The generalized hydrodynamic framework for the Sawada-Kotera equation and its kinetic equations

String cavitation in injector nozzles has been shown to improve spray atomization while mitigating cavitation erosion. Herein, to comprehensively investigate flow behaviors under realistic engine conditions, we employ a validated computational fluid dynamics model to simulate coupled in-nozzle wall-bounded cavitation flow and near-nozzle spray flow. The characteristics of multiphase flow are extracted using the Omega vortex identification method and Lamb vector analysis. Under nine sets of representative operating conditions, injection performance is assessed using flow coefficient, total pressure recovery coefficient, vapor phase distribution, and kinetic energy transport equation. Near-nozzle spray behavior is evaluated based on the momentum flux, liquid breakup rate, and vorticity transport equation. The results indicate that the high-disturbance nozzle has good application prospects and exhibits a flow coefficient of 0.7–0.8, whereas the total pressure recovery coefficient varies between 0.6 and 0.7. Optimal injection performance is observed under conventional conditions, whereas atomization quality is enhanced under idle conditions. Additionally, cylinder pressure causes jet momentum attenuation under accelerating conditions and considerably affects the development of string cavitation in the jet core under idle and normal conditions, forming bidirectional tearing and one-way tearing of liquid film with different vorticity transport terms, thus affecting the atomization process.

Kinetic equation of water electrolysis at HER in SOEC systems determined from molecular modelling

Optimizing particle beam thermoradiotherapy is hindered by the lack of methods to quantify the biological effects of temporal temperature changes. This study proposes the "dynamic Temperature-dependent Stochastic Microdosimetric Kinetic (TSMK) model," which extends the conventional TSMK model to account for temporal temperature changes, and assesses its capability to predict cell survival by incorporating the temporal dynamics of hyperthermia (HT) after irradiation.
Approach. We hypothesized that the kinetic parameters of the TSMK model hold valid at any given moment, even under time-varying temperature conditions. Based on this, we solved the kinetic differential equations for radiation damage to derive a formula for cell survival dependent on the temporal conditions of HT. To evaluate the dynamic TSMK model, we used survival data from human glioblastoma A-172/neo and A-172/mp53 cells irradiated with X-rays or carbon ions with varying HT durations, and human gastric adenocarcinoma MKN-45 cells irradiated with fast neutrons with varying intervals between irradiation and HT. Model parameters were fitted to the experimental results for each cell line to evaluate the model's accuracy. Subsequently, we estimated how the relationship between HT duration and cell survival changes with absorbed dose and the time interval between irradiation and HT.
Main Results. The dynamic TSMK model successfully reproduced cell survival fractions across varying HT durations and intervals relative to irradiation. The study demonstrated the model's ability to estimate the time window for synergistic effects of combined HT and radiation. Model calculations predicted that the degree of synergy and this time window vary significantly with radiation conditions.
Significance. The dynamic TSMK model is the first biophysical model to quantitatively estimate cell survival fraction in particle beam thermoradiotherapy under time-varying temperatures. Providing a theoretical foundation for these biological effects, this model offers a potential tool for treatment planning systems to optimize thermoradiotherapy.
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Glycidyl azide polymer (GAP)-based polyurethane, a kind of energetic thermoplastic elastomer (ETPE), is a promising binder for advanced solid propellants, but its thermal decomposition involves overlapping competitive reactions that conventional single-step kinetic models cannot characterize accurately, limiting its engineering applications. To address this limitation, a constrained asymmetric Gaussian deconvolution strategy with fixed peak area ratios and shape constraints was developed in this work. This strategy was applied to resolve overlapping reaction rate curves converted from derivative thermogravimetric data of GAP-based ETPEs with 50 wt% GAP content at four heating rates of 5, 10, 15 and 20 K·min-1. The complex decomposition process was successfully split into five stages, assigned to azide cleavage, polyether backbone scission, carbamate cleavage, hydrocarbon product degradation and residue decomposition, with a goodness of fit of R2 > 0.998. Apparent activation energies of the five stages were determined through cross-validation by the Friedman and Flynn-Wall-Ozawa methods without prior assumption of reaction mechanisms, following the order of residue decomposition (181.4 ± 1.0 kJ·mol-1) > hydrocarbon product degradation (159.9 ± 1.0 kJ·mol-1) ≈ azide cleavage (156.5 ± 0.6 kJ·mol-1) > backbone scission (135.1 ± 0.7 kJ·mol-1) > carbamate cleavage (111.9 ± 1.1 kJ·mol-1). Pre-exponential factors with lnA0 values ranging from 22.2 to 34.0 were derived via the kinetic compensation effect. Finally, generalized master plots were employed to compare with classic solid-state reaction models for mechanistic insight, and the Šesták-Berggren model fit three major stages excellently (R2 > 0.996) by accounting for synergistic nucleation-growth and phase boundary mechanisms, enabling high-precision kinetic equations. It should be noted that the constrained deconvolution method proposed in this work has general applicability for kinetic analysis of GAP-based ETPEs with different formulations and other complex energetic polymer systems, while the obtained kinetic parameters are composition-specific and only applicable to the corresponding ETPE formulation studied herein.

For much of the 20th century, enzyme kinetic analysis relied on deriving simplified rate equations under the steady-state approximation and later by analytical integration of differential equations for transient kinetics. This approach has since been surpassed by computational methods using numerical integration of rate equations to directly fit experimental data based on a complete user-defined model. This paradigm shift removes the constraints imposed by solving analytical equations, enabling far greater flexibility in experimental design and model complexity. Modern global fitting methods allow data from diverse experiments to be analyzed simultaneously using the minimum number of parameters supported by the information content of the data set. Global data fitting is more than just an algorithm for data analysis─it represents a fundamental change in how we design and interpret experiments, and eliminates many of the restrictions, approximations, and ambiguities inherent to equation-based analyses. In this review, we describe the principles and practice of global data fitting, compare the outcomes to conventional equation-based methods, and demonstrate its power through examples involving multiple experiments with distinct conditions and readouts. We explain why the common practice of making measurements in triplicate introduces uncertainty and we outline advanced methods for rigorously estimating errors in measurement and for establishing robust confidence limits on fitted parameters.

Dysphagia is common among older adults and frequently necessitates the use of thickening agents to facilitate safe swallowing of medicines, which may in turn alter their bioavailability. This study investigated the impact of two commercially available lubricants—Gloup® Forte and extremely thick water—on the in vitro dissolution behaviour of immediate-release gliclazide tablets. Dissolution studies were conducted using crushed and whole tablets in different media consisting of reverse osmosis water, phosphate buffer (pH 6.8), and 0.1 N HCl at 37 °C. Dissolution profiles were compared using similarity factor (f2) analysis and modelled using established kinetic equations. Gliclazide dissolution was significantly delayed in the presence of Gloup® Forte across all media for both crushed and whole tablets, with f2 values below 50, indicating dissimilar profiles. Dissolution kinetics confirmed that mixing the formulated gliclazide with Gloup® Forte delayed the release and reduced the dissolution rate constant for drug from both crushed and whole gliclazide tablets in media studied.

With the aim of exploring chemical systems that may undergo metallization when irradiated with hard X-rays, we selected silver acetate (AgC2H3O2) for the study. X-ray-induced decomposition of silver acetate under ambient and high-pressure conditions was observed in a diamond anvil cell (DAC), leading to the formation of metallic nanograins of silver at ambient pressure and 1.65 GPa. At 4 GPa, no decomposition was observed. The Avrami kinetics equation also provides information about novel structural formation at ambient pressure and 1.65 GPa. By modeling of the XRD data, it was found that the size of the silver nanocrystallites formed at 1.65 GPa pressure steadily increased to ∼5 nmafter 600 min of X-ray irradiation as determined by applying the Scherrer equation to the diffraction peak widths. Time-resolved X-ray diffraction (XRD) revealed pressure-dependent kinetics, demonstrating that coupling pressure with irradiation enables controlled photochemical pathways in this model system. Concurrent with previous studies, the application of high pressure (HP) can be considered as a means of controlling X-ray synthetic photochemistry.

An explicit conservative finite volume scheme based on multi-scale characteristic lines is proposed for the simulation of advection and convection in fluid flows. By representation of the Navier–Stokes equation in a kinetic manner, the evolution of particle distribution functions on discrete velocity space is governed by the kinetic advection equation. The control equation is discretized and integrated along particle velocity characteristic lines via a temporal/spatial related reconstruction to obtain accurate macroscopic fluxes. With a D2Q37 lattice velocity model, the collision processes are modeled by a relaxation term expressed with Hermite expansion to reduce complexity and computational cost. Several cases, including the Sod shock tube case, lid-driven cavity flows, and natural convection flows on Rayleigh numbers of 103–106, Rayleigh–Bénard convection flows on Rayleigh numbers of 104–106 and Rayleigh–Taylor instability on the Reynolds number of Re = 62 990 are simulated and analyzed. Simulation results show satisfactory accuracy with a relative L2-norm error less than 1% as compared with benchmark data, and reveal several steady and unsteady mechanisms, including advection in the Riemann problem, buoyancy-driven motion, temperature-driven mass transfer, interface dynamical behaviors, and vortex evolution in convective flows.

We study vacuum polarization due to strong fields, in the presence of an electron-positron plasma. For this purpose, we expand quantum kinetic equations using weak fields and slow temporal scales as expansion parameters. It is demonstrated that the evolution of the Dirac field can be described by classical-like distribution functions for electrons and positrons, which are weakly coupled through quantum interactions. Furthermore, we deduce that these coupling terms give rise to well-known expressions for vacuum polarization, in addition to quantum modifications proportional to the content of real particles. Depending on the initial plasma density, the dominant quantum corrections to classical evolution may arise from real particle couplings or from the vacuum polarization associated with virtual particles. The implications of our results are discussed.

The work is devoted to the study and analysis of finite element (FE) calculations performed by a large cycle of computational experiments of plate deformation with a section under steady-state creep conditions, which revealed a power-law self-similar distribution of the continuity function (damage) and stress components in the immediate vicinity of the tip of the section at the second and third stages of creep in a damaged medium in a related formulation of the problem, when the continuity parameter is included in the constitutional relations. The FE computations of stress fields and continuity near the tip of the defect were carried out using the powerful SIMULIA Abaqus platform using the UMAT utility, which integrates the process of damage development into the computational scenario of the finite element method (FEM). The paper implements computer modeling of uniaxial stretching of a plate weakened by a central horizontal section or an inclined section in creep mode, in which computational algorithms include damage growth that progresses over time according to the classical mechanical model of damage growth by Kachanov–Rabotnov according to a power law for various values of exponents of the kinetic equation and the power determining equation with the concept of true tension in a related formulation. Numerical study and analysis of the obtained FE representations of stress and continuity fields in the vicinity of the crack tip for a number of material constants clearly reveals a self-similar distribution of stress fields and damage near the tip of a power-type defect. The structure of the solution is revealed and the values of the exponents in the self-similar variable and the self-similar representation of the solution are found, which can be interpreted as an intermediate self-similar solution of the second type according to the classification of G.I. Barenblatt. It is shown that the discovered self-similar property of the solution can be interpreted as self-similar asymptotics of the far field of continuity and stresses. Also, the stress dependences extracted from FEM calculations on the distance from the tip of the incision, reproduced in double logarithmic coordinates, clearly demonstrate the asymptotic behavior corresponding to the near-field stress, characterized by the complete absence of a singularity in the immediate vicinity of the tip of the incision.

Analysis of Coupled Steady Navier-Stokes and Turbulent Kinetic Energy Equations with Velocity-Dependent Boundary Conditions

The recombination coefficient of hydrogen plasma using the six thermal hydrogen species in the afterglow condition was analyzed through MATLAB computational modeling to determine the logarithmic density, and then to determine the difference between conduction and convection. This study aims to model the dynamics of recombination and determine the recombination coefficients of hydrogen species against temperature variations. This modeling was carried out using zero-dimensional chemical kinetic equations derived from the continuity equation, namely the reaction rate calculated using modified Arrhenius. This modeling is integrated numerically using the Runge-Kutta method. The density results of hydrogen species show a consistent decrease in temperature variation related to the ideal gas law, but the recombination coefficient increases with increasing temperature. This upward trend indicates that there is a dominance of three-body recombination processes over atmospheric pressure and afterglow conditions.

Argillaceous slate exhibits distinct disintegration characteristics during the interaction between water and rock. To investigate the disintegration of argillaceous slate, its macroscopic disintegration characteristics were examined through disintegration resistance tests. The mineral types and contents of the rock samples were determined using X-ray diffraction, while microstructural evolution during disintegration was analyzed via scanning electron microscopy. Nuclear magnetic resonance was employed to explore the mesoscopic mechanisms of argillaceous slate disintegration. A nonlinear dynamic equation was formulated based on nonlinear dynamics theory to quantitatively characterize the disintegration process of argillaceous slates under water-rock interaction. The results indicate that: 1) The disintegration process of argillaceous slate exhibits staged characteristics, with crack development categorized into three distinct stages. 2) During disintegration, the microstructure of argillaceous slate transitions to a more porous and loose state, as evidenced by the detachment of local flakes from the sample, the accumulation of flakes on the surface, and the formation of numerous pores. As the duration of water immersion increases, the internal pore radius of the argillaceous slate expands, leading to a continuous increase in the proportion of larger-sized pores. 3) The micro-scale fracture surface area of argillaceous slate increases with prolonged soaking time and shows a negative correlation with the anti-disintegration index. 4) Predictions derived from the nonlinear kinetic equation align well with the experimental data, demonstrating the equation's effectiveness in modeling the disintegration of argillaceous slates under the nonlinear quantification of water-rock interactions. The research results can provide a reference for the research and treatment of soft rock disintegration.

It is shown that the Hamiltonian formalism proposed previously in Ref. 1 to describe the nonlinear dynamics of only soft fermionic and bosonic excitations contains much more information than initially assumed. In this paper, we have demonstrated in detail that it also proved to be very appropriate and powerful in describing a wide range of other physical phenomena, including the scattering of colorless plasmons off hard thermal (or external) color-charged particles moving in a hot quark–gluon plasma. A generalization of the Poisson superbracket including both anticommuting variables for hard modes and normal variables of the soft Bose field, is presented for the case of continuous medium. The corresponding Hamilton equations are defined, and the most general form of the third- and fourth-order interaction Hamiltonians is written out in terms of the normal boson field variables and hard momentum modes of the quark–gluon plasma. The canonical transformations involving both bosonic and hard mode degrees of freedom of the system under consideration, are discussed. The canonicity conditions for these transformations based on the Poisson superbracket, are derived. The most general structure of canonical transformations in the form of integro-power series up to sixth order in a new normal field variable and a new hard mode variable, is presented. For the hard momentum mode of quark–gluon plasma excitations, an ansatz separating the color and momentum degrees of freedom, is proposed. The question of approximation of the total effective scattering amplitude when the momenta of hard excitations are much larger than those of soft excitations of the plasma, is considered. The self-consistent system of Boltzmann-type kinetic equations taking into account the time evolution of the mean value of the color charge of the hard particle is obtained.

Crystallinity determines the performance of polymers, and inhomogeneity in crystallinity occurs in both planar and depth dimensions of polymers during the manufacturing process. However, it is challenging to provide a multidimensional, visualized, and quantified evaluation of the polymer crystallization process. In this contribution, we proposed a three-dimensional strategy to visualize the isothermal cold crystallization behaviors of poly(lactic acid) (PLA) based on fluorescence labeling targeting carboxyl groups. The uniform fluorescence distribution at different depths was observed for the amorphous state of PLA, while decayed fluorescence sites along depths were identified for PLA with an oriented polymer chain and ordered crystalline structure. Such a phenomenon could be ascribed to the diffusion affinity differences between the amorphous and crystalline regions for the fluorescence probe. The temperature and time dependencies of the fluorescence volume were quantitatively studied, conforming to the classical isothermal crystallization Avrami kinetic equation. Accordingly, the progressive cold crystallization process, interpreted as the decayed fluorescence volumes, resulted in the preferred crystalline structure and enhancement of Young's modulus for PLA. Therefore, we have realized the three-dimensional visualization and quantification of PLA cold crystallization, guiding the structural evaluation and performance prediction for polymers. It is anticipated that such a strategy could broaden the evaluation scope for the physical and chemical properties of various polymers.

Abstract This paper deals with the kinetic equations and Lagrangians of vector bosons and spinor fermions. Its goals are mainly pedagogical and methodological, and no claim of novelty is made. But the relevant equations are here derived from the fundamental Lorentz invariants, namely the two Casimir operators for a massive particle with spin-1/2 and spin-1. Special attention is paid to the chiral symmetry and its effects on the Lorentz transformation. A new road leading to the Dirac equation and its polarization spinors is thus shown. Using the spin matrices stemming from the vectorial Lorentz transformation permits one to determine directly the polarization of vector bosons and to establish their Lagrangian including these spin matrices. This approach permits one to rederive also the Maxwell equations, but more importantly to determine the origin of its spin for the massive vector boson. The kinetic helicity of the particles plays a key role in these calculations.

In this work, we develop a computational model for ultra-short laser–matter interaction performing detailed simulations of fs pulsed 800 nm laser heating of amorphous Ge2Sb2Te5 (αGST) films, which are at the heart of re-writable optical disks and the latest generation of non-volatile electronic memory. The developed model shows good agreement with related experimental data revealing various effects of ultra-fast dynamics of the electronic subsystem photoexcitation followed by relaxation, ultra-fast cooling, re-amorphization, and partial crystallization. First, our simulations show that additional generation of free electrons by impact ionization leads to a significant decrease of the effective absorption coefficient combined with a significant temperature decrease at the film surface and a simultaneous temperature increase inside the film. Second, our simulations demonstrate the nonlinear dynamics of the dielectric function and related optical parameters. Third, our computations of the post-relaxation ultra-fast cooling dynamics combined with the equations of Arrhenius-type kinetics for crystallization elucidate the thermally controlled mechanism for the experimentally observed generation of the amorphous-crystalline-amorphous nanostructure inside the bulk of the αGST film irradiated by a fs pulsed laser. Additionally, the generation of this nanostructure is associated with an order of magnitude difference between the attempt rates involved in phase transitions (i) in the near-surface melted part and (ii) in the bulk non-melted part of the film. Finally, our study shows that a single fs pulsed laser-induced melting does not lead to the crystallization on the surface of irradiated amorphous and crystalline GST films due to onset of post-relaxation high-rate cooling 1011–1012 K/s.

ABSTRACT This study investigates the decomposition kinetics of azodicarbonamide (ACA) as a chemical blowing agent (1 wt%) in polypropylene composites with varying pine fiber concentrations (5, 10, and 15 wt%). The thermal decomposition curves of azodicarbonamide were determined using a capillary rheometer, which served as a batch reactor to measure pressure and temperature as a function of time. To obtain all the information, tests were performed on neat polypropylene, polypropylene/pine fiber composites, and polypropylene/pine fiber composites containing ACA. The results showed that a higher fiber content resulted in increased pressure generated due to the release of volatiles (humidity and extractives) by the fibers. However, the addition of the ACA significantly increased the pressure due to gas generation from its decomposition. Taking all the effects into account, the experimental data were well fitted to the Kamal–Sourour kinetics equation. Then, the kinetic parameters of ACA decomposition were used to determine that the overall reaction order is 1.5. Finally, 10% pine fiber was shown to decrease the activation energy of its autocatalytic reaction and produce foamed samples with a high number of small and uniform cells.

The Dalat Nuclear Research Reactor (DNRR), Vietnam’s primary nuclear research facility, requires modernized instrumentation to support its expanding role in radioisotope production and scientific research. This work presents a novel, independent field-programmable gate array (FPGA)–based real-time monitoring system to complement the existing ASUZ-14 R control and protection system—which uses six separate calculation units to process signals from three independent detector assemblies. The proposed system demonstrates significant improvements in computational speed, critical for the DNRR’s frequent operational transients. Implemented on a single Xilinx Artix-7 FPGA board, this solution consolidates the computation of all critical parameters (period, power, and reactivity) for all three detector channels into one unified board. The system performs simultaneous real-time sampling of neutron flux signals, applies digital filtering, and executes reactor point kinetics equations. Experimental validation at the DNRR confirms comparable accuracy and superior response time compared to the existing monitoring feature. This integrated architecture represents a significant consolidation of hardware, replacing multiple units with a single, highly cost-effective platform. Coupled with a signal isolation unit, the FPGA board ensures complete noninterference with normal reactor operations. This work provides a valuable tool for enhancing operational awareness and contributes to the strategic diversification of instrumentation.