Different solutions of the diffusion equation and its applications

In this report, we solved the advection–diffusion equation under pollutants deposition on the ground surface, taking wind speed and vertical diffusion depend on the vertical height. Also, we estimated a simple diffusion model from point source in an urban atmosphere and the conservative material with downwind was evaluated. Then, we calculated the extreme ground-level concentration as a function of stack height and plume rise in two cases. Comparison between the proposed models and the emission from the Egyptian Atomic Research Reactor at Inshas had been done. Lastly, we discussed the results in this report.

Après-ski: The spread of coronavirus from Ischgl through Germany

The Austrian ski resort of Ischgl is commonly claimed to be ground zero for the diffusion of the SARS-CoV-2 virus in the first wave of infections experienced by Germany. Drawing on data for 401 German counties, we find that conditional on geographical latitude and testing behavior by health authorities, road distance to Ischgl is indeed an important predictor of infection cases, but – in line with expectations – not of fatality rates. Were all German counties located as far from Ischgl as the most distant county of Vorpommern-Rügen, Germany would have seen about 45 % fewer COVID-19 cases. A simple diffusion model predicts that the absolute value of the distance-to-Ischgl elasticity should fall over time when inter- and intra-county mobility are unrestricted. We test this hypothesis and conclude that the German lockdown measures have halted the spread of the virus.

A Simple Diffusion Model for Psychometric Analyses

The emergence of computer-based assessments has made response times, in addition to response accuracies, available as a source of information about test takers’ latent abilities. The predominant approach to jointly account for response times and accuracies are statistical models. Substantive approaches such as the diffusion model, on the other hand, have been slow to gain traction due to their unwieldy functional form. In the present work we show how a single simplifying assumption yields a highly tractable diffusion model. This simple diffusion model is straightforward to analyse using Gibbs sampling and can be readily extended with a latent regression framework. We demonstrate the superior computational efficiency of our model compared to the standard diffusion model in a simulation study and showcase the theoretical merit of our model in an example application.

Imaging light transport at the femtosecond scale

Paper, milk, clouds and white paint share a common property: they are opaque disordered media through which light scatters randomly rather than propagating in a straight path. For very thick and turbid media, indeed, light eventually propagates in a ‘diffusive’ way, i.e. similarly to how tea infuses through hot water. Frequently though, a material is neither perfectly opaque nor transparent and the simple diffusion model does not hold. In this work, we developed a novel optical-gating setup that allowed us to observe light transport in scattering media with sub-ps time resolution. An array of unexplored aspects of light propagation emerged from this spatio-temporal description, unveiling transport regimes that were previously inaccessibile due to the extreme time scales involved and the lack of analytical models.

Using Diffusion Model for Prediction and Optimization of Drying Process of Building Material

The aim of this chapter is to confirm the possibility of using the simple diffusion model to predict the behavior of a building material during the application of drying process under variable operating conditions. This approach can be considered as a simulation of the effect of the variable climatic conditions on the building material. During this research, the thermo-physical properties of the tested material as well as the drying air are considered as variable and changing with the operating conditions. Accordingly, diffusion coefficient is determined experimentally and is considered as variable with the temperature and the humidity and represented as function of the wet bulb temperature. Two sorts of conditions are tested: constant flux and convective flux. Furthermore, two types of changes are also tested: sudden changes and progressive changes of the drying conditions. The results of the study are mainly represented by the drying curves or the drying kinetics.

Complex genetic patterns in human arise from a simple range-expansion model over continental landmasses

Although it is generally accepted that geography is a major factor shaping human genetic differentiation, it is still disputed how much of this differentiation is a result of a simple process of isolation-by-distance, and if there are factors generating distinct clusters of genetic similarity. We address this question using a geographically explicit simulation framework coupled with an Approximate Bayesian Computation approach. Based on six simple summary statistics only, we estimated the most probable demographic parameters that shaped modern human evolution under an isolation by distance scenario, and found these were the following: an initial population in East Africa spread and grew from 4000 individuals to 5.7 million in about 132 000 years. Subsequent simulations with these estimates followed by cluster analyses produced results nearly identical to those obtained in real data. Thus, a simple diffusion model from East Africa explains a large portion of the genetic diversity patterns observed in modern humans. We argue that a model of isolation by distance along the continental landmasses might be the relevant null model to use when investigating selective effects in humans and probably many other species.

Use of radium isotopes to estimate mixing rates and trace sediment inputs to surface waters in northern Marguerite Bay, Antarctic Peninsula

In the western Antarctic Peninsula region, micronutrient injection facilitates strong plankton blooms that support productive food webs, unlike large areas of the low-productivity Southern Ocean. We use naturally occurring radioisotopes of radium to constrain rates of chemical fluxes into Ryder Bay (a small coastal embayment in northern Marguerite Bay), and hence to evaluate possible sources of sediment-derived micronutrients and estimate sediment-ocean mixing rates. We present the first coupled, short-lived radium isotope (223Ra and 224Ra) measurements from Antarctic waters, both present at very low activities (mean 0.155 and 3.21 dpm m-3, respectively), indicating much lower radium inputs than in other coastal environments. Longer-lived 228Ra activity was also lower than existing nearshore values, but higher than open ocean waters, indicating some degree of coastal radium input on timescales exceeding the week-to-month range reflected by 223Ra and 224Ra. Using a simple diffusion model along a shore to mid-bay transect, effective horizontal eddy diffusivity estimates ranged from 0.22–0.83 m2 s-1 from 223Ra and 224Ra, respectively, much lower than already-low mixing estimates for the Southern Ocean. Significant radium enrichment and much faster mixing (18 m2 s-1) was found near a marine-terminating glacier and consequently any sediment-derived micronutrient inputs in this location are more probably dominated by glacial processes than groundwater, land runoff, or marine sediment sources.

Evaluation of Aerosol Fire Extinguishing Agent Using a Simple Diffusion Model

Aerosol fire extinguishing agents have been recognized as an effective replacement of Halon. The uniform diffusion time and the effective concentration of the aerosol fire extinguishing agent are important parameters for putting out a fire. In this work, the effective concentration is derived based on the diffusion equation, and its variation with changing diffusion coefficient and diffusion time is analyzed. The uniform diffusion time could then be conveniently estimated using this equation. Based on experimental data, the concentration kinetics of the aerosol is drawn and the relation between the diffusion coefficient and the uniform diffusion time is analyzed. It was found that the uniform diffusion time is not dependent on the shape of the closed room but dependent on the total room volume and the position of its diffusion source. This model is demonstrated as a facile tool for the convenient evaluation and reasonable application of the aerosol fire extinguishing agent by predicting the uniform diffusion times of extinguishing aerosol in closed rooms.