Kinetic Growth Model Research Articles

Kinetic growth model and metabolic effect of a bacterial consortia from a petrochemical processing plant

AbstractThis study focused on presenting the newly developed growth model for bacterial species present in a petrochemical processing plant in South Africa. The findings of the study serve as a theoretical basis for future experiments aimed at understanding the formation of bacterial metabolites as the bacteria develops. An unstructured kinetic model using AQUASIM 2.3, together with experimental spectrophotometric results, were used to evaluate the growth of Gram‐negative bacteria in a batch reactor system. Spectrophotometer results showed the absence of a stationary phase. The exponential bacterial growth phase supported the total organic carbon (TOC) results, showing that bacterial growth occurred on days 6 and 13; this is rarely reported in literature, as the growth in this system was much slower than the growth of single‐strain studies. The TOC concentration values indicated that carbon sources did not deplete in the death phase, suggesting the presence of a long‐term stationary phase and the production of acetate. The presence of Pseudomonas sp. and sulphate‐reducing bacteria (SRB) are commonly reported in industrial systems as they play a role in equipment failure in industry. However, in this multispecies study, methods using third generation sequencing together with high‐performance liquid chromatography (HPLC) have shown that the selective attachment and production of acetate by abundant Clostridium sp. has ascertained their role in equipment failures in the petrochemical environment.

Parameterized Gompertz-Guided Morphological AutoEncoder for Predicting Pulmonary Nodule Growth.

The growth rate of pulmonary nodules is a critical clue to the cancerous diagnosis. It is essential to monitor their dynamic progressions during pulmonary nodule management. To facilitate the prosperity of research on nodule growth prediction, we organized and published a temporal dataset called NLSTt with consecutive computed tomography (CT) scans. Based on the self-built dataset, we develop a visual learner to predict the growth for the following CT scan qualitatively and further propose a model to predict the growth rate of pulmonary nodules quantitatively, so that better diagnosis can be achieved with the help of our predicted results. To this end, in this work, we propose a parameterized Gempertz-guided morphological autoencoder (GM-AE) to generate any future-time-span high-quality visual appearances of pulmonary nodules from the baseline CT scan. Specifically, we parameterize a popular mathematical model for tumor growth kinetics, Gompertz, to predict future masses and volumes of pulmonary nodules. Then, we exploit the expected growth rate on the mass and volume to guide decoders generating future shape and texture of pulmonary nodules. We introduce two branches in an autoencoder to encourage shape-aware and textural-aware representation learning and integrate the generated shape into the textural-aware branch to simulate the future morphology of pulmonary nodules. We conduct extensive experiments on the self-built NLSTt dataset to demonstrate the superiority of our GM-AE to its competitive counterparts. Experiment results also reveal the learnable Gompertz function enjoys promising descriptive power in accounting for inter-subject variability of the growth rate for pulmonary nodules. Besides, we evaluate our GM-AE model on an in-house dataset to validate its generalizability and practicality. We make its code publicly available along with the published NLSTt dataset.

Monitoring and prediction of Aeromonas veronii dynamics via absolute quantification microbiome sequencing facilitated the development of a risk assessment tool in a shrimp farm

The outbreak of infectious bacterial diseases in aquaculture is a major concern in the industry. Among those pathogens, Aeromonas species are one of the most important bacterial pathogens of cultured animals. From May to June of 2022, an unexplained Aeromonas veronii outbreak was observed in a shrimp farm with high morbidity and mortality. To develop a risk assessment tool, the dynamics of the microbiome were monitored via absolute quantification of 16S rRNA amplicon sequencing for 18 consecutive days in a recirculating aquaculture system (RAS) for rearing water and the gut of whiteleg shrimp (Litopenaeus vannamei). A growth model was also developed for predicting the growth of Aeromonas in the shrimp gut and rearing water. The results showed that A. veronii is a dominant bacterial strain isolated from sick L. vannamei. The comparison of the bacterial community in the shrimp gut and rearing water over time showed remarkable shifts in A. veronii and probiotic Bacillus in the rearing water, with a significant decline in probiotic Bacillus. The rapid increase in A. veronii in rearing water subsequently altered A. veronii populations in the shrimp gut, with over 80% of A. veronii found on day 18. Linear regression analysis revealed a strong positive relationship between the abundance of A. veronii in the shrimp gut and the rearing water. The growth kinetic model agreed well with the observed values. Collectively, the temporal dynamics of the bacterial community in the rearing water offer valuable information for the fate of administered probiotics and pathogens. Growth kinetic models provide useful information to reduce the abundance of pathogens, which can be used as an early warning tool. These observations offer crucial insights into the dynamics of the bacterial community in shrimp and their environment, which can significantly impact shrimp health and productivity.

Optimizing SRT for improved biomass production and nutrient removal from wastewater secondary effluent in a continuous mode MPBR system with Monoraphidium sp.: An experimental and growth kinetics model approach

This study aimed to evaluate the impacts of solids retention time (SRT) and influent nutrient concentration on the specific growth rate and nutrient removal efficacy of Monoraphidium sp. in a continuous mode membrane photobioreactor (MPBR). At SRT of 1 d, maximum biomass productivity of 421 mg·L−1·d−1 and nutrient removal rates of 59.9 % and 79.8 % for total nitrogen (TN) and total phosphorus (TP) were achieved. After reducing the influent nutrient concentration, Monoraphidium sp. maintained high biomass productivity of 385 mg·L−1·d−1 and nutrient removal rates of >95 % for TN and TP. The most important factor in Monoraphidium sp. growth assessment was intracellular nitrogen concentration (QN) rather than extracellular nutrient concentration. Flynn modified Droop model showed a better fit when the dimensionless parameter (Kq) was 0.235 for the relationship between the specific growth rate (μ) and QN. The model also revealed that even at low nitrogen concentrations (0.1 mg·L−1), the nitrogen removal capacity of Monoraphidium sp. was equal to its maximum removal capacity. Even at different extracellular nutrient concentrations, the Flynn model showed a linear relationship between μ and light irradiance per unit algae biomass (Iavp), when Iavp was below 18 μmol·g−1·s−1. This study highlights the promising potential of Monoraphidium sp. in MPBR. It demonstrates that considering QN and Iavp is essential for optimizing MPBR to achieve high biomass production and inorganic nutrient removal from secondary wastewater effluent.

Electromigration enhanced growth kinetics of intermetallics at the Cu/Al interface

The growth kinetic behaviors of the Cu/Al system under current were investigated. The current was shown to significantly promote the growth of the intermetallic (IMC) layer. The growth rate constant of the Al4Cu9 layer under current was approximately 3.26 times higher than that processed without current. Moreover, the current direction leads to a significant difference in the growth rate of the IMC layer, which was attributed to the electromigration effect. Based on the traditional thermal-activated theory and electromigration theory, an electromigration and thermal dual-activated growth kinetic model incorporating the contributions of Joule heat and the nonthermal effect was constructed. The growth kinetic behaviors of the Al4Cu9 layer were investigated by applying this model. The calculated growth activation energies under different current densities were almost constant and close to 130 kJ/mol. The experimental data were applied to verify the model, and the results showed that the model was in good agreement with the experimental results.

A modelling workflow for quantification of photobioreactor performance

In this work we have developed a comprehensive modelling workflow for the quantification of photobioreactor performance. Computational Fluid Dynamics (CFD) modelling combined with Lagrangian particle tracking was used to characterise the flow field inside the reactor; this information was combined with a Monte-Carlo model of light attenuation and a kinetic growth model to predict the performance of the system over the duration of the entire batch. The CFD model was validated against measurements of the overall hold-up, local hold-up and mixing time for superficial velocities between 0.6 and 6 cm s−1 in a pilot-scale bubble column photobioreactor, with the CFD predictions agreeing with the experimental data. Comparison was also made between the predicted biomass concentration and experimental measurements using the diatom Phaeodactylum tricornutum, with the model predictions being in good agreement with the experimental results. The model was used to investigate a range of operating conditions and reactor designs, with the most promising predicted to give a 40 % increase in the biomass productivity. Results from this work can be used for the in-silico design and optimisation of photobioreactor systems, thereby enabling their wider use as a sustainable production technology.

Response of preosteoblasts on micromachined Ti-6Al-4V surface to microstructure dimension.

The cell incubation depends on the cultured surface, but various machining methods produce different surface topographies, but it has not been clear how it is related to the topographic feature until now. Hence, the machined Ti-6Al-4V surface is characterized for preosteoblasts incubation via different mechanical fabrication. The relationship between surface topography created by various machining methods and cell incubation behaviour was explored. The objective is to control the surface preosteoblasts growth in machining of biological titanium alloy. According to the cell growth kinetic, the cell incubation behaviour was first proposed and modelled in relation to microstructural dimension and culture duration. Then, the topological cultured microstructure surface was fabricated via mechanical fabrication. Finally, the cell initial adhesion and incubation behaviour on microstructured surface was investigated. It is shown that the surface undulation on machined microstructure is conducive to controlling the direction and distribution of cell incubation from cell growth kinetic model. The cell culture can be controlled on the peak with a small undulation, while it is concentred on the sidewall with a high aspect ratio. Increasing the aspect ratio extends cell growth, while low aspect ratio promotes initial cell adhesion and growth rate. Within the optimal cultured duration, the microstructured surface is more favourable for cell survival, and the cell growth keep positive beyond critical aspect ratio. As a result, the cell adhesion ability is topologically controlled to 5.4 times higher and the growth rate can be improved by 101.7% on milled microgrooved surface. It may be applied to the rapid production of biomedical Ti-6Al-4V implant.

Effect of macronutrients (carbon, nitrogen, and phosphorus) on the growth of Chlamydomonas reinhardtii and nutrient recovery under different trophic conditions.

More stringent discharge standards have led to the development of an alternative nutrient recovery system from wastewater. Microalgae cultivation in wastewater treatment works has presented considerable promise from the perspective of sustainable resource management. Growth kinetics models are useful tools to optimize nutrient recovery from wastewater by algal uptake. Therefore, this research aims to identify the growth kinetics of Chlamydomonas reinhardtii under both heterotrophic and phototrophic conditions with different nutrient concentrations that typify those found in wastewater treatment works. In addition, the effects of macronutrients (C, N, and P) on heterotrophic and phototrophic microalgae growth and nutrient recovery were studied. Greater specific growth rates were achieved under heterotrophic conditions than in phototrophic cultivation. The maximum specific growth rates and nutrient recovery efficiencies were achieved at 5 mg P L-1 under both heterotrophic and phototrophic growth conditions. Nitrate was the preferred form of nitrogen source under heterotrophic conditions, while nitrogen sources did not present any significant influences in the phototrophic cultivation. Specific growth rates reported for both heterotrophic and phototrophic microalgae at lower carbon concentrations (3.10 d-1 and 0.46 d-1, sequentially) were higher than those at higher carbon concentrations (1.95 d-1 and 0.22 d-1, respectively). C. reinhardtii presented an extreme capacity to adapt and grow at all experimental conditions tested in heterotrophic and phototrophic cultivations.

Mathematical Model for Growth and Rifampicin-Dependent Killing Kinetics of Escherichia coli Cells.

Antibiotic resistance is a global health threat. We urgently need better strategies to improve antibiotic use to combat antibiotic resistance. Currently, there are a limited number of antibiotics in the treatment repertoire of existing bacterial infections. Among them, rifampicin is a broad-spectrum antibiotic against various bacterial pathogens. However, during rifampicin exposure, the appearance of persisters or resisters decreases its efficacy. Hence, to benefit more from rifampicin, its current standard dosage might be reconsidered and explored using both computational tools and experimental or clinical studies. In this study, we present the mathematical relationship between the concentration of rifampicin and the growth and killing kinetics of Escherichia coli cells. We generated time-killing curves of E. coli cells in the presence of 4, 16, and 32 μg/mL rifampicin exposures. We specifically focused on the oscillations with decreasing amplitude over time in the growth and killing kinetics of rifampicin-exposed E. coli cells. We propose the solution form of a second-order linear differential equation for a damped oscillator to represent the mathematical relationship. We applied a nonlinear curve fitting solver to time-killing curve data to obtain the model parameters. The results show a high fitting accuracy.

Growth kinetic model of Bacillus pasteurii under different pH and temperature conditions in sodium carboxymethyl cellulose solid-free drilling fluid

Increasing the bonding force between broken blocks to form a complete borehole wall is essential to solving borehole wall destabilization in broken strata, and introducing microbial-induced calcite deposition (MICP) technology into the field of drilling fluids establishes a novel research idea for manifesting this technical method. However, during drilling, the pH value and temperature of the drilling fluid constantly change, affecting the activities of microorganisms and the effect of MICP. Therefore, exploring the growth law of microorganisms in drilling fluid environments under different temperatures or pH conditions is necessary. This study used experimental research and theoretical analysis to compare the growth of Bacillus pasteurii in sodium carboxymethyl cellulose (CMC) solid-free and xanthan gum biopolymer solid-free drilling fluid. The growth of B. pasteurii in CMC solid-free drilling fluid in pH = 7.0–9.8 and temperatures from 30 to 50 °C was studied, and the growth kinetic model of B. pasteurii was constructed. The mean square error, decision coefficient (R2), accuracy factor (Af), and deviation factor (Bf) were used to verify the accuracy of the model. CMC solid-free drilling fluid is more suitable for B. pasteurii survival than XG solid-free drilling fluid. The optimum growth temperature of B. pasteurii in CMC solid-free drilling fluid was 32 °C, and the OD600 reached 2.146 at 24 h pH = 8.2 was the optimum pH environment for B. pasteurii in CMC solid-free drilling fluids; the OD600 reached 2.065 at 24 h. As a first-order growth kinetic model, the modified Gompertz model accurately described B. pasteurii growth in CMC solid-free drilling fluid under different temperature strips or pH values. As a secondary growth kinetic model, the square root model accurately described the pattern of pH (7.0–8.2) and temperature effects on the maximum specific growth rate (μmax), with R2 = 0.961, Af = 1.084, Bf = 0.9979, and an error of less than ±0.05. The Arrhenius model accurately described the pattern of pH effects on B. pasteurii (μmax) at pH = 8.6–9.8, with R2 = 0.9996, Af = 1.0036, Bf = 0.999, and an error of less than ±0.02. The effect of temperature was inversely proportional to the growth of B. pasteurii; the higher the temperature, the lesser the B. pasteurii growth. In the pH range of 7.0–8.2, the higher the pH value, the better the B. pasteurii growth; however, at an increased pH range of 8.6–9.8, the higher pH value decreased the B. pasteurii growth. This study is the first to investigate the effect of temperature or pH on B. pasteurii growth in CMC solid-free drilling fluid. Our study provides a scientific basis and theoretical reference for the subsequent research on the induced domestication of B. pasteurii in high-temperature and strong alkaline environments and its engineering application.

Development of a centrifugal bioreactor for rapid expansion of CD8 cytotoxic T cells for use in cancer immunotherapy.

One of the current difficulties limiting the use of adoptive cell therapy (ACT) for cancer treatment is the lack of methods for rapidly expanding T cells. As described in the present report, we developed a centrifugal bioreactor (CBR) that may resolve this manufacturing bottleneck. The CBR operates in perfusion by balancing centrifugal forces with a continuous feed of fresh medium, preventing cells from leaving the expansion culture chamber while maintaining nutrients for growth. A bovine CD8 cytotoxic T lymphocyte (CTL) cell line specific for an autologous target cell infected with a protozoan parasite, Theileria parva, was used to determine the efficacy of the CBR for ACT purposes. Batch culture experiments were conducted to predict how CTLs respond to environmental changes associated with consumption of nutrients and production of toxic metabolites, such as ammonium and lactate. Data from these studies were used to develop a kinetic growth model, allowing us to predict CTL growth in the CBR and determine the optimal operating parameters. The model predicts the maximum cell density the CBR can sustain is 5.5 × 107 cells/mL in a single 11-mL conical chamber with oxygen being the limiting factor. Experimental results expanding CTLs in the CBR are in 95% agreement with the kinetic model. The prototype CBR described in this report can be used to develop a CBR for use in cancer immunotherapy.

Preparation of Dendrobium officinale flower oligosaccharides and the value-added effects on three types of probiotics

The present study prepared Dendrobium officinale flower oligosaccharides and investigated their added value in vitro. The crude oligosaccharides obtained by water extraction and alcohol precipitation were purified by ultrafiltration, and the value-added effects of different concentrations of D. officinale flower oligosaccharides on Saccharomycetes, Lactobacillus bulgaricus, and Streptococcus thermophilus were examined. The in vitro growth kinetic models for the three types of probiotics were established according to the logistic equation. Our results showed that a concentration of 8 g/L D. officinale flower oligosaccharides was most suitable for promoting the growth of the three types of probiotics, and the growth rates were significantly improved compared to the control group. Nonlinear fitting was performed for the in vitro growth kinetic models of the three bacteria according to the logistic equation, and the degrees of fit reached 0.9895, 0.9899, and 0.99, respectively, indicating a good fit. These kinetic models suitably depicted the in vitro growth processes of the three bacteria. D. officinale flower oligosaccharides promote the growth of Saccharomycetes, L. bulgaricus and S. thermophilus and improve the physiological activities of these microorganisms. This study provides a theoretical basis for the application of D. officinale flower oligosaccharides in the development of probiotic products.

Modeling Battery Formation: Boosted SEI Growth, Multi-Species Reactions, and Irreversible Expansion

This work proposes a semi-empirical model for the SEI growth process during the early stages of lithium-ion battery formation cycling and aging. By combining a full-cell model which tracks half-cell equilibrium potentials, a zero-dimensional model of SEI growth kinetics, and a semi-empirical description of cell thickness expansion, the resulting model replicated experimental trends measured on a 2.5 Ah pouch cell, including the calculated first-cycle efficiency, measured cell thickness changes, and electrolyte reduction peaks during the first charge dQ/dV signal. This work also introduces an SEI growth boosting formalism that enables a unified description of SEI growth during both cycling and aging. This feature can enable future applications for modeling path-dependent aging over a cell’s life. The model further provides a homogenized representation of multiple SEI reactions enabling the study of both solvent and additive consumption during formation. This work bridges the gap between electrochemical descriptions of SEI growth and applications toward improving industrial battery manufacturing process control where battery formation is an essential but time-consuming final step. We envision that the formation model can be used to predict the impact of formation protocols and electrolyte systems on SEI passivation and resulting battery lifetime.

Obtaining lactic acid through microbial fermentation from corn residues

The production and kinetics of lactic acid (LA) by batch fermentation were studied, using corn residues as substrate with Lactobacillus delbrueckii spp. Bulgaricus. A factorial design was developed for the pretreatment stage of the residue and lactic fermentation to determine the best conditions for obtaining total reducing sugars and lactic acid. In the pretreatment, the best conditions were obtained by working with HCl at 3% (v/v), 75 °C, and 30 minutes of reaction. Fermentation was carried out, keeping the medium at a pH between 5.5-6, and the best working conditions were 100 µl of the microorganism, 37ºC, and 24 hours of fermentation, reaching a maximum concentration of 19.9 g/L. Kinetic models for LA production, bacterial growth, and substrate consumption were proposed. Likewise, to verify the observed data, different statistical indices were calculated to evaluate the accuracy of the models. Finally the Luedeking-Piret and logistic models, were selected as they presented the best fit to the experimental data for LA production, substrate consumption, and bacterial growth, respectively.

Preparation of CoCrFeMnNi-based high-entropy/aluminide laminated composites: Multielement interdiffusion reactions

CoCrFeMnNi-based high-entropy/aluminide laminate (HAL) composites were produced following the hot pressing diffusion sintering method. The microstructure of the samples was analyzed using the SEM, EDS, and EBSD techniques, and the results revealed that the diffusion reaction phases of the HAL composite consisted of a four-layer aluminide structure based on the Al13(Cr, Mn, Fe, Co, Ni)4 phase. The diffusion behavior of iron dominated the resulting phase, leading to the formation of Fe-Al compounds. Under the influence of the hysteresis diffusion effect of high entropy alloys, Al13(Cr, Mn, Fe, Co, Ni)4 phase layers (ASL I–III) with different grain sizes and growth orientations are formed due to the difference of diffusion rates at different interfaces. At the front end of the diffusion reaction, the aggregation layer of the secondary phase Al9(Fe, Co, Ni)2 appears due to the segregation of Co and Ni elements. The growth kinetics model of HAL composites was explored, and it was observed that a mixture diffusion type controlled the growth of the aluminide layer via ‘grain boundary and lattice diffusion’. The mechanical properties and failure modes of the HAL composites were investigated through quasi-static and dynamic mechanical tests. The fracture toughness reached 25 MPa·m1/2, and the main energy dissipation modes were the deformation of the ductile layer and the fracture of the hard, brittle layer. The dynamic impact failure modes were primarily deformation and 45% adiabatic shear bands, and the impact strength and energy consumption reached up to 1800 MPa and 2260 J/mm3. HAL composites with high alumina content exhibited prominent crack propagation and fragmentation properties under high-speed impact. The stress wave was significantly attenuated in the crushed aluminide layer, which significantly improved the energy absorption effect of aluminide.

Kinetics of biomass and polyhydroxyalkanoates synthesis using sugar industry waste as carbon substrate by Alcaligenes sp. NCIM 5085

Aim: o optimize the operating parameters and further determine the kinetics of biomass and polyhydroxyalkanoate synthesis using sugar industry waste as a carbon substrate by Alcaligenes sp. NCIM 5085. Methodology: Molasses, clarified and pretreated with sulphuric acid, was taken in a batch reactor for fermentation to generate biomass and further for polyhydroxyalkanoate synthesis where Alcaligenes sp. NCIM 5085 was used as a culture. A number of parameters were observed during fermentation experiments to optimize the biomass and PHA namely: initial substrate concentration, incubation period, C/N ratio, inoculum concentration and pH. Fermented solution was filtered to account the yield of biomass from the solution at each time interval decided for each experiment and polyhydroxyalkanoate was extracted from the biomass by chloroform and methanol extraction. Growth kinetics of biomass was modeled by Monod and Logistic models whereas Luedeking-Piret model was used for polyhydroxyalkanoate production rates. Results: From the fermentation experiments, it was found that for 40 g l-1 of molasses at neutral pH, 4.48 g l-1 of biomass was synthesized when fermentation was observed for 48 hr. One percent of cell dry weight of biomass was extracted as polyhydroxyalkanoate. Logistic model for growth kinetics and Luedeking-Piret model for polyhydroxyalkanoate production rate were found in agreement with the experiments where regression coefficient was maximum with minimum error. Interpretation: The PHA growth kinetics and PHA production kinetics done in this work can be utilized to design a bioreactor for PHA production at industrial scale. Key words: Alcaligenes sp., Biomass, Cane molasses, Growth kinetics, Polyhydroxyalkanoates

Experimental kinetic study of interdiffusion behavior and intermetallic compound Zr(Fe,Cr)2 formation at the Cr/Zry4 interface under elevated temperatures

Interdiffusion behavior at the Cr-Zr interface under elevated temperatures in Cr-coated Zr-based accident tolerant fuel cladding is a key phenomenon for understanding its microstructural stability during the reactor's long-term operation. The interdiffusion behavior of the Cr/Zircaloy-4 (Zry4) diffusion couple and microstructural evolution at the interface were studied under vacuum conditions in the temperature range 973 K to 1323 K. Results show that interdiffusion results in the formation of a Zr(Fe,Cr)2 intermetallic compound layer irrespective of the annealing temperature. Segregation of Fe in the Zr(Fe,Cr)2 interlayer is confirmed, which is enhanced by annealing temperature within the α-Zr phase temperature regime and dropped greatly within the β-Zr temperature regime. The kinetic growth model for Zr(Fe,Cr)2 is found to follow the parabolic law in both α-Zr and β-Zr phase regions, and the diffusion activation energy (Q) of Cr in Zr(Fe,Cr)2 is determined as 7.23×104Jmol−1 for α-Zr phase annealing. Extrapolation of the diffusion coefficients measured within the α-Zr phase predicts a much lower value within the β-Zr phase compared to the experimental result, indicating that the α→β(Zr) phase transformation promotes the growth rate of Zr(Fe,Cr)2 interlayer formation, likely due to the enhancement in both diffusion ability and solubility of Cr in β-Zr relative to α-Zr. The insights obtained in this study will help to improve the understanding of the cladding's microstructure stability and its related degradation behaviors during practical application.

Optimization of drug scheduling for cancer chemotherapy with considering reducing cumulative drug toxicity

An improved optimal drug scheduling model with considering two control drugs is proposed and the Gauss pseudospectral-based optimization method is studied to decrease the tumor size and drug toxicity in this work. Firstly, the Dexrazoxane drug, which has significant clinical effect to reduce the toxicity of the anticancer drug, is introduced. By analyzing the growth kinetics model of cancer chemotherapy, the toxicity reduction drug is regarded as the second input in the cancer dynamic equations. Correspondingly, the drug scheduling optimization problem with particular optimization goal and necessary constraints is established. Next, a model transformation technique is proposed to reduce the complexity of dynamic equations. With deriving the Gaussian time grid discretization detailly, the Gauss pseudospectral method (GPM)-based cancer chemotherapy drug scheduling algorithm is presented to test the performance of the proposed model within different rates. Finally, the implementation structure of drug scheduling optimization is given in detail. To test and validate the performance of proposed chemotherapy model, extensive simulation results and comparative evaluation are carried out on a specific mathematical model. Simulation results show that the improved optimization model is superior to other literature studies, resulting in the average improvement of performance index by 66.54% and revealing the significant guiding property for cancer chemotherapy.

Microstructure and Mechanical Properties of Zr‐4 Alloy and 316 Stainless Steel Diffusion Bonding Joint Using Nb/Ni Composite Interlayer

Diffusion bonding of Zr‐4 alloy and 316 stainless steel (SS) without and with the Nb/Ni composite interlayer has been performed. The maximum shear strength of the joint without interlayer is 131 MPa at 900 °C for 30 min under 10 MPa. The results show that the fracture occurs at the diffusion layer as a result of the limited mutual solubility between Zr and Fe and detrimental residual stress. Sound diffusion bonding joints without defects are obtained at lower bonding temperatures due to the addition of Nb/Ni interlayer, and the maximum shear strength is 380 MPa at 820 °C. The typical microstructure of the Zr‐4/Nb/Ni/316SS joint is Zr‐4/Zr(Nb)/Zr(Fe, Nb)2 /Zr(Nb)/Nb/Ni3Nb/Ni/(Fe, Cr, Ni)/316SS. The highest hardness value of the joint is 422 HV at the Ni3Nb phase, and cracks appear at the interface between Ni3Nb and the remaining Ni foil. The shear strength first increases and then drops as the Ni3Nb layer thickened. The peak residual stress of the joint reduces from 698 to 466 MPa due to the addition of the Nb/Ni composite interlayer. Finally, the growth kinetic model of the Ni3Nb layer is calculated, which provides a pathway for the regulation of joint properties.

Primary Growth Behavior of Sulfur Particles through the Throttle Valve in the Transmission System of High Sulfur Content Natural Gas

The deposition of sulfur particles in gathering and transportation pipeline system can cause serious safety problems and economic losses. When the high sulfur content natural gas (HSCNG) flows through the throttle valve of the gathering and transportation system, it will cause the supersaturation of elemental sulfur in the gas phase, and then the sulfur crystal nuclei and sulfur particles will appear in the pipeline system. Studying the initial growth behavior of sulfur crystal nuclei and sulfur particles can lay a necessary prerequisite for the accurate prediction of sulfur particle deposition in high sulfur content natural gas gathering and transportation (HSCNGGT) pipelines. Based on the homogeneous nucleation theory in crystallization kinetics, a mathematical model of elemental sulfur nucleation was established. Taking the throttling condition in the process of HSCNGGT as an example, the effects of temperature, pressure and H2S concentration in HSCNG on the critical nucleation radius and nucleation rate of elemental sulfur were explored. The results show that: (1) after the supersaturation of elemental sulfur, sulfur crystal nuclei with nanoscale radius will be precipitated. The temperature and pressure after throttling have great influence on the nucleation radius, and the influence of H2S concentration on the nucleation radius is more complex. (2) The temperature, pressure and H2S concentration after throttling also have great influence on the nucleation rate. By solving the growth kinetics model of sulfur particles based on Brownian condensation, it is found that the nano-sized sulfur crystal nuclei can grow into micron-sized sulfur particles in a very short time.