Mathematical model and computational scheme for multi-phase modeling of cellular population and microenvironmental dynamics in soft tissue

In this paper we introduce a system of partial differential equations that is capable of modeling a variety of dynamic processes in soft tissue cellular populations and their microenvironments. The model is designed to be general enough to simulate such processes as tissue regeneration, tumor growth, immune response, and many more. It also has built-in flexibility to include multiple chemical fields and/or sub-populations of cells, interstitial fluid and/or extracellular matrix. The model is derived from the conservation laws for mass and linear momentum and therefore can be classified as a continuum multi-phase model. A careful choice of state variables provides stability in solving the system of discretized equations defining advective flux terms. A concept of deviation from normal allows us to use simplified constitutive relations for stresses. We also present an algorithm for computing numerical approximations to the solutions of the system and discuss properties of these approximations. We demonstrate several examples of applications of the model. Numerical simulations show a significant potential of the model for simulating a variety of processes in soft tissues.

Diurnal and Seasonal Variation of Area-Fugitive Methane Advective Flux from an Open-Pit Mining Facility in Northern Canada Using WRF

Greenhouse Gas (GHG) emissions pose a global climate challenge and the mining sector is a large contributor. Diurnal and seasonal variations of area-fugitive methane advective flux, released from an open-pit mine and a tailings pond, from a facility in northern Canada, were simulated in spring 2018 and winter 2019, using the Weather Research and Forecasting (WRF) model. The methane mixing ratio boundary conditions for the WRF model were obtained from the in-situ field measurements, using Los Gatos Research Ultra-Portable Greenhouse Gas Analyzers (LGRs), placed in various locations surrounding the mine pit and a tailings pond. The simulated advective flux was influenced by local and synoptic weather conditions in spring and winter, respectively. Overall, the average total advective flux in the spring was greater than that in the winter by 36% and 75%, for the mine and pond, respectively. Diurnal variations of flux were notable in the spring, characterized by low flux during thermally stable (nighttime) and high flux during thermally unstable (daytime) conditions. The model predictions of the methane mixing ratio were in reasonable agreement with limited aircraft observations (R2=0.68). The findings shed new light in understanding the area-fugitive advective flux from complex terrains and call for more rigorous observations in support of the findings.

Evidence of ketene emissions from petrochemical industries and implications for ozone production potential

Ketene, a rarely measured reactive VOC, was quantified in the emission plumes from Daesan petrochemical facility in South Korea using airborne PTR-TOF-MS measurements. Ketene mixing ratios as high as ~ 40–50 ppb were observed in the emission plumes. Emission rates of ketene from the facility were estimated using a horizontal advective flux approach and ranged from 84–316 kg h−1. These emission rates were compared to the emission rates of major VOCs such as benzene, toluene, and acetaldehyde. Significant correlations (r2 > 0.7) of ketene with methanol, acetaldehyde, benzene, and toluene were observed for the peak emissions, indicating commonality of emission sources. The calculated average ketene OH reactivity for the emission plumes over Daesan ranged from 3.33–7.75 s−1, indicating the importance of the quantification of ketene to address missing OH reactivity in the polluted environment. The calculated average O3 production potential for ketene ranged from 2.98–6.91 ppb h−1. Our study suggests that ketene has the potential to significantly influence local photochemistry and therefore, further studies focusing on the photooxidation and atmospheric fate of ketene through chamber studies is required to improve our current understanding of VOC OH reactivity and hence, tropospheric O3 production.

The Influence of Submesoscales and Vertical Mixing on the Export of Sinking Tracers in Large-Eddy Simulations

We use idealized large-eddy simulations (LES) and a simple analytical theory to study the influence of submesoscales on the concentration and export of sinking particles from the mixed layer. We find that restratification of the mixed layer following the development of submesoscales reduces the rate of vertical mixing which, in turn, enhances the export rate associated with gravitational settling. For a neutral tracer initially confined to the mixed layer, subinertial (submesoscale) motions enhance the downward tracer flux, consistent with previous studies. However, the sign of the advective flux associated with the concentration of sinking particles reverses, indicating reentrainment into the mixed layer. A new theory is developed to model the gravitational settling flux when the particle concentration is nonuniform. The theory broadly agrees with the LES results and allows us to extend the analysis to a wider range of parameters.

Exploring the Synergies between Urban Overheating and Heatwaves (HWs) in Western Sydney

There is no consensus regarding the change of magnitude of urban overheating during HW periods, and possible interactions between the two phenomena are still an open question, despite the increasing frequency and impacts of Heatwaves (HW). The purpose of this study is to explore the interactions between urban overheating and HWs in Sydney, which is under the influence of two synoptic circulation systems. For this purpose, a detailed analysis has been performed for the city of Sydney, while considering an urban (Observatory Hill), in the Central Business District (CBD), and a non-urban station in Western Sydney (Penrith Lakes). Summer 2017 was considered as a study period, and HW and Non-Heatwave (NHW) periods were identified to explore the interactions between urban overheating and HWs. A strong link was observed between urban overheating and HWs, and the difference between the peak average urban overheating magnitude during HWs and NHWs was around 8 °C. Additionally, the daytime urban overheating effect was more pronounced during the HWs when compared to nighttime. The advective flux was found as the most important interaction between urban overheating and HWs, in addition to the sensible and latent heat fluxes.

Cumulative distribution function solutions of advection–reaction equations with uncertain parameters

We derive deterministic cumulative distribution function (CDF) equations that govern the evolution of CDFs of state variables whose dynamics are described by the first-order hyperbolic conservation laws with uncertain coefficients that parametrize the advective flux and reactive terms. The CDF equations are subjected to uniquely specified boundary conditions in the phase space, thus obviating one of the major challenges encountered by more commonly used probability density function equations. The computational burden of solving CDF equations is insensitive to the magnitude of the correlation lengths of random input parameters. This is in contrast to both Monte Carlo simulations (MCSs) and direct numerical algorithms, whose computational cost increases as correlation lengths of the input parameters decrease. The CDF equations are, however, not exact because they require a closure approximation. To verify the accuracy and robustness of the large-eddy-diffusivity closure, we conduct a set of numerical experiments which compare the CDFs computed with the CDF equations with those obtained via MCSs. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties of the two input parameters, such as their correlation lengths and variance of the coefficient that parametrizes the advective flux.

Simulation of Removal of MTBE in Groundwater by Biosparging

Biosparging is one of the effective in situ-technology to removal the organic contaminants. The experiments of removing MTBE by biosparging were carried out in a soil column. the results showed that there were the tailing of contaminants in the column without microorganism according with the microorganism. The removal of organic contaminants by biosparging was simulated by a mathematical model, which considered the advective flux, diffusion, mechanical dispersion, interphase mass transfer and biodegrade. The simulation results agreed with the experimental results well.