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This paper investigates the fast chemical diffusion limit from a parabolic-parabolic Keller-Segel system to the corresponding parabolic-elliptic Keller-Segel system by constructing approximate solutions with an appropriate order via an asymptotic expansion. Nonlinear stability of the precise initial layer is characterized with an exact convergence rate by using basic energy method.

The chemical diffusion coefficient in LiNi 1/3 Mn 1/3 Co 1/3 O 2 was determined via the galvanostatic intermittent titration technique in the voltage range 3 to 4.2 V. Calculated diffusion coefficients in these layered oxide cathodes during charging and discharging reach a minimum at the open-circuit voltage of 3.8 V and 3.7 V vs. Li/Li + , respectively. The observed minima of the chemical diffusion coefficients indicate a phase transition in this voltage range. The unit cell parameters of LiNi 1/3 Mn 1/3 Co 1/3 O 2 cathodes were determined at different lithiation states using ex situ crystallographic analysis. It was shown that the unit cell parameter variation correlates well with the observed values for chemical diffusion in NMC cathodes; with a notable change in absolute values in the same voltage range. We relate the observed variation in unit cell parameters to the nickel conversion into the trivalent state, which is Jahn-Teller active, and to the re-arrangement of lithium ions and vacancies.

This paper presents an advanced simulation-based investigation of tumor growth and chemical diffusion in biological tissues, using ϑ-fractional stochastic integral equations. Based on the theoretical framework developed in [Fractal Fract. 2025, 9(1), 7], we develop an innovative computational model to explore the practical applications of these equations in the biological field. The model focuses on providing new insights into the dynamic interaction between stochastic effects of a fractional nature and complex biological tissue environments, contributing to a deeper understanding of the mechanisms of chemical diffusion within tissues and tumor growth under different conditions. The paper details the numerical techniques used to solve the ϑ-fractional stochastic integral equations, focusing on the stability and accuracy of the solutions, while demonstrating their ability to accurately and effectively capture key biological phenomena. Through extensive computational experiments, the model demonstrates its ability to replicate realistic tumor growth patterns and complex chemical transport dynamics, providing a powerful and flexible tool for understanding tumor behavior and interaction with potential therapies. These results represent an important step toward improving biological models and enhancing biomedical applications, particularly in the areas of targeted drug design and analysis of tumor dynamics under chemotherapeutic influence.

The oxygen chemical diffusion coefficient in (U, Pu)O2-x was determined by thermo-gravimetry as functions of the Pu content, oxygen-to-metal ratio and temperature. The surface reaction was considered in the diffusion coefficient determination. The activation energy for the chemical diffusion coefficient was 60 kJ/mol and 65 kJ/mol, respectively, in (U0.8Pu0.2)O2-x and (U0.7Pu0.3)O2-x.

The model explaining the occurrence of the electron concentration step front during oxidation of nitrogen-doped TiO2-δ thin films is presented. This model is based on ambipolar chemical diffusion coefficient analysis, for which immobile and uniformly distributed nitrogen component is assumed. The diffusion species and oxygen activity (pressure) profiles are obtained by numerical and approximate analytical simulation of the chemical diffusion. The profiles indicate the presence of two separate singularities: the electron concentration step front, and the electron-hole recombination reaction front. The electron concentration step front relates to the singularity of the ambipolar diffusion of three types of charged species with essentially different diffusion coefficients.

This is a theoretical study of species profiles during the oxygen chemical diffusion in an acceptor doped oxide crystal driven by large changes in the ambient oxygen partial pressure. The oxide crystal containing three species: mobile oxygen vacancy, mobile electron, immobile dopant ion, is considered. Our analysis is based on the expression of the chemical diffusion coefficient obtained in the framework of the concept of conservative ensembles (Maier J., 1993). It is shown that the dependence of chemical diffusion coefficient on ambient oxygen partial pressure in double-logarithmic coordinates is divided into distinct intervals. For each pressure interval the chemical diffusion equation is reduced to the diffusion equation with a diffusion coefficient which exhibits a power dependence on concentration. First, we analyzed the chemical diffusion under pressure inside each interval. As a result two singularities on the species diffusion profiles can be found: an internal reaction diffusion front, and an ambipolar diffusion front. This ambipolar diffusion front is characterized by a step of the electron concentration, moving inside a specimen. Afterwards, we consider a crystal in which the range of partial pressure spans all considered pressure intervals.

The chemical diffusion coefficients of lithium ion ( DLi+ ) in Li1 + xVPO4F (0 ≤ x ≤ 2) between 3.0 and 0.01 V are systematically analyzed by cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), and galvanostatic intermittent titration technique (GITT). The results indicate that the DLi+ values depend heavily on the voltage state. Based on the results from EIS and GITT, the diffusion coefficients ( DLi+ ) measured in a single-phase region below 1.7 V have relatively steady values of about 10−9 (EIS) and 10−10 (GITT) cm2 s−1, respectively, while the DLi+ values in the single-phase region above 1.9 V decrease rapidly from 10−9 to 10−11 cm2 s−1 due to concentration of lithium ions in the bulk LiVPO4F. The Li+ chemical diffusion coefficients measured in the two-phase region by GITT range a lot from 10−9 to 10−14 cm2 s−1, while the DLi+ values in the two-phase region determined by CV are around 10−10 cm2 s−1. By the GITT, the DLi+ values in the two-phase region vary in non-linear shape with the charge–discharge voltage, which is ascribed to strong interactions of Li+ with other ions.

Low-grade heat accounts for >50% of the total dissipated heat sources in industries. An efficient recovery of low-grade heat into useful electricity not only reduces the consumption of fossil-fuels but also releases the subsequential environmental-crisis. Thermoelectricity offers an ideal solution, yet low-temperature efficient materials have continuously been limited to Bi 2 Te 3 -alloys since the discovery in 1950s. Scarcity of tellurium and the strong property anisotropy cause high-cost in both raw-materials and synthesis/processing. Here we demonstrate cheap polycrystalline antimonides for even more efficient thermoelectric waste-heat recovery within 600 K than conventional tellurides. This is enabled by a design of Ni/Fe/Mg 3 SbBi and Ni/Sb/CdSb contacts for both a prevention of chemical diffusion and a low interfacial resistivity, realizing a record and stable module efficiency at a temperature difference of 270 K. In addition, the raw-material cost  to the output power ratio in this work is reduced to be only 1/15 of that of conventional Bi 2 Te 3 -modules. Thermoelectric materials for low-grade heat recovery applications are limited to Bi 2 Te 3 -based alloys containing expensive Te for decades. Here, the authors demonstrate on a module level, cheap antimonides could enable an efficiency not inferior to that of expensive tellurides.

Subseafloor microbial activities are central to Earth’s biogeochemical cycles. They control Earth’s surface oxidation and major aspects of ocean chemistry. They affect climate on long timescales and play major roles in forming and destroying economic resources. In this review, we evaluate present understanding of subseafloor microbes and their activities, identify research gaps, and recommend approaches to filling those gaps. Our synthesis suggests that chemical diffusion rates and reaction affinities play a primary role in controlling rates of subseafloor activities. Fundamental aspects of subseafloor communities, including features that enable their persistence at low catabolic rates for millions of years, remain unknown. Subseafloor microbial activities are central to global biogeochemical cycles, affecting Earth’s surface oxidation, ocean chemistry, and climate. Here the authors review present understanding of subseafloor microbes and their activities, identify research gaps, and recommend approaches to fill those gaps.

Volumetric additive manufacturing techniques are a promising pathway to ultra-rapid light-based 3D fabrication. Their widespread adoption, however, demands significant improvement in print fidelity. Currently, volumetric additive manufacturing prints suffer from systematic undercuring of fine features, making it impossible to print objects containing a wide range of feature sizes, precluding effective adoption in many applications. Here, we uncover the reason for this limitation: light dose spread in the resin due to chemical diffusion and optical blurring, which becomes significant for features ⪅0.5 mm. We develop a model that quantitatively predicts the variation of print time with feature size and demonstrate a deconvolution method to correct for this error. This enables prints previously beyond the capabilities of volumetric additive manufacturing, such as a complex gyroid structure with variable thickness and a fine-toothed gear. These results position volumetric additive manufacturing as a mature 3D printing method, all but eliminating the gap to industry-standard print fidelity.