Kinetic Equation Research Articles

Polymerization Kinetics Optimization for Synthesizing Biobased Long Carbon‐Chain Polyamide Elastomers With Tunable Hardness and Mechanical Properties

ABSTRACTBiomass‐based long carbon‐chain polyamide elastomers (LCPAEs) have attracted widespread attention due to their favorable physical and mechanical properties, excellent flexibility, and good heat resistance, and so on. However, the precise structure and molecular weight control of long carbon‐chain polyamide (LCPA) hard segments remains underexplored, yet is pivotal for fabricating high‐performance LCAPEs. Herein, the effects of temperature and time on the polymerization of dicarboxylic‐terminated polyamide 1010 prepolymer (PA1010dC) are detailedly studied by end‐group titration technique, and the reaction kinetic equation of PA1010dC prepolymerization stage is established. By optimizing the polymerization process based on kinetic parameters, different PA1010dC with ideal chemical structures and molecular weights (ca. 500 ~ 2700 g·mol−1) is obtained. Subsequently, a series of LCPAEs with various wholly‐biobased hard segment (PA1010dC) contents are successfully prepared via polycondensation reaction with polytetramethylene ether glycol (PTMG) soft segments. The resulting LCPAEs show excellent comprehensive properties that can be tuned orientationally by varying the relative content of hard and soft segments. Their Shore hardness, tensile strength, and elongation at break can be varied within 20–55 D, 13–45 MPa, and 340%–1080%, respectively. This work provides a facile method for the efficient and stable preparation of LCPA hard segments and corresponding biomass LCPAEs.

Kinetic Equation Modeling-Guided Luminescence Modulation in Photochemical Afterglow.

Photochemical reaction-based afterglow has been widely applied in information storage, biodetection, and bioimaging. It is achieved through a cascade of photophysical processes and chemical reactions. However, comprehensive kinetic study of its complex processes remains limited. In this work, we conducted numerical simulations of the entire afterglow process based on chemical reaction kinetic equations, focusing on key kinetic processes and identifying the rate-determining step. By varying the rate constants of the key steps, we provided theoretical insights into effectively regulating the afterglow intensity and lifetime. Furthermore, we designed and synthesized several derivative molecules for experimental validation, achieving optimization of both intensity and lifetime. Through the integration of chemical kinetic analysis with experimental validation, this study develops an in-depth comprehension of complex kinetic processes and establishes a robust framework for molecular design in photochemical afterglow and related systems.

Theoretical Insights into the Racemization Kinetics of Helical Foldamers: Extended Chain Inhibits Propagation of Helical Reversal from One End to Another.

Helical foldamers have garnered significant attention recently with their unique chiral structures and diverse functionalities. However, their kinetic stability and racemization dynamics remain poorly understood. In this work, we introduced a novel model to describe the racemization of helical foldamers, deriving both general and approximated solutions to the kinetic equations. The general solution was in the double exponential form, while the approximated solution was in the single exponential form. The approximated solution clarified that the kinetic constant is in inverse proportion to the number of helical units (n). Analysis of the previously reported helical foldamers (o-phenylene oligomers and aromatic oligoamide) revealed that the two ends of the helical units are capped by the loose end domains. The theory suggests that the larger n stabilizes the helical structure because the fraction of the helical domain relative to the loose domain increases, and the multiple inversion barriers in the helical domain prevent the helical reversal from traveling from one end to the other.

Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted L ∞ spaces

Inspired by ideas stemming from the analysis of the Boltzmann equation, in this article, we expand the well-posedness theory of the spatially inhomogeneous 4-wave kinetic equation and also analyze an infinite hierarchy of PDEs associated with this nonlinear equation. More precisely, we show global in time well-posedness of the spatially inhomogeneous 4-wave kinetic equation for polynomially decaying small initial data. For the associated infinite hierarchy, we construct global in time solutions using the solutions of the wave kinetic equation and the Hewitt-Savage theorem. The uniqueness of these solutions is proved by using a combinatorial board game argument tailored to this context, which allows us to control the factorial growth of the Dyson series.

A geometric perspective on kinetic matter–radiation interaction and moment systems

In this paper, we provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the coupling of matter, described by the Boltzmann equation, and radiation, described by the radiation transport equation. We explore the transition from kinetic systems to their corresponding moment systems, provide a Hamiltonian description of such moment systems, and give a geometric interpretation of the moment closure problem for kinetic theories. As an application, we discuss in detail diffusion radiation hydrodynamics as an example of a pair bracket formulation on a space of moments corresponding to kinetic matter–radiation interaction. Additionally, using the variable moment closure framework of Burby [J. W. Burby, Variable-moment fluid closures with Hamiltonian structure, Sci. Rep. 13 (2023) 18286, doi:10.1038/s41598-023-45416-5], we show how to construct Hamiltonian moment closures for kinetic transport equations with arbitrary Hamiltonian. Using this general construction, we derive novel Hamiltonian moment closures for pure radiation transport.

Preparation of NaA Zeolite Composite Polyacrylonitrile Membranes (TiO2-NaA@PANMs) Doped with TiO2 and Adsorption Study of Sr2+

As a rarefied metallic element, strontium (Sr) is susceptible to significant environmental radioactive contamination risks during industrial mining and refining processes. In this study, NaA molecular sieves were prepared by alkali excitation using synthetic powders, which were homogeneously blended with the polyacrylonitrile (PAN) matrix, and nanoscale TiO2 reinforcing phases were introduced. Finally, composite separation membranes (TiO2-NaA@PANMs) with stable adsorption properties were constructed by electrostatic spinning technology. The micro-morphology and interfacial properties were characterized by SEM, XRD, and FT-IR systems. The adsorption experiments demonstrated that the equilibrium adsorption capacity of the system for Sr2+ reached 55.00 mg/g at the optimized pH = 6.0, and the theoretical saturated adsorption capacity at 298 K was 80.89 mg/g. The isothermal process conformed to the Langmuir’s model of monomolecular layer adsorption, and the kinetic behavior followed the quasi-secondary kinetic equation. Following three cycles of regeneration by elution with a 0.3 mol/L sodium citrate solution, the membrane material exhibited 81.60% Sr2+ removal efficacy. The composite membrane passages exhibited remarkable potential for utilization in engineering applications involving the treatment of complex nuclear wastewater.

A dynamic modeling and trajectory tracking control method for dual-arm mechanism for cabin docking

A new track tracking control method based on Lagrange dynamic equation is proposed. Firstly, the kinetic energy equation and potential energy equation of the left and right robotic arms are derived and calculated based on Lagrange function and the robot dynamics equation in the generalized coordinate system. The friction model of the left and right robotic arms is designed based on the Stribeck model, and the Lagrangian dynamic equation of the dual-arm mechanism for the hatch docking is established. Secondly, based on the Lagrange dynamic model, the collaborative control system of the docking mechanism is designed, and the backstepping sliding mode controller is designed and analyzed. A fuzzy backstepping sliding mode controller is designed to control the gain matrix β of the backstepping sliding mode controller by adjusting the output of the system with fuzzy logic, which further improves the robustness of the control system. Finally, the effectiveness of the design, dynamic modeling and control algorithm design of the cabin docking mechanism is verified by software simulation and real experiment. The experimental results show that the control method can realize the accurate tracking and control of the motion trajectory and velocity trajectory of the dual-arm mechanism, and has good robustness. The maximum absolute error and standard deviation of the axis Angle of the mobile cabin after docking are 0.501° and 0.004°, which can meet the requirements of the actual production process.

Removal of the phthalocyanine dye from acidic solutions using resins with the polystyrene divinylbenzene matrix

Two resins of polystyrene divinylbenzene matrix: the macroporous strong base Purolite A 500PS anion exchanger and hypercrosslinked non-functionalized Macronet MN 200 were proofed as suitable adsorbents for the removal of hazardous copper phthalocyanine dye – Acid Blue 249 (CuPc). The sorption isotherms and kinetics of CuPc in acidic aqueous solutions were investigated using batch experiments. The resins surface texture was evaluated using a scanning electron microscope. The FTIR study of unloaded and CuPc dye loaded resins identified the functional groups of resins and dye anion and the specific sorption mechanisms: ion exchange in participation of the protonated quarternary amino groups of Purolite A 500P and the electrostatic interaction in participation of the fenolic groups of Macronet MN 200. The kinetic data were correlated with intraparticle diffusion and the pseudo-second order kinetic equations. The activation energies such as intraparticle diffusion (Ea–ki) and chemical sorption (Ea–k2) were calculated using the Arrhenius relationship. The CuPc dye sorption on Purolite A 500PS is limited by the intraparticle diffusion, whereas sorption on Macronet MN 200 is limited by the intraparticle diffusion depending on pore size distribution and on the boundary layer thickness.Purolite A 500PS is substantially more effective for the sorption of CuPc dye than Macronet MN 200. The amount of CuPc dye sorbed at equilibrium on Purolite A 500PS and on Macronet MN 200 was 86.9 μmol/g and 2.3 μmol/g, respectively.

Analytical and Geometric Foundations and Modern Applications of Kinetic Equations and Optimal Transport

We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like structures in probability spaces, resolves degeneracies inherent in kinetic operators. Centered around the Boltzmann and Fokker–Planck equations, we derive sharp exponential convergence estimates under minimal regularity assumptions, improving on prior methods by incorporating Wasserstein gradient flow techniques. Our framework is further applied to the study of hydrodynamic limits, collisional relaxation in magnetized plasmas, the Vlasov–Poisson system, and modern data-driven algorithms, highlighting the central role of entropy as both a physical and variational tool across disciplines. By bridging entropy dissipation, optimal transport, and geometric analysis, our work offers a new perspective on stability, convergence, and structure in high-dimensional kinetic models and applications.

Modification of the Eddy Viscosity Based on the Wall Law at Adverse Pressure Gradient

This paper presents an attempt to enhance the predictive accuracy of the k−ω-type Reynolds-averaged Navier–Stokes turbulence model for adverse pressure gradient (APG) flows. The approach is grounded in refining the wall law governing the mean velocity profile within the inner layer of the turbulent boundary layer (TBL) under APG conditions. Drawing insights from direct numerical simulations (DNS), the wall law has been modified to maintain good consistency with the mean velocity profile provided by DNS data in flows with strong nonequilibrium effects. Further theoretical analysis shows that the analytical solutions of turbulent quantities satisfying the wall law under APG cannot satisfy the turbulent kinetic energy transport equation (k-equation). Based on the analysis, an approximate solution for the eddy viscosity coefficient (νt) that complies with the k-equation in flows with slight APG to correct νt in APG flows is proposed. Leveraging this approximate solution, the eddy viscosity in the shear stress transport model has been modified. The resultant modification induces an elevation of the mean velocity profile within the inner layer of the TBL at APG, leading to augmentation of the skin-friction coefficient.

A facile approach to lignin-based biochar derived from black liquor and the study of its removal to tetracycline from water.

A facile approach to lignin-based biochar derived from black liquor and the study of its removal to tetracycline from water.

Short-time character of corrections to the generalized Kadanoff–Baym Ansatz

An approximation of the Green function based on the Generalized Kadanoff–Baym Ansatz and its correction is tested on the electron tunneling through a single atom, incorporating the on-site second-order Born interaction. Time evolution resulting from the corresponding kinetic equation for the density matrix is compared with the direct solution of the non-equilibrium Green functions. It is demonstrated that the short-time nature of corrections beyond the Generalized Kadanoff–Baym Ansatz enables their effective numerical approximation.Graphical abstract

Propagation of moments and regularity for the Vlasov-Maxwell-Bopp-Podolsky model and its Pauli-Villars type generalizations

. We consider a class of hyperbolic systems that can be interpreted as approximations of the relativistic Vlasov-Maxwell system. These equations are derived by taking into account radiation-reaction effects occurring at a microscopic level. They involve a small length ℓ ∈ R + ∗ , called the Bopp-Podolsky parameter. In this context, we address common issues in kinetic equations, such as the propagation of moments, regularity properties, and well-posedness. We also investigate semiclassical limits appearing when ℓ goes to zero.

Nonlinear Magnetic Response Measurements in Study of Magnetic Nanoparticles Uptake by Mesenchymal Stem Cells

Stem cells therapies offer a promising approach in translational oncology, as well as in regenerative medicine due to the tropism of these cells to the damage site. To track the distribution of stem cells, the latter could be labeled by MRI-sensitive superparamagnetic (SPM) iron oxide nanoparticles. In the current study, magnetic properties of the magnetic nanoparticles (MNPs) incorporated into the bone marrow-derived fetal mesenchymal stem cells (FetMSCs) were evaluated employing nonlinear magnetic response measurements. Synthesized dextran-coated iron oxide nanoparticles were additionally characterized by X-ray diffraction, transmission electron microscopy, and dynamic light scattering. The MNP uptake by the FetMSCs 24 h following coincubation was studied by longitudinal nonlinear response to weak alternating magnetic field with registration of the second harmonic of magnetization. Subsequent data processing using a formalism based on the numerical solution of the Fokker–Planck kinetic equation allowed us to determine magnetic and dynamic parameters and the state of MNPs in the cells, as well as in the culture medium. It was found that MNPs formed aggregates in the culture medium; they were absorbed by the cells during coincubation. The aggregates exhibited SPM regime in the medium, and the parameters of the MNP aggregates remained virtually unchanged in the cells, indicating the preservation of the aggregation state of MNPs inside the cells. This implies also the preservation of the organic shell of the nanoparticles inside FetMSCs. The accumulation of MNPs by mesenchymal stem cells gradually increased with the concentration of MNPs. Thus, the study confirmed that the labeling of MSCs with MNPs is an effective method for subsequent cell tracking as incorporated nanoparticles retain their magnetic properties.

Research on the Stability and Marginal Habitat Effect of Agro-ecosystems Based on the Logistic Model

The paper constructed a model of the food web underlying a new agro-ecosystem. It reflected the changes in the population size of various organisms through a new model formed by partially adjusting the logistic model, and then optimized the population trends of multiple populations through a multi-objective optimization algorithm and hierarchical analysis, and ultimately selected the most reasonable population allocation scheme in the agro-ecosystem in order to maintain the stability of the agro-ecosystem. The paper found that the use of chemicals was not the most important factor in agro-ecosystem stability. In addition, the paper assumed the introduction of species 1 (herbivore) and species 2 (predator), and constructed the kinetic equations for the changes in the populations of plants, insects, species 1, and species 2, respectively, through logistic modeling, and after data review as well as quantification obtained a visual representation of the changes in crop health over time. The paper found that reasonable application of marginal habitat effect can reduce pest populations, improve soil health, increase plant reproduction with ecological diversity and stability, and contribute to environmental protection, with a fast growth rate in crop yields, and superior long-term economic benefits.

Adsorption isotherms, thermodynamics, and kinetics of activated carbon as adsorbent to water pollutants: a review

Water pollutants, such as dyes and heavy metals, which cause various health and environmental problems, challenge researchers to investigate activated carbon-based adsorbents. These adsorbents are obtained from natural sources or waste, so they are environmentally friendly. The literature reveals that the adsorption capacities of activated carbons obtained from experiments, isotherm equations, and kinetic equations are relatively high but vary in value. The abundance of functional groups as active sites and the spread of pores or cavities on the adsorbent surface affect the efficiency of adsorption. This review aims to overview the adsorption isotherms, thermodynamic properties, and kinetic behaviors of several activated carbons from natural sources and waste. The maximum adsorption capacity of the dyes is in the range of 2.0–1169.25 mg∙g–1, while the maximum adsorption capacity of heavy metals is in the range of 0.488–312.5 mg∙g–1. The different adsorption mechanisms, the convenience of adsorption, adsorption energy, the spontaneity of adsorption, and the rate-determining step are described for each type of activated carbon. Therefore, specified information about their performances toward different water pollutants can be evaluated. Moreover, potential improvements in the performance of existing adsorbents can be gained through further research based on the findings of this review.

Residue Patterns and Dietary Risk Assessment of Picarbutrazox and Its Metabolite TZ-1E in a Ginseng Planting System.

This study established a simple, sensitive, and rapid method for the residual analytical method of picarbutrazox and its metabolites (E)-picarbutrazox (TZ-1E) in ginseng plants, fresh ginseng, and dried ginseng. The samples were extracted and purified using an improved QuEChERS method and determined by HPLC-MS/MS. The linear relationship of the method was good (R2 ranging from 0.9935 to 0.9999), the limit of detection was 7.19 × 10-5 to 1.65 × 10-3 ng, the limit of quantitation was 0.01 mg/kg, the intra- and interday addition recovery rates ranged from 87.33 to 107.2%, and the relative standard deviation range was 0.58-8.21%. This method was applied to detect residual samples in the field. The results showed that the degradation of picarbutrazox in ginseng plants followed first-order kinetic equations; the R2 values were 0.9293 and 0.9430, and the half-lives (t1/2) were 8.24 and 11.5 d, respectively. It was an easily degradable pesticide (t1/2 < 30 d). The final residual levels of picarbutrazox in ginseng plants, fresh ginseng, and dried ginseng ranged from 0.0184 to 19.223 mg/kg. A dietary risk assessment was conducted based on the final residual levels of picarbutrazox in fresh and dried ginseng, and the results showed that the chronic exposure risk quotient values of both fresh and dried ginseng were less than 100% (0.1303% for both fresh and dried ginseng). This indicated that the dietary risk of using 10% picarbutrazox suspension concentrate in ginseng was very low and did not pose an unacceptable risk to public health. The results of this study can provide a basis for the development of maximum residue limit for picarbutrazox in ginseng.

Relativistic approach to manipulating angular distribution of charged particles via kinetic equations

Deflection angles of charged particles interacting with materials play a critical role in various plasma applications. The development of a mathematically well-posed kinetic collision operator that accounts for deflection angles of strong Coulomb interactions remains a fundamental open problem. This paper presents a relativistic method for modifying the electromagnetic field in an anisotropic and adjustable manner to manipulate a system of charged particles, specifically by the transfer of angular momentum from a superluminal wave source to particles at specific times and locations. The method provides a mechanism to influence the scattering outcomes of strong interactions by manipulating the angular distribution of particles, and thus the deflection angles of their interactions with a solid surface, without requiring detailed knowledge of the kinetic collision operator. To this end, we demonstrate how a specific type of singularity, generated by Maxwell's equations for a superluminal wave source at the boundary of the plasma, can modify the electromagnetic field in a highly directional manner. The proposed method can lead to the development of novel approaches for controlling interactions of charged particles with a material in plasma systems. Published by the American Physical Society 2025

Comparing of Using Different Systems of Kinetic Equations for Numerical Simulation of Deflagration Initiation in Hydrogen-Air Mixtures Flows

Comparing of Using Different Systems of Kinetic Equations for Numerical Simulation of Deflagration Initiation in Hydrogen-Air Mixtures Flows

Calorimetric Monitoring of the Sub-Tg Crystal Growth in Molecular Glasses: The Case of Amorphous Nifedipine.

Non-isothermal differential scanning calorimetry (DSC) and Raman microscopy were used to study the crystallization behavior of the 20-50 μm amorphous nifedipine (NIF) powder. In particular, the study was focused on the diffusionless glass-crystal (GC) growth mode occurring below the glass transition temperature (Tg). The exothermic signal associated with the GC growth was indeed directly and reproducibly recorded at heating rates q+ ≤ 0.5 °C·min-1. During the GC growth, the αp polymorphic phase was exclusively formed, as confirmed via Raman microscopy. In addition to the freshly prepared NIF samples, the crystallization of the powders annealed for 7 h at 20 °C was also monitored-approx. 50-60% crystallinity was achieved. For the annealed NIF powders, the confocal Raman microscopy verified a proportional absence of the crystalline phase on the sample surface (indicating its dominant formation along the internal micro-cracks, which is characteristic of the GC growth). All DSC data were modeled in terms of the solid-state kinetic equation paired with the autocatalytic model; the kinetic complexity was described via reaction mechanism based on the overlap of 3-4 independent processes. The kinetic trends associated with decreasing q+ were identified, confirming the temperature-dependent kinetic behavior, and used to calculate a theoretical kinetic prediction conformable to the experimentally performed 7 h annealing at 20 °C. The theoretical model slightly underestimated the true extent of the GC growth, predicting the crystallinity to be 35-40% after 7 h (such accuracy is still extremely good in comparison with the standard kinetic approaches nowadays). Further research in the field of kinetic analysis should thus focus on the methodological ways of increasing the accuracy of considerably extrapolated kinetic predictions.