Logistic Function Research Articles

Simultaneous removal of heavy metals and Escherichia coli from water using silver-doped hydroxyapatite-coated activated carbon nano composite-alginate beads

The scarcity of clean water due to heavy metal and microbial contamination is a global issue. In many parts of the world, heavy metals such as Pb, Cd, and U, along with bacteria like Escherichia coli, have been found to exceed permissible limits in groundwater and other water sources that the public depends on for daily drinking water. To address this, we have synthesized a novel composite material consisting of Ag-impregnated hydroxyapatite-coated activated carbon nanoparticles embedded in alginate beads, for the simultaneous removal of heavy metals (U, Pb, and Cd) and Escherichia coli from drinking water. The material's efficiency was evaluated through a series of batch and column experiments. Batch studies indicate 90 % sequestration of U within 5 hours and Pb and Cd within 7 hours, while Escherichia coli (107 cfu/mL) was eradicated instantly. The study confirms that sorption follows pseudo-second-order kinetics via chemisorption and ion-exchange mechanisms. Fixed-bed column studies, using a logistic growth model, showed strong agreement between theoretical and experimental parameters for the Bohart-Adams, Thomas, and Yoon-Nelson models. The beads demonstrated a high affinity for heavy metals, achieving complete removal and disinfection within an empty bed contact time of 1.12 minutes. Reusability studies indicate that even after the third regeneration and reuse cycle, removal efficiency remained about 95 % for U and Pb, and 85 % for Cd. Furthermore, the effects of variations in water quality parameters such as pH, dissolved carbonates, humic acid, and ionic strength (except for Cd) on removal efficiency were minimal. In summary, the study revealed that the Ag-impregnated hydroxyapatite-coated activated carbon nanoparticles embedded in alginate beads are an efficient, sustainable, and cost-effective material for the simultaneous removal of Pb, Cd, U, and Escherichia coli from water with diverse physicochemical properties.

Stability of solutions to the logistic equation with delay, diffusion and nonclassical boundary conditions

Stability of solutions to the logistic equation with delay, diffusion and nonclassical boundary conditions

Numerical study on Prandtl number dependence of thermal convection in an internally heated pool

Large-eddy simulations have been conducted to study natural convection in a corium pool. The study focuses on a hemispherical pool with uniform volumetric heat generation, complemented by isothermal cooling on all exterior surfaces. The internal Rayleigh number (Rai), correlated with the internal heat generation, is fixed at 1015. The Prandtl numbers (Pr) examined vary from 0.32 to 10. While previous experimental studies have explored internally heated pool convection primarily in the Pr≥3 range using liquids, the present research extends the investigation to the Pr<3 range, including the value for corium of about 0.5. The simulation results indicate that the overall Nusselt number (Nu), defined as the volume averaged pool temperature relative to the total heat flux adheres to power laws of Nu∼Pr0.073 for 0.32≤Pr≤1 and Nu∼Pr0.021 for 3.2≤Pr≤10. Consequently, the Nu at the Pr of 0.32 is observed to be 17% lower than that at the Pr of 10. A correlation for Nu is proposed as Nu=1+0.0636Rai0.231+1.39Pr−1.18−0.0847 using a generalized logistic function that combines theoretical scaling laws of Nu∼Pr0.1 for Pr≪1 and Nu∼Pr0 for Pr≫1. This study also includes theoretical analyses, elucidating dependencies of Pr on various parameters, such as the Nusselt number, Reynolds number, the proportion of the heat flux at the upper cooling wall relative to the total generated heat, and the height of the stratified zone.

A stochastic model for the bacterial growth exhibiting staged growth, desynchronization, saturation and persistence

We consider a model of population growth based on the stochastic variation of the population size-controlled duplication of bacterial cells. It is shown that the proper choice of the control function allows for reproducing a variety of regimes: a logistic growth with saturation, a hindered growth typical for persistent bacterial systems, and a linear population growth detected for some mycobacterial populations. When supplied with the rectangular function having the width equal to the generation time, this approach represents the solution generalizing Rubinow’s age-maturity model reproducing systems with desynchronisation and saturation. The model’s plausibility is confirmed by the direct comparison with real data for the growth of M. tuberculosis populations obtained with the BACTEC MGIT system under different conditions of growth synchronisation.

Development of Piophila megastigmata (Diptera: Piophilida) at seven constant temperatures

In forensic entomology, the time-related growth and development of carrion insects allows for the estimation of the minimum postmortem interval (PMImin). Piophila megastigmata (Diptera: Piophilidae) is of great significance in estimating PMImin in the late stage of corpse decay. In this paper, the development of P. megastigmata was investigated under the seven constant temperatures of 16–34 °C. The total development time at each temperature was 970.38, 824.50, 593.13, 498.25, 392.00, 385.63 and 405.87 h, respectively. The isomorphen diagram shows the trend of development during different developmental stages at different temperatures. By using a revised linear regression model, the estimated lower lethal developmental thresholds (TL) and thermal summation constant (K) were found to be 10.57 °C and 6936.78 degree hours, respectively. According to a nonlinear model, the TL, upper lethal developmental thresholds (TH), and intrinsic optimum temperature (TΦ) were determined to be 7.53, 34.68, and20.43 °C, respectively. Also, logistic function and an isomegalen diagram were constructed according to the continuous changes in larval body length, and illustrates the time required to develop to a certain length at different temperatures. The obtained results offer crucial fundamental developmental information regarding P. megastigmata, which can be applied in PMImin estimation.

A hybrid framework for Detection of Multivariate porphyry Cu Signatures and Anomaly Enhancement: Incorporation of SFA, GMPI, and Grey Wolf Optimization

Geochemical data from stream sediment are commonly employed for regional scale mineral exploration, as they can be utilized to detect geochemical anomalies associated with mineralization processes. However, recognizing efficient multielement geochemical signatures related to target mineralization using stream sediment geochemical data can be challenging due to the intricate nature of mineralization events. To achieve this goal, this article proposes a combination of statistics, logistic functions and machine learning techniques. Initially, the staged factor analysis (SFA) approach was applied to the data to determine the geochemical footprints associated with porphyry copper mineralization in the Varzaghan area. Subsequently, the geochemical mineralization probability index (GMPI) was utilized to facilitate appropriate separation, more precise identification, and the transfer of data into a fuzzy space. By using a combination of SFA and GMPI, it was feasible to enhance the detection of geochemical halos and concealed anomalies. Ultimately, the output of these two approaches was subjected to an improved clustering technique known as GWO-K-means to detect geochemical anomalies. The findings indicated that there is a strong relationship between known mineral occurrences (KMOs) and the identified anomalous areas. The success rate curve demonstrated that the optimized model outperformed the K-means model, proposing that optimization can boost the accuracy in identifying geochemical targets. Overall, the outcomes of this study can be beneficial for proper planning of future exploration activities.

Investigation of the polysaccharides synthesis enhancement mechanism from Agaricus bitoquis (Quél.) Sacc Chaidam and its fermentation regulation technology system based on multi-omics technologies

The polysaccharides (PS) of Agaricus bitoquis (Quél.) Sacc. Chaidam (ABSC) had attracted the attention of researchers due to their strong anti hypoxia, antioxidant, and anti fatigue activities. Therefore, this article focuses on studying the regulatory channels of exogenous additives-Lycium ruthenicum Murr. Anthocyanin (LRA) to delay fungus cell aging and promote the incremental synthesis of PS from ABSC, and optimizing the regulation system for pilot fermentation experiments. The joint analysis of Ultra High Performance Liquid Chromatography-Quadrupole-Time of Flight Mass Spectrometry (UHPLC-Q-TOFMS) and RNA sequencing (RNA-seq) database elucidates that at the molecular level, the crude extract of LRA inhibits the Telecommunications Association (TCA) cycle, transferring carbon metabolism to the synthesis of polysaccharide precursors (UDP-glucose, UDP-galactose, etc.), promoting the synthesis of PS, promoting the formation of key antioxidant substances (including flavonoids such as quercetin and alginate), improving cell membrane fluidity (saturated fatty acid to unsaturated conversion) and enhancing the degradation of toxic substances (oxidized glutathione), thereby promoting the anti-aging activity and PS synthesis ability of mycelial cells; LRA-adding could enhance the activity in the pilot fermentation of ABSC, which make the mycelia biomass, EPS and IPS production were significantly increased (89.04 %, 65.46 % and 37.64 % respectively) compared with the untreatment control. Based on the optimal fermentation system of PS synthesized in mycelium by adding LRA, Logistic, Gauss, and Asymptotic kinetic equations were used to describe the cell growth, product synthesis and regulatory substrate consumption from ABSC. The correlation coefficients of three models were all above 0.95, indicating a good fit between the experimental values and predicted value, this indicated ABSC fermentation kinetics model could better simulate the actual production process and provide theoretical data for the industrial production of polysaccharides. The results demonstrated that the present proposed LRA intensification approach could be useful to boost up the fermentation of ABSC, which possibly applied to yield increase and fermentation product acquisition of macrofungi.

Association between joint physical activity and sleep duration and hypertension in US adults: Cross-sectional NHANES study

BackgroundPrevious studies have adequately demonstrated that physical activity or healthy sleep duration can reduce the risk of hypertension. However, the combined effects of physical activity and healthy sleep on hypertension have not been well explored in studies using nationally representative samples. MethodsThe data were obtained from the National Health and Nutrition Examination Survey (2007-2018). Sleep duration and physical activity were obtained from self-reported questionnaires. Survey logistic regression and restricted cubic spline curves were used to evaluate the joint effects of physical activity and healthy sleep duration on hypertension. ResultsA total of 18,007 participants were enrolled in the main study. Physical activity was categorized into insufficient physical activity (600 < Met-min/week) and sufficient physical activity (≥600 Met-min/week). Sleep duration of ≤6 or ≥9 hours was defined as unhealthy sleep duration, and 7-8 hours was defined as healthy sleep duration. Compared to the individuals with unhealthy sleep duration and insufficient physical activity, only the participants with healthy sleep duration and sufficient physical activity (adjusted odds ratio: 0.76, 95% CI 0.66-0.88) were negatively associated with hypertension, while the participants with healthy sleep duration but insufficient physical activity or sufficient physical activity but unhealthy sleep duration were not associated with hypertension. Physical activity was nonlinearly associated with hypertension in the healthy sleep duration group, whereas in the unhealthy sleep duration group, physical activity was not associated with hypertension. ConclusionOur findings indicate that sufficient physical activity and healthy sleep duration were negatively associated with hypertension. This underscores the importance of integrating both sufficient physical activity and healthy sleep duration in strategies aimed at reducing hypertension risk.

Analyzing steady-state equilibria and bifurcations in a time-delayed SIR epidemic model featuring Crowley-Martin incidence and Holling type II treatment rates

This article presents a time-delayed SIR epidemiological model that has been quantitatively examined. The model incorporates a logistic growth function for the susceptible population, a Crowley-Martin type incidence, and Holling type II treatment rates. We investigated two separate time delays. The first delay refers to the rate at which new infections occur, allowing us to evaluate the impact of the latent period. The second delay relates to the rate of treatment for those who have contracted the infection, which allows us to examine the consequences of postponed access to therapy. The investigation of the steady-state behavior of the model emphasizes two equilibria, namely, the infection-free equilibrium and the endemic equilibrium. The determination of critical values involves the use of the fundamental reproduction number, denoted R0, which serves as a predictive measure to determine the potential elimination of a disease within a specific population. Using the fundamental reproduction number, it can be shown that infection-free equilibrium exhibits local asymptotic stability when the value of R0 is less than 1. In contrast, when R0 exceeds 1, the infection-free equilibrium becomes unstable in the context of the time-delayed system. Furthermore, an analysis of the steady-state dynamics of the endemic equilibrium indicates the appearance of oscillations and periodic solutions with the Hopf bifurcation for all feasible combinations of two-time delays as the bifurcated parameter. In sensitivity analysis, a sensitivity index is utilized to evaluate the relative modification in the fundamental reproduction number caused by each parameter. In summary, numerical simulations are employed to offer empirical evidence for the theoretical findings.

The complexity of cerebral blood flow regulation: the interaction of posture and vasomotor reactivity.

Arterial carbon dioxide ([Formula: see text]) and posture influence the middle (MCAv) and posterior (PCAv) cerebral artery blood velocities, but there is paucity of data about their interaction and need for an integrated model of their effects, including dynamic cerebral autoregulation (dCA). In 22 participants (11 males, age 30.2 ± 14.3 yr), blood pressure (BP, Finometer), dominant MCAv and nondominant PCAv (transcranial Doppler ultrasound), end-tidal CO2 (EtCO2, capnography), and heart rate (HR, ECG) were recorded continuously. Two recordings (R) were taken when the participant was supine (R1, R2), two taken when the participant was sitting (R3, R4), and two taken when the participant was standing (R5, R6). R1, R3, and R5 consisted of 3 min of 5% CO2 through a mask and R2, R4, and R6 consisted of 3 min of paced hyperventilation. The effects of [Formula: see text] were expressed with a logistic curve model (LCM) for each parameter. dCA was expressed by the autoregulation index (ARI), derived by transfer function analysis. Standing shifted LCM to the left for MCAv (P < 0.001), PCAv (P < 0.001), BP (P = 0.03), and ARI (P = 0.001); downward for MCAv and PCAv (both P < 0.001), and upward for HR (P < 0.001). For BP, LCM was shifted downward by sitting and standing (P = 0.024). For ARI, the hypercapnic range of LCM was shifted upward during standing (P < 0.001). A more complete mapping of the combined effects of posture and arterial CO2 on the cerebral circulation and peripheral variables can be obtained with the LCM over a broad physiological range of EtCO2 values.NEW & NOTEWORTHY Data from supine, sitting, and standing postures were measured. Modeling the data with logistic curves to express the effects of CO2 reactivity on middle cerebral artery blood velocity (MCAv), posterior cerebral artery blood velocity (PCAv), heart rate, blood pressure (BP), and the autoregulation index (ARI), provided a more comprehensive approach to study the interaction of arterial CO2 with posture than in previous studies. Above all, shifts of the logistic curve model with changes in posture have shown interactions with [Formula: see text] that have not been previously demonstrated.

A novel rigid Foot-Ground contact model for Predicting ground reaction forces and center of pressure during normal gait

Ground reaction forces (GRFs) and center of pressure (COP) are essential for understanding human motion and evaluating biomechanical parameters, but measuring them with force plates is often limited in many scenarios. In this study, we propose a novel methodology for estimating GRFs and COP during normal gait based on a rigid foot–ground contact model, referred to as the COP phase transition continuity model (COP-PTCM). The GRFs and COP are calculated based on the Newton-Euler Equations during the single support phase (SSP). Considering the spatiotemporal continuity of the COP trajectory during normal gait, the COP data for the double support phase (DSP) is obtained by an improved logistic function fitted using the COP data from the SSP. GRFs during the DSP are optimized using the minimum energy hypothesis. The COP-PTCM method is used to estimate the GRFs and COP of ten participants during normal gait, and the results are compared with simultaneously measured force plate data, yielding the relative root mean square error (rRMSE) between measured and estimated GRFs in the anterior-posterior, vertical, and medial–lateral directions are 10.90 ± 2.09 %, 4.73 ± 1.44 %, and 15.17 ± 1.69 %, respectively. Additionally, the rRMSE between measured and estimated COP in the anterior-posterior direction is 11.23 ± 0.03 %. The above comparison validates the effectiveness and accuracy of the proposed method.

A Stochastic SIR Epidemic with Nonlinear Power Functions and Logistic Growth

This research conducts a comprehensive analytical investigation into a stochastic SIR epidemic model that integrates nonlinear power functions and logistic growth dynamics. We examine the intricacies of model behavior, demonstrating its capability to produce a positive global solution. Utilizing precisely defined Lyapunov functions, we demonstrate the essential prerequisites for establishing the ergodicity of this particular model. Furthermore, the research deduces adequate criteria for predicting the eventual eradication of infectious diseases within this theoretical framework. Ultimately, we supplement the study with numerical simulations to elucidate and substantiate the analytical findings. This work contributes to comprehending epidemic systems with nuanced growth patterns and intricate disease transmission mechanisms, offering insights into real-world epidemic potential behaviors and outcomes.

Modeling the Two-Strain Dynamics of COVID-19 in Ghana Using a Logistic Growth Model

Through mutation, viruses constantly change, bringing into existence new variants; SARS-CoV-2 is no different. In December 2020, variants with different characteristics that could affect transmissibility and death emerged around the world of which Ghana is not an exception. To address this new phenomenon, a two-strain mathematical model of SARS-CoV-2 was formulatedto analyzed thetransmission dynamicsin Ghana. Thedisease-free equilibriumwas calculated. The basicreproduction number, &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;/sub&amp;gt;= max{&amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0A&amp;lt;/sub&amp;gt;, &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0B&amp;lt;/sub&amp;gt;} = max(0.9957945674, 1.109170840), associated with the model is computed using the next generation matrix operator. The disease-free equilibrium is found to be locally asymptotically stable when both &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;I&amp;gt;A&amp;lt;/I&amp;gt;&amp;lt;/sub&amp;gt;, &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;I&amp;gt;B&amp;lt;/sub&amp;gt; &amp;lt;sub&amp;gt;&amp;lt;/I&amp;gt;&amp;lt;/sub&amp;gt;&amp;lt; 1, but unstable otherwise. In addition to the disease-free, the boundary equilibrium for strain &amp;lt;I&amp;gt;A&amp;lt;/I&amp;gt; and strain &amp;lt;I&amp;gt;B&amp;lt;/I&amp;gt; was also calculated. Using the Gershgorin’s circle theorem, it was shown that the boundary equilibrium is locally asymptotically stable when both &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;I&amp;gt;A&amp;lt;/I&amp;gt;&amp;lt;/sub&amp;gt;, &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;0&amp;lt;I&amp;gt;B&amp;lt;/sub&amp;gt; &amp;lt;sub&amp;gt;&amp;lt;/I&amp;gt;&amp;lt;/sub&amp;gt;&amp;gt; 1, but unstable when otherwise. Simulations of the model were carried out. Results indicate that the government should intensify its efforts to vaccinate a larger proportion of the population and also recommends implementing comprehensive control measures, such as the use of face masks, social distancing, and contact tracing, to mitigate the spread of the disease.

Estimating genetic parameters and trends in growth curve traits of Zandi sheep using the SAEM algorithm.

The objectives of this study were to evaluate the influence of environmental effects on growth curve traits of Zandi lambs and estimate their genetic parameters with the best-fit animal model. For this purpose, live body weight (BW) records (n = 10,607) of 2,519 individuals (which were progeny of 278 rams and 1,485 ewes) were used to estimate genetic effects on growth curve traits from birth to yearling age of Zandi lambs. Using the Stochastic Approximation Expectation Maximization (SAEM) algorithm the growth curve parameters of five different mixed functions (i.e., Brody, Richards, Von Bertalanffy, Gompertz and Logistic) were obtained, then for the most appropriate model the genetic parameters were estimated using a Bayesian approach fitted multivariate animal model and ignoring or including maternal genetic effect. Except Richards model, all other mixed functions used here closely fitted actual BW records (R2 > 0.96). However, the Logistic function provided the best fit in every type. So, studied growth curve traits were estimated asymptotic weight which considered as mature weight (a), rate parameter (b), rate of maturing (k), and age (Ai)/weight (Wi) at the point of inflection. Of the fixed effects studied (i.e., gender, birth type, dam age, season and year of birth), the only non-significant relationship was the effect dam age on b and Ai. Based on the best-fitted model, posterior means of heritability estimates for a, b, k, Wi and Ai were 0.142 ± 0.036, 0.094 ± 0.029, 0.143 ± 0.063, 0.149 ± 0.039 and 0.029 ± 0.013, respectively. Posterior means of genetic correlations between mentioned traits ranged from -0.018 ± 0.069 (b-k) to 0.959 ± 0.029 (a-b), whereas the phenotypic correlation varied from -0.047 ± 0.014 (b-k) to 0.836 ± 0.007 (a-b). It was concluded that the model including only direct additive effect was sufficient to explain the variation in all investigated growth traits of Zandi lambs, selection for these traits results in slow genetic gain (due to the lack of sufficient genetic variation), but it would not be difficult to improve their mature weight and rate of maturing jointly. The results indicate that although the rate of genetic change for mature weight has been small (0.008 ± 0.003 kgyear-1; P < 0.05) but in the favorable direction for this breed.

Advancing timber construction: historical growth, research frontiers, and time series forecasting

ABSTRACT Lauded for its capacity to curtail building energy consumption and enhance environmental performance compared to traditional mineral-based materials, wood has gained substantial traction in the construction sector. Timber construction, which is a focal point of growing interest in both industry and academia, warrants a reassessment of its historical trajectory and future prospects. This study examines publications on timber construction from 1990 to 2022 to analyze the growth path, shifting hotspots, and potential research directions in this field. By employing scientometric analysis, influential journals, articles, countries, and keywords are identified. Integration into a logistic growth model (LGM) showcases publication trends, while the Prophet model forecasts global growth. Research frontiers and emerging themes are revealed through keyword bursts surge evolution. This study offers a visualized knowledge framework, bridging current research with future trends and enabling practitioners and researchers to comprehensively grasp the evolution of timber construction.

Modeling and Analysis of Resistance-Sensing Characteristics for Two-Way Shape Memory Alloy-Based Deep-Sea Actuators

Deep-sea actuators based on shape memory alloys (SMAs) are an emerging frontier field of multidisciplinary crossover, and the resistive sensing characteristics are the basis for the drive control of SMA deep-sea actuators. The resistance and resistivity of SMAs are complex and highly dependent on temperature and stress, and there is no complete description of SMAs for extreme environments of high pressure, low temperature, and high salinity in the deep sea. In this study, the logistic function is introduced to improve the kinetic equation of phase transition, and the macromechanical model, the law of resistance, and the resistivity mixing rule are integrated to model and analyze the resistive self-awareness characteristics of two-way shape memory alloy deep-sea actuators. The complex coupling relationships among resistance, strain, stress, resistivity, and temperature under constant load conditions are investigated, and the validity of the resistance-sensing model is verified by the water bath cycling test. The results show that the predicted values of the model agree well with the measured values. The self-perceived relationship between the resistance and deformation of the two-way shape memory alloy can be effectively expressed, which provides theoretical model support for the design of memory alloy deep sea actuators and sensorless drive control.

Mahgoub Transform And Ulam Stability Of Logistic Growth Differential Equation

Mahgoub Transform And Ulam Stability Of Logistic Growth Differential Equation

Modelling the impact of host galaxy dust on type Ia supernova distance measurements

ABSTRACT Type Ia Supernovae (SNe Ia) are a critical tool in measuring the accelerating expansion of the universe. Recent efforts to improve these standard candles have focused on incorporating the effects of dust on distance measurements with SNe Ia. In this paper, we use the state-of-the-art Dark Energy Survey 5 year sample to evaluate two different families of dust models: empirical extinction models derived from SNe Ia data and physical attenuation models from the spectra of galaxies. In this work, we use realistic simulations of SNe Ia to forward-model different models of dust and compare summary statistics in order to test different assumptions and impacts on SNe Ia data. Among the SNe Ia-derived models, we find that a logistic function of the total-to-selective extinction $R_V$ best recreates the correlations between supernova distance measurements and host galaxy properties, though an additional 0.02 mag of grey scatter is needed to fully explain the scatter in SNIa brightness in all cases. These empirically derived extinction distributions are highly incompatible with the physical attenuation models from galactic spectral measurements. From these results, we conclude that SNe Ia must either preferentially select extreme ends of galactic dust distributions, or that the characterization of dust along the SNe Ia line-of-sight is incompatible with that of galactic dust distributions.

Inactivation kinetics of dairy phages using photocatalytic paint under diverse environmental conditions and radiation sources

This article investigates the efficacy of a photocatalytic paint for bacteriophages inactivation under various levels of incident radiation flux, relative humidity and radiation sources. Two phages that infect lactic acid bacteria were selected: J-1, infective of Lacticaseibacillus casei ATCC 27139, and M13-G1b, infective of Streptococcus thermophilus G1b. Phage suspensions were deposited on coated and uncoated plates and exposed to radiation typically used for indoor illumination (λ = 360–720 nm). A first-order inactivation kinetics was proposed with respect to the Plaque Forming Units per mL (PFU/mL) that correlates the inactivation constant with the operating conditions. The kinetic constant of this novel model combines a potential function for the incident radiation flux and a logistic function for the relative humidity. The results showed that as these variables increased, phage inactivation turned higher for both uncoated and coated plates. Photonic and quantum efficiencies were also calculated for both phages, when treated with photocatalytic paint under UV-A radiation. The photonic efficiencies were 8.03 × 1012 PFU/Einstein for J-1 and 4.05 × 1012 PFU/Einstein for M13-G1b, while the quantum efficiencies were 1.19 × 1013 PFU/Einstein for J-1 and 6.03 × 1012 PFU/Einstein for M13-G1b. Good agreement was obtained between predictions of the proposed kinetic model and experimental data, with a Root Mean Square Error of 4.43 % for J-1 and 2.98 % for M13-G1b. The developed model would be useful to predict phage inactivation under diverse combinations of operating conditions levels in environments of dairy plants, different from those tested in this work.

The Logistic Function in Glass Transition Models of Amorphous Polymers: A Theoretical Framework for Isobaric Cooling Processes

AbstractStudying the macroscopic‐phenomenological behavior of amorphous polymers at glass transition is often subject to limitations because the ordinary differential equations that describe the material behavior require numerical solution. To avoid these limitations, ad‐hoc‐formulated models of the glass transition have been proposed. However, their scope of application is expected to be limited due to insufficient theoretical foundation. This work establishes a theoretical framework for models that use the logistic function to approximate the macroscopic‐phenomenological behavior of amorphous polymers at glass transition. For this purpose, an exactly‐solvable Riccati equation is derived within thermodynamics with internal state variables. A closed‐form expression in terms of mathematical functions for the temperature derivative of a single internal state variable is the result. This closed‐form expression contains the logistic function thus featuring a continuous transition region centered around a pressure and cooling‐rate dependent transition temperature. Based on comparison of existing models with the exact solution derived from the Riccati equation, generalized models that approximate the thermal expansion coefficient and heat capacity at glass transition are proposed. This work thus demonstrates the validity of the logistic function in glass transition models of amorphous polymers and provides suggestions as to how existing models can be extended in their applicability.