Constant Growth Rate Research Articles

Comments on Mathematical Aspects of the Biró–Néda Model

We address two mathematical aspects of the Biró–Néda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions.

Synthesis of silver nanoparticles by sonogalvanic replacement on aluminium powder in sodium polyacrylate solutions

The process of the formation of silver nanoparticles (AgNPs) via the method of galvanic replacement (GR) of Ag+ with aluminum powder in sodium polyacrylate (NaPA) solutions in the ultrasonic (US) field has been studied. It was observed, that the yellow colloidal solutions of stabilized AgNPs with the absorption maximum at ∼ 410 nm were obtained under the application of US power by 20 W and frequency by 20 kHz in the wide range of AgNO3 and NaPA concentrations (0.1 – 0.5 mM and 0.5 – 5.0 g/L respectively) at 25 0C. It was shown, that the GR process under US field occurs without of the significant induction period. Using the UV–vis spectroscopy the kinetics of AgNPs formation has been studied and it was observed the first order kinetics with respect to Ag+ ions both for the nucleation and growth processes. It was found that observable rate constants of nucleation are close for the all experimental conditions but the observable rate constants of growth decreased with increasing of initial concentration of AgNO3. Based on the obtained kinetic data it was proposed a mechanism of the formation of AgNPs consisted of the following two main stages: 1) the nucleation with the formation of primary nanoclusters (AgNCs) on aluminum surface followed by their ablation from the surface of the sacrificial metal by ultrasound into bulk of solution; 2) the transformation of AgNCs in AgNPs via growth from the Al surface and / or agglomeration of AgNCs. Using TEM it was found that the size of obtained AgNPs does not exceed of 25 nm and slightly depends on the initial concentrations of precursors. High antimicrobial activity of obtained colloidal solutions against gram-negative and gram-positive bacteria as well as against fungi was observed.

The coalescent with replication-independent mutations.

We develop the mathematical structure of the neutral coalescent with both replication-dependent and replication-independent mutations. This allows us to explain and quantify empirical results that explore differences in genetic diversity in bacterial cultures with different growth rates. We also derive an unbiased and consistent estimator for the replication-independent mutation rate that is based on a comparison of total single nucleotide polymorphism counts for two independent well-mixed cultures with different growth rates. In addition to explaining differences in genetic diversity between well-mixed cultures with different (but constant) growth rates, our coalescent also quantifies the effects of fluctuating growth rates—a situation that can be common in natural populations.

Interfacial reactions between magnesia refractory and electric arc furnace (EAF) slag with use of direct reduced iron (DRI) as raw material

Interfacial reactions between the electric arc furnace (EAF) slag, i.e., CaO–SiO 2 –FeO–MgO–Al 2 O 3 –MnO system, and the magnesia refractory as a function of direct reduced iron (DRI) addition (0, 10, 20, 30 wt%) were investigated at 1550 °C under an Ar atmosphere. MgO solubility increases with increasing DRI content by decreasing basicity (i.e., CaO/SiO 2 ratio), which is due to an increase in SiO 2 supplied from DRI. The measured MgO content was always lower than the theoretical MgO saturation level irrespective of DRI content because the magnesiowüstite (MW) intermediate layer, which formed at the slag/refractory interface, retarded the direct dissolution of the refractory by acting as a self-protective layer. The thickness of the MW intermediate layer and dissolution depth were proportional to DRI content. However, the penetrativity decreased with increasing DRI content by decreasing the fluidity of the slag. Several kinetic parameters were estimated, including the dissolution rate constant of the MW intermediate layer, the dissolution rate of the MgO refractory, and the rate constant of MW growth. Dissolution of MgO refractory is controlled by the dissolution of the MW intermediate layer. Increasing the growth rate is very important for protecting refractory after the formation of a MW intermediate layer. In addition, we provided a schematic diagram of the slag/refractory interfacial reaction phenomena that compares situations of low and high DRI content. The results of the present study show that it is necessary to control DRI content to minimize refractory degradation during the EAF process. If a large amount of DRI must be used in the EAF process, then MgO content in the slag should be at the saturation limit at first, which accelerates growth of the MW intermediate layer.

Formation mechanism and growth kinetics of TiAl3 phase in cold-rolled Ti/Al laminated composites during annealing

Cold-rolled Ti/Al laminated composites were annealed at 525–625 °C for 0–128 h, and the interfacial microstructure evolution was investigated. The results indicate that only the TiAl3 phase was formed at the Ti/Al interface; most of TiAl3 grains were fine equiaxed with average sizes ranging from hundreds of nanometers to several microns and the TiAl3 grain size increased with increasing annealing time and/or temperature, but the effect of annealing temperature on the TiAl3 grain size was far greater than that of annealing time. The growth of the TiAl3 phase consisted of two stages. The initial stage was governed by chemical reaction with a reaction activation energy of 195.75 kJ/mol, and the reaction rate constant of the TiAl3 phase was larger as the Ti/Al interface was bonded with fresh surfaces. At the second stage, the growth was governed by diffusion, the diffusion activation energy was 33.69 kJ/mol, and the diffusion growth rate constant of the TiAl3 phase was mainly determined by the grain boundary diffusion owing to the smaller TiAl3 grain size.

Coalescence of ultrathin films by atomic layer deposition or chemical vapor deposition: Models of the minimum thickness based on nucleation and growth rates

Ultrathin, pinhole-free, and atomically smooth films are essential for future development in microelectronic devices. However, film morphology and minimum thickness are compromised when growth begins with the formation of islands on the substrate, which is the case for atomic layer deposition or chemical vapor deposition (CVD) on relatively unreactive substrates. Film morphology at the point of coalescence is a function of several microscopic factors, which lead to measurable, macroscopic rates of island nucleation and growth. To quantify the effect of these rates on the morphology at the point of coalescence, we construct two models: (1) a Monte Carlo simulation generates the film height profile from spatially random nucleation events and a constant island growth rate; simulated films resemble AFM images of the physical films; (2) an analytical model uses Poisson point statistics to determine the film thickness required to cover the last bare site on the substrate as a function of the nucleation rate and growth rate. Both models predict the same maximum thickness required to reach 99% coverage and reveal a power law relationship between the maximum thickness and the ratio of the nucleation rate divided by the growth rate. The Monte Carlo simulation further shows that the roughness scales linearly with thickness at coverages below 100%. The results match well with experimental data for the low-temperature CVD of HfB2 on Al2O3 substrates, but there are significant discrepancies on SiO2 substrates, which indicate that additional surface mechanisms must play a role.

Output-Feedback stabilization for stochastic nonlinear systems with Markovian switching and time-varying powers.

This paper investigates the output-feedback stabilization for stochastic nonlinear systems with both Markovian switching and time-varying powers. Specifically, by developing a novel dynamic gain method and using the Itô formula of Markovian switching systems, a reduced-order observer with a dynamic gain and an output-feedback controller are designed. By using advanced stochastic analysis methods, we show that the closed-loop system has an almost surely unique solution and the states are regulated to the origin almost surely. A distinct feature of this paper is that even though there is no Markovian switching, our design is also new since it can deal with nonlinear growth rate, while the existing results can only deal with constant growth rate. Finally, the effectiveness of the design method is verified by a simulation example.

Prediction models for the kinetics of iron boride layers on AISI 316L steel

Abstract The boronizing kinetics of AISI 316L steel has been analyzed by employing five prediction models. The boron diffusion coefficients as well as the growth rate constants in the FeB and Fe2B phases were firstly evaluated in the range of 1123-1223 K. Afterwards, the values of boron activation energies in FeB and Fe2B were secondly deduced by adopting the Arrhenius relationships.In addition, the prediction models have been validated experimentally for two boronizing conditions (1170 K for 1.6 h and 1210 K for 1.1 h). The predicted results were deemed very concordant with the experiments. Furthermore, advantages and limitations about the applicability of these models were also discussed.

Impact of the diffusion coefficient calculation on predicting Fe2B boride layer thickness

Abstract In this study, a single-phase boride layer thickness Fe2B is predicted on two different substrates (Armco iron and XC38 steel) by following the integral method. This method is a mathematical model based on a system of differential algebraic equations that help to deduce the diffusion coefficient, which is the key factor on predicting the layer thickness. Literatures cover different diffusion coefficients for each substrate, albeit researchers usually extract from experimental data, variations of growth rate constants within only one time treatment and deduce the diffusion coefficient from them. This deduction is done via an estimation of a frequency factor and an activation energy from the growth rate constants. Therefore, our main aim is to illustrate the impact of the deduction of the diffusion coefficient on predicting the boride layer thickness. Lastly, the impact with and without incubation time on the boriding kinetics of both substrates was also examined.

Synthesis and antimicrobial activity of silver nanoparticles stabilized by ramnolipid

Silver nanoparticles stabilized by rhamnolipid, which was separated from the supernatant of the supernatant the fluid of the genus Pseudomonas sp . PS-17, were synthesized. Using TEM it was found that the mean size of obtained AgNPs is 2.6 nm and does not depend on the initial concentration of Ag + . The kinetics of the formation of AgNPs was studied using UV-vis spectroscopy. It was observed that in the all of cases the kinetic curves are sigmoidal shape and are characterized by well-notable induction period that confirms the homogeneous nucleation of AgNPs as well as may indicate the absence of agglomeration of the particles at the stage of their growth. Experimental kinetic curves were fitted using Finke-Watzky 2-stage scheme of conti­nuous nucleation and fast autocatalytic growth of particles and the observable rate constants of nucleation and growth were estimated. Based on the calculated kinetic parameters of the reaction compared with the results of TEM-investigations the effective concentration of nucleui and the number of silver atoms in the nucleus and it was assumed that in the studied conditions the cluster Ag13 may be considered as the centre of AgNPs nucleation. The antimicrobial activity of the obtained “AgNPs-RL” solutions against a few test microorganisms, namely Escherichia coli , Staphylococcus aureus , Pseudomonas aeruginosa , Mycrococcus luteus , Agrobacterium tumefaciens and Xanthomonas campestris was studied and the high bactericidal effect was observed in the all of cases. Besides, the lowest values of the minimum bactericidal concentration (MBC ~ 1.5 mg/mL) were observed in the case of phytopathogens A. tumefaciens and X. campestris as well as for the genus Mycrococcus . Such low values of MBC compared with the low cost of obtained “AgNPs–RL” solutions make them attractive in the terms of development of antimicrobial drugs with a broad spectrum of action. Keywords: silver nanoparticles, “green” synthesis, antimicrobial activity.

Fungal Biofilms in Drinking Water Storage Containers: Flipping through their Health Risks. A Case-Study of Households at Diobu, Port Harcourt, Nigeria

The formation of fungal biofilm in drinking water storage containers has not been giving considerable attention over the years despite the challenges posed by bacterial biofilms. Hence, the study aimed to determine the fungal occurrence and the associated biofilm formation capacity from domestic drinking water storage containers in Diobu homes of Port Harcourt. Fifty water samples were obtained from domestic storage containers in different house units, and the sample was subjected to the standard microbiological procedure. The spread and streak techniques were applied on antibiotics treated Saboraud Dextrose and Congo red growth media. The results shows that the mean fungi count of 6.2 x 102 and 6.1 x 102 CFU/ml in household sizes of 4 and 5 persons respectively were less than that of the household population of 2, 6, and 8 persons with the fungal count of 8.7x102, 8.3x102 and 8.0x102CFU/ml respectively. Positive, negative and zero relationships were established between the household sizes and the fungal recovered. The analysis further revealed a total of 25 fungal isolates of which three genera were distinguished morphologically, namely, Aspergillus flavus, Candida albicans and Penicillium notatum. All isolates were able to form a heavy mass of biofilm; except Candida albicans which had a delayed formation after 24hours with less biofilm development potential, and thus signifies its inability to persist, despite having the highest count or load. The success of fungi biofilm is based on the constant growth rate of Aspergillus flavus and Penicillium notatum biofilms for which, the household size has reasonably be attributed. The study recommends that storage facilities in the homes be regularly cleaned and always disinfected to inhibit the successes of fungal biofilm.

Dynamic Optimization Approach to Estimate Kinetic Parameters of Monod-Based Microalgae Growth Models.

The biomass concentration of microalgae growth in photobioreactor was predicted using the Monod-based growth models. Kinetic parameters such as maximum specific growth rate and saturation constant of light intensity were evaluated by nonlinear least squares methods that focused on minimizing the sum of squares error (SSE). The importance of good initial guess for the nonlinear least squares method was also discussed. The optimal control problem of the microalgae growth model was determined based on parameter sensitivity. Therefore, a dynamic optimization approach was used where an optimal input design method was formulated to obtain a control function of a problem. The dynamic state equations, additional state equations, cost function, and Hamiltonian function were used to establish a control function of microalgae growth in a photobioreactor. Hence, the biomass production of microalgae can be predicted using numerical methods such as the Taylor series method.

Pressure-Jump Kinetics of Liquid-Liquid Phase Separation: Comparison of Two Different Condensed Phases of the RNA-Binding Protein, Fused in Sarcoma.

The RNA-binding protein fused in sarcoma (FUS) undergoes liquid-liquid phase separation (LLPS) both in vivo and in vitro. Self-assembled liquid droplets of FUS transform into reversible hydrogels and into more irreversible and toxic aggregates. Although LLPS can be a precursor of irreversible aggregates, a generic method to study kinetics of the formation of LLPS has not been developed. Here, we demonstrated the pressure-jump kinetics of phase transition between the 1-phase state and FUS-LLPS states observed at low pressure (<2 kbar, LP-LLPS) and high pressure (>2 kbar, HP-LLPS) using high-pressure UV/vis spectroscopy. Absorbance (turbidity) changes were reproduced repeatedly using pressure cycles. The Johnson-Mehl-Avrami-Kolmogorov theory was used to understand droplet formation occurring via nucleation and growth. The Avrami exponent n, representing the dimensionality of growing droplets, and the reaction rate constant k were calculated. The HP-LLPS formation rate was ∼2-fold slower than that of LP-LLPS. The Avrami exponent obtained for both LLPS states could be explained by diffusion-limited growth. Nucleation and growth rates decreased during LP-LLPS formation (n = 0.51), and the nucleation rate decreased with a constant growth rate in HP-LLPS formation (n = 1.4). The HP-LLPS vanishing rate was ∼20-fold slower than that of LP-LLPS. This difference in vanishing rates indicates a stronger intermolecular interaction in HP-LLPS than in LP-LLPS, which might promote transformation into irreversible aggregates in the droplets. Further, direct transition from HP-LLPS to LP-LLPS was observed. This indicates that interconversion between LP-LLPS and HP-LLPS occurs in equilibrium. Formation of reversible liquid droplets, followed by phase transition into another liquid phase, could thus be part of the physiological maturation process of FUS-LLPS.

Low-temperature atomic layer deposition of indium oxide thin films using trimethylindium and oxygen plasma

Indium oxide (InxOy) thin films were deposited by plasma-enhanced atomic layer deposition (PEALD) using trimethylindium and oxygen plasma in a low-temperature range of 80–200 °C. The optical properties, chemical composition, crystallographic structure, and electrical characteristics of these layers were investigated by spectroscopic ellipsometry (SE), x-ray photoelectron spectroscopy (XPS), x-ray diffraction (XRD), as well as current-voltage and capacitance-voltage measurements. The SE results yielded a nearly constant growth rate of 0.56 Å per cycle and a thickness inhomogeneity of ≤1.2% across 4-in. substrates in the temperature range of 100–150 °C. The refractive index (at 632.8 nm) was found to be 2.07 for the films deposited at 150 °C. The PEALD-InxOy layers exhibit a direct (3.3 ± 0.2 eV) and an indirect (2.8 ± 0.1 eV) bandgap with an uptrend for both with increasing substrate temperature. Based on XPS characterization, all InxOy samples are free of carbon impurities and show a temperature-dependent off-stoichiometry indicating oxygen vacancies. XRD diffraction patterns demonstrate an onset of crystallization at 150 °C. Consistent with the optical, XPS, and XRD data, the films deposited at ≥150 °C possess higher electrical conductivity. Our findings prove that a low-temperature PEALD process of InxOy is feasible and promising for a high-quality thin-film deposition without chemical impurities on thermally fragile substrates.

Influence of coating thickness on the microstructure, composition and optical properties of aluminum nitride thin films grown on silicon substrates via low-temperature PEALD

Within the framework of the study, fine-grained nanocrystalline aluminum nitride films were obtained using the PEALD method at the temperature of 250 °С and the number of deposition cycles from 80 to 500 on single-crystal silicon substrates. Low-temperature synthesis processes were carried out in the self-limited growth regime of the PEALD method at the constant growth rate of ∼0.115 nm/cycle. The obtained samples were studied by ellipsometry, FTIR-spectroscopy, X-ray diffraction analysis, Auger spectroscopy, Scanning electron and Atomic force microscopy. It was found that the samples in the IR-absorption spectra and ω/2θ-scans had bands and reflections characteristic for wurtzite AlN with hexagonal structure. It was shown that an increase in the coating thickness led to an increase in the crystallinity and optical density of the film material, the crystallites size, and values of the root-mean-square (RMS) roughness. In this case, significant changes in the crystal lattice parameter and relaxation of internal mechanical stresses within the obtained values of the AlN layers thicknesses were not observed.

In Vitro Pharmacokinetic/Pharmacodynamic Modelling and Simulation of Amphotericin B against Candida auris

The aims of this study were to characterize the antifungal activity of amphotericin B against Candida auris in a static in vitro system and to evaluate different dosing schedules and MIC scenarios by means of semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) modelling and simulation. A two-compartment model consisting of a drug-susceptible and a drug-resistant subpopulation successfully characterized the time-kill data and a modified Emax sigmoidal model best described the effect of the drug. The model incorporated growth rate constants for both subpopulations, a death rate constant and a transfer constant between both compartments. Additionally, the model included a parameter to account for the delay in growth in the absence or presence of the drug. Amphotericin B displayed a concentration-dependent fungicidal activity. The developed PK/PD model was able to characterize properly the antifungal activity of amphotericin B against C. auris. Finally, simulation analysis revealed that none of the simulated standard dosing scenarios of 0.6, 1 and 1.5 mg/kg/day over a week treatment showed successful activity against C. auris infection. Simulations also pointed out that an MIC of 1 mg/L would be linked to treatment failure for C. auris invasive infections and therefore, the resistance rate to amphotericin B may be higher than previously reported.

Biodegradation of acid red 3BN dye in sequential batch reactor: parameters and kinetics studies

Abstract Textile and dye industries generate wastewater which is considered as highly polluted and carcinogenic. Due to this, treatment of wastewater is required earlier to discharge or recycle. In the present studies, treatment of dye bearing water (DBW) has been explored. The treatment was performed using activated sludge (mixed culture) for aerobic process in sequential batch reactor (SBR). The fill volume (V F) and fill time (t F) variation in the treatment of DBW was taken place. The initial value of dye concentration, chemical oxygen demand (COD), sludge, and hydraulic retention time (HRT) were found to play important role in the treatment. At optimum condition (HRT = 2.5 d), the 86.84% COD reduction of 190 mg/L COD, and 92.33% dye reduction of 339 mg/L dye were achieved. These values are equal to overall 94.85% dye reduction of 500 mg/L, and 93.15% COD reduction of 380 mg/L. As a result, 500 mg/L dye was reduced to 26 mg/L, and 380 mg/L COD was reduced to 25 mg/L. The biodegradation fitted to Monod kinetics, for which kinetics parameter values of specific growth rate constant of biomass µ = 0.0047 h−1, yield coefficient (Y) = 1.059, and substrate utilization rate (q) = 0.0044 h−1 were evaluated at HRT = 2.5 d. The results show, this process can be applied to treat Acid Red 3BN Dye Water (AR3BNDW).

Atomic layer deposition of palladium thin film from palladium (II) hexafluoroacetylacetonate and ozone reactant

Palladium thin films have been grown by thermal atomic layer (ALD) process using Palladium (II) hexafluoroacetylacetonate (Pd(hfac)2) and O3 as the precursors without molecular hydrogen or formalin in a temperature range of 180–220 °C. The palladium films were deposited on sapphire (α-Al2O3, (0001)), silicon (Si, (111)) and silica (SiO2, (100)) substrates at a constant growth rate of about 0.25 Å per cycle. The metallic palladium films produced were highly uniform without fluorine contamination. The surface roughness was only 0.2 nm. The resistivity of the metallic palladium film at ∼25 nm in thickness deposited at 200 °C was around 63 μΩ cm. The morphology of Pd thin films on sapphire, silicon and silica surfaces revealed the island growth and these islands finally coalesced after applying 800 cycles. Thickness-controllable palladium films were obtained with shortened pulse time of both reactants (Pd(hfac)2 and ozone). Our work provides important guidelines for fabrication of metals by adjusting reaction parameters in thermal ALD process.

A proposal for the equivalence between the rates of net photosynthesis and growth rate constants for submerged aquatic plants

A proposal for the equivalence between the rates of net photosynthesis and growth rate constants for submerged aquatic plants

The growth kinetic behaviors of the intermetallics at W/Co interface under the current of spark plasma sintering

The interdiffusion behaviors of elements at the W/Co interface under the application of current during SPS were investigated. It is found that Co7W6 and Co3W are formed at the W/Co bonding interface. The growth of the Co3W layer is apparently improved by the high current during SPS. The growth rate constant of the Co3W layer undercurrent is 1.73–3.03 times faster than that without current. The research shows that the growth rate is increased with the current density. The growth activation energy of the Co3W layer is calculated to be 229.51 ± 27 kJ mol−1 undercurrent, which is smaller than that without current (279.38 ± 11 kJ mol−1). Moreover, the growth activation energy of the Co3W layer is decreased with the increase of the current density. The mechanism of current-improved growth of the Co3W layer is suggested to be the fact that the current lowers the nucleation barrier of intermetallic layer, which accordingly promotes chemical reactions.