и 8,626 · 10–9 м2/с. Предложено уравнение регрессии для коэффициента диффузии в форме зависимости Аррениуса с предэкспоненциальным множителем 1,91 · 10–7 м2/с и энергией активации 8,18 кДж/моль. The parameters of the drying process of potato cylinders in the circulating fluidized bed at different temperature conditions are investigated. The experiments were performed at the temperatures of the drying agent 30, 35, 40, 45°C and the fictitious speed of the liquefying air 8,0 m/s. The initial moisture content of particles was about 4,15 kg/kg and the final moisture content was in range (0,20 ± 0,05) kg/kg. The proposed statistical model is based on the analogy between the main term of the numerical solution of the diffusion equation by the Crank–Nicolson method and the regression equation for the relative moisture content of the material. Effective moisture diffusivity of the potato particles varied between 7,402 · 10–9 m2/s and 8,626 · 10–9 m2/s. The regression equation for moisture diffusivity coefficient were obtained in form of Arrhenius relationship with the constant diffusivity basis equal 1,91 · 10–7 m2/s and the activation energy equal 8,18 kJ/mol.