diffusional model
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Given the importance of understanding long-term dynamics of radionuclides in the environment in general, and major gaps in the knowledge of 137Cs particulate forms in Chernobyl exclusion zone water bodies, three heavily contaminated water bodies (Lakes Glubokoe, Azbuchin, and Chernobyl NPP Cooling Pond) were studied to reconstruct time changes in particulate concentrations of 137Cs and its apparent distribution coefficient Kd, based on 137Cs depth distributions in bottom sediments. Bottom sediment cores collected from deep-water sites of the above water bodies were sliced into 2 cm layers to obtain 137Cs vertical profile. Assuming negligible sediment mixing and allowing for 137Cs strong binding to sediment, each layer of the core was attributed to a specific year of profile formation. Using this method, temporal trends for particulate 137Cs concentrations in the studied water bodies were derived for the first time and they were generally consistent with the semiempirical diffusional model. Based on the back-calculated particulate 137Cs concentrations, and the available long-term monitoring data for dissolved 137Cs, the dynamics of 137Cs solid–liquid distribution were reconstructed. Importantly, just a single sediment core collected from a lake or pond many years after a nuclear accident seems to be sufficient to retrieve long-term dynamics of contamination.

Abstract The Poisson–Nernst–Planck (PNP) diffusional model is a successful theoretical framework to investigate the electrochemical impedance response of insulators containing ionic impurities to an external ac stimulus. Apparent deviations of the experimental spectra from the predictions of the PNP model in the low frequency region are usually interpreted as an interfacial property. Here, we provide a rigorous mathematical analysis of the low-frequency limiting behavior of the model, analyzing the possible origin of these deviation related to bulk properties. The analysis points toward the necessity to consider a bulk effect connected with the difference in the diffusion coefficients of cations and anions (ambipolar diffusion). The ambipolar model does not continuously reach the behavior of the one mobile ion diffusion model when the difference in the mobility of the species vanishes, for a fixed frequency, in the cases of ohmic and adsorption–desorption boundary conditions. The analysis is devoted to the low frequency region, where the electrodes play a fundamental role in the response of the cell; thus, different boundary conditions, charged to mimic the non-blocking character of the electrodes, are considered. The new version of the boundary conditions in the limit in which one of the mobility is tending to zero is deduced. According to the analysis in the dc limit, the phenomenological parameters related to the electrodes are frequency dependent, indicating that the exchange of electric charge from the bulk to the external circuit, in the ohmic model, is related to a surface impedance, and not simply to an electric resistance.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. 2. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with p-branches leaving each vertex. Such trees are endowed with algebraic structure, the p-adic number fields. We apply theory of the p-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling dynamics on energy landscapes. To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing barriers. This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

The present work has the objective to study the water diffusion in the process of intermittent solar drying of mangabas. Osmotic dehydration (OD) pretreatment was performed in sucrose solution and the drying took place in a direct solar dryer with the fruits arranged in stainless steel screens, temperatures varying between 30 and 45°C along the day with peaks of 70°C. The period of intermittence was approximately 16 h reaching equilibrium after 6 days. The diffusional model based on the second Fick’s law was proposed for each of the daily drying periods of 360 minutes, considered that the process is controlled by internal diffusion, negligible external resistance, spherical geometry, shrinkage based on the average radius. The coefficients of effective diffusion (Def) obtained by using 4 terms of the infinite series, present values of Def ranging from 0.2 to 3.30x10-10 m2/s with R2≥ 0.868 and average relative deviations MRD≤10-2.