Class Of Growth Models Research Articles

Location-Dependent Phase Transformation Kinetics During Laser Wire Deposition Additive Manufacturing of Ti–6Al–4V

This work models the microstructural evolution as a function of position in laser-wire deposited Ti–6Al–4V parts using a classical multi-component JMAK nucleation and growth model with additive isothermal time-steps. Model predictions are compared to experimental observations. The model can be used to interpret nucleation and growth kinetics of various characteristic features of the microstructure that are inaccessible by experiments. It explains the presence of “layer bands” at specific locations unrelated to the weld bead structure. The last re-heating (of multiple thermal cycles) of a solidified layer, and where it peaks, plays a key role in increasing the nucleation density at specific locations, resulting in full α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-colony microstructures constituting the “layer bands,” while the rest of the build is predominantly basketweave. Additionally, changes in the basketweave α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-lath thickness as a function of the distance from the substrate are studied and compared with an Arrhenius-type function, with results highlighting a more complex relationship than an Arrhenius-type function would suggest.

A Panel Analysis on the Nexus between Financial Development, Oil Production, and Trade-Openness and Its Impact on Sustainable Economic Growth: Evidence from Selected Arab Economies

In accordance with the United Nations Sustainable Development Goals agenda for decent and sustainable economic growth highlighted in the UNSDGs-8, several economies over the years have been on the quest for drivers for decent and sustainable economic growth, of which the Arab bloc is no exception. To this end, the present study draws strength from the classical growth model while exploring the dynamic nexus between oil production and economic growth while accounting for other key growth drivers like gross capital formulation accumulation, labour, trade openness, and financial development for a balanced panel of selected Arab economies. To operationalise the study objectives, the present study leverages second-generational panel econometric approaches. The econometrics techniques applied circumvent the cross-sectional dependency and slope heterogeneity in the sampled bloc. For co-integration analysis, the Westerlund’s panel co-integration test affirms a long-run equilibrium relationship between the study’s outlined variables. Furthermore, for long-run estimates, the present study leverages the common correlated effects mean group (CCEMG) methodology and the augmented mean group (AMG) method for robustness and soundness of the results and coefficients. The present study corroborates the trade-induced growth hypothesis in the entire panel at a p < 0.001 statistical level, which resonates with the mercantilism school of thought. Additionally, the present study also affirms the Solow–Swan hypothesis, where gross capital formation accumulation and labour drive economic growth. Interestingly, the panel bloc shows that oil production is a key driver to the nation’s economic growth, at a p < 0.05 statistical level. However, from a policy standpoint, there are policy suggestions for diversification of the Arab economies to move from a mono-economy dependent on oil production to other sectors like service, industry, and manufacturing, which require labour, capital accumulation, and more. Further policy caveats are outlined in the concluding section.

RADIOCARBON AGES OF PLANT REMAINS IN MASSIVE GROUND ICE AND UNDERLYING SEDIMENTS OF THE BARROW PERMAFROST TUNNEL, ALASKA

ABSTRACT Massive ground ice found in the Barrow Permafrost Tunnel at 3–7 m depths from the surface has been interpreted as an ice wedge and used to reconstruct early Holocene environmental changes. To better understand the development of this ground ice, we conducted radiocarbon dating for 34 samples of plant remains from the massive ground ice and underlying sediment layer. A significantly large gap in the measured radiocarbon ages (more than 24 ka) between massive ice and the underlying sediment layer throughout the tunnel profile suggested at least two possibilities. One is that the lower and older sediment layer had thrust upwards at the boundary between intruding ice wedge and adjacent sediment, and the growing ice had pushed the sediment sideways. Another is that erosional events had removed surface materials at about 12–36 ka BP (14–41 cal ka BP) before the overlaying sediment layer with massive ground ice developed. The overall distribution of radiocarbon ages from the massive ice supported the ice-wedge hypothesis as a formation mechanism, although our results showed several age inversions and large fluctuations. Dating of densely spaced samples revealed two ground-ice regions with similar ages around 11–11.5 and 10–10.5 ka BP divided by a relatively narrow region of transitional ages along the tunnel long-axis. This distribution may be explained by a possible misalignment between the sampling direction and the ice-wedge growth line or by intermittent ice growth with repeated cracking at more random locations than the classic ice-wedge growth model suggested.

Deciphering the effect of nucleation/growth kinetics on the morphology of Li plating/stripping on vertically aligned carbon nanofibers - A low-tortuosity 3-D nanostructured carbon host

Reversible lithium metal anodes (LMAs) are the holy grail for future rechargeable lithium metal batteries. Three-dimensional (3-D) conductive hosts have been extensively explored as an effective approach to suppressing dendrite formation and enabling reversible Li plating/stripping. However, the microscopic morphologies of Li plating and their correlation with the cell performance are not clear. Herein we unravel these issues using the vertically aligned carbon nanofiber (VACNF) array as a model 3-D conductive carbon host which has a well-defined vertical low-tortuosity structure allowing observation of the intrinsic Li morphologies infiltrated into the 3-D host. The VACNF array indeed provides much higher stability and reversibility for Li plating/stripping due to its high surface area and lithiophilic properties. We found that Li plating on both VACNF array and planar Cu electrodes follows the classical nucleation and growth model. Though the low plating current density (≤0.10 mA/cm2) provides better cycling stability consistent with the Sand’s equation, it forms sparse irregular grains stacked with dendrite-like long Li fibers. In contrast, the moderate to high plating current densities (1.0 − 5.0 mA/cm2) produce more uniform Li morphologies consisting of smaller micro-columns or micro-spheres. By decoupling the plating and stripping current densities, we unravel that the more uniform micro-columnar Li infiltrated in the VACNF array obtained at the moderate plating current density (∼1.0 mA/cm2) indeed exhibits the highest cycling performance. This provides new insights into the relationship between macroscopic electrochemical tests and microscopic Li morphologies, aiding in optimizing the performance of LMAs based on 3-D conductive hosts.

A criterion of periodic point stability based on Lyapunov exponent

The logistics equation is the most classical model of population growth. Influenced by external environmental factors and growth inertia, the total population is in a state of periodic equilibrium. so, studying the stability of the periodic solution of the logistics equation is an important issue. If the logistics equation is considered as a function, the general method to judge the stability of the periodic point is to bring in the derivative of the function after iterating n times to take the value. The Lyapunov exponent is originally an important method used to judge the stability of dynamical systems. If the logistics map is considered as a discrete dynamical system, applying the Lyapunov exponent to the determination of the periodic solution will largely reduce the computational effort.

A calibration and uncertainty quantification analysis of classical, fractional and multiscale logistic models of tumour growth

Background and Objective: The validation of mathematical models of tumour growth is frequently hampered by the lack of sufficient experimental data, resulting in qualitative rather than quantitative studies. Recent approaches to this problem have attempted to extract information about tumour growth by integrating multiscale experimental measurements, such as longitudinal cell counts and gene expression data. In the present study, we investigated the performance of several mathematical models of tumour growth, including classical logistic, fractional and novel multiscale models, in terms of quantifying in-vitro tumour growth in the presence and absence of therapy. We further examined the effect of genes associated with changes in chemosensitivity in cell death rates. Methods: The multiscale expansion of logistic growth models was performed by coupling gene expression profiles to the cell death rates. State-of-the-art Bayesian inference, likelihood maximisation and uncertainty quantification techniques allowed a thorough evaluation of model performance. Results: The results suggest that the classical single-cell population model (SCPM) was the best fit for the untreated and low-dose treatment conditions, while the multiscale model with a cell death rate symmetric with the expression profile of OCT4 (Sym-SCPM) yielded the best fit for the high-dose treatment data. Further identifiability analysis showed that the multiscale model was both structurally and practically identifiable under the condition of known OCT4 expression profiles. Conclusions: Overall, the present study demonstrates that model performance can be improved by incorporating multiscale measurements of tumour growth when high-dose treatment is involved.

Optimal allocations in growth models with private information

This paper considers a class of growth models with idiosyncratic human capital risk and private information about individual effort choices (moral hazard). Households are infinitely-lived and have preferences that allow for a time-additive expected utility representation with a one-period utility function that is additive over consumption and effort as well as logarithmic over consumption. Human capital investment is risky due to idiosyncratic shocks that follow a Markov process with transition probabilities that depend on effort choices. The production process is represented by an aggregate production function that uses physical capital and human capital as input factors. We show that constrained optimal allocations are simple in the sense that individual effort levels and individual consumption growth rates are history-independent. Further, constrained optimal allocations are the solutions to a recursive social planner problem that is simple in the sense that exogenous shocks are the only state variables. We also show that constrained optimal allocations can be decentralized as competitive equilibrium allocations of a market economy with a simple tax- and transfer scheme. Finally, it is always optimal to subsidize human capital investment in the market economy.

Off-Eutectic Growth Model for Solidifying Alloy from an Undercooled State

Classical eutectic growth models are based on the use of eutectic composition. These models neglect the effect of primary phase formation, and their direct use in the rapid solidification process of off-eutectic (hypoeutectic and hypereutectic) alloys is absent. Combining the effect of the primary phase in the eutectic transformation and an off-eutectic composition, the solidification growth model is derived in the present work. The effect of the model and material parameters on solidification kinetics is discussed in comparison with experimental data. Computational results on the off-eutectic growth model show that the model agrees well with experimental data on the solidification kinetics of Ni–B and Ti–Si alloys.

Reliability of Self-Driving Cars: When Can We Remove the Safety Driver?

Self-driving cars and other vehicles are being increasingly demonstrated, released, and deployed on roads. Yet only a handful of special-case vehicles have obtained a permit to go fully driverless, and our passenger cars still require drivers at the steering wheel to correct the car if something goes wrong. Safety drivers, which operate autonomous vehicles in testing phases, upon occasions were unable to correct the faulty behavior of their vehicles, inducing accidents and, unfortunately, casualties. This article proposes a method to analyze the reliability of autonomous vehicles applying the classical reliability theory and software reliability growth models (SRGMs). This method is then applied to real-world data to get some predictions on what is really needed to safely remove the driver and go fully driverless.

Fractional calculus in mathematical oncology

Even though, nowadays, cancer is one of the leading causes of death, too little is known about the behavior of this disease due to its unpredictability from one patient to another. Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, improvements are still necessary on these models. The primary objective of the present research is to prove the efficiency of fractional order calculus in mathematical oncology, more specifically in tumor growth modeling. For this, a generalization of the four most used differential equation models in tumor volume measurements fitting is realized, using the corresponding fractional order equivalent. Are established the fractional order Exponential, Logistic, Gompertz, General Bertalanffy-Pütter and Classical Bertalanffy-Pütter models for a treated and untreated dataset. The obtained results are compared by Mean Squared Error (MSE) with the integer order correspondent of each model. The results prove the superiority of the fractional order models. The MSE of fractional order models are reduced at least at half in comparison with the MSE of the integer order equivalent. It is demonstrated in this way that fractional order deterministic models can offer a good starting point in finding a proper mathematical model for tumor evolution prediction. Fractional calculus is a suitable method in this case due to its memory property, aspect that particularly characterizes biological processes.

Rough FTO electrode interface effect upon ferroelectric switching dynamics in Ag/P(VDF‐HFP)/FTO capacitor structures

AbstractRough FTO electrode interface effect upon the characteristic ferroelectric polarization parameters and switching dynamics in Ag/P(VDF‐HFP)/FTO junctions is systematically evaluated by varying electric field amplitude and frequency. Structural and microstructural studies confirm the ferroelectric phase formation of P(VDF‐HFP) on FTO surface. Tilted rectangular P‐E loops have been recorded in the applied fields ranging over 156.25–468.75 MV/m measured between 250 mHz and 5 Hz frequency ranges. Giant saturation of 21.7 μC/cm2 and remnant polarization of 34.9 μC/cm2 has been noted at low frequencies due to the influence of high electric field induced leakage currents. The coercive field, saturation and remnant polarization response with increase in electric field amplitude and frequency of the applied signal are well fitted with classic domain growth model proposed by Kolmogorov‐Avrami‐Ishibashi. A switching time scales of 32.2–693 ms has been observed for forward switching while for backward switching it is noted as 22.1–618.8 ms, when measured at frequencies from 5 Hz to 250 mHz. Furthermore, the tilted P‐E loops are attributed to the excessive leakage currents due to the high surface roughness of FTO bottom electrode.

Robotic platform for accelerating the high-throughput study of silver nanocrystals in sensitive/selective Hg2+ detection

Colorimetric determination of trace mercury ions (Hg2+) with high reproducibility and sensitivity is urgently required for water safety and environmental monitoring. Herein, an automated robotic platform is described for high-throughput and controllable synthesis of colloidal silver nanocrystals (Ag NCs) and sensitive/selective colorimetric determination of Hg2+ in aqueous solutions. The predicted models of optical simulation are constructed as data-driven models to evaluate the quality of Ag NCs synthesized by a wet-chemical method. Based on an experimental database derived by optical characterization, the machine-learning (ML) model which covers multiple synthesis parameters is established for uniform synthesis of Ag NCs with controllable sizes matching the classical growth model. Moreover, the database of more than 1,200 valid samples established for the optical properties of Ag NCs is digitized to correlate with their average size. Optimized manual re-synthesis of high-quality Ag NCs demonstrates the practical feasibility and scalability of established models. The prepared Ag NCs can be used directly or modified with polymer ligands for quantitative detection of Hg2+ in the linear range from 0.01 to 200 µM with a detection limit of 3 nM. The strategy provides a scientific and effective way for the high-throughput study of nanoscale optical materials in chemical engineering and environmental monitoring.

Modeling of SrTiO3 polycrystalline substrate grain growth for tuning thin film functional properties

In the Combinatorial Substrate Epitaxy (CSE) approach, a thin film is grown at high temperature on a polycrystalline substrate. Those substrates induce a local film epitaxy on each substrate grain and an overall polycrystalline character on the macroscopic scale. Compared to single-crystalline films, this approach provides the possibility to introduce, in a controlled way, grain boundaries providing new functionalities. Therefore, controlling the microstructure and grain size of the substrates is an important step for tuning the film properties. In this paper, a complete study of the granular growth of the standard substrate material for the deposition of perovskite thin films, SrTiO3, has been carried out with different isothermal cycles highlighting the grain growth mechanisms. From these results, we are able to predict the sintering thermal cycle necessary for targeting very precisely a desired grain size and the corresponding physical properties. Indeed, highly restraint physical properties specifications are needed for advanced electronic applications. Since a classic granular growth model was used, this approach can be generalized to the broad family of oxides.

Role of institutional quality on women's empowerment—A case of highly gender unequal Asian countries

AbstractEqual access to rights and opportunities for women and men is one of the indicators of women's empowerment. Classical economic growth models ignored gender differences in the labor force, but the literature now acknowledges the merits of equal participation of both genders in economic activities. This study investigates the determinants of gender equality as an instrument of women's empowerment. This study focused on Asian countries with a high gender gap in several domains. This lag in women's empowerment is hypothesized to be due to low‐quality institutions. The data for this investigation is compiled from World Development Indicators, Global Gender Gap reports, the Polity IV project, World Governance Indicators, and Human Development Reports. The Panel Feasible Generalized Least Squares results show that female unemployment and good governance tend to increase the gender gap in Asian countries, while Human Development Index, trade openness and democracy reduce the gender gap. This quantitative assessment is instrumental for policymakers in socially empowering women on equal terms with men in Asia.

Toward a sustainable growth path in Arab economies: an extension of classical growth model

Background/ObjectivesMany economies are on the trajectory of alternative growth drivers other than conventional capital and labor. Access to credit facilities is a pertinent indicator of economic growth. In line with the United Nations Sustainable Development Goals (UNSDGs-8) agenda, the national goal for sustainable development for most economies and Arab economies is no exception. Therefore, the current study adopts a traditional growth model by exploring the relationship between gross domestic product (GDP) per capita, credit for private sectors, ratio of exports, real GDP, and per labor force participants for selected Arab economies annually from 2001 to 2020.Research designThis study leverages the Fourier Kwiatkowski–Phillips–Schmidt–Shin (KPSS) unit root test and second-generation panel econometrics as estimation techniques, such as Westerlund and Edgerton panel cointegration test, and the use of two estimators, namely the augmented mean group (AMG) and common correlated error mean group (CCEMG), to obtain robust results.FindingsEmpirical findings from Westerlund and Edgerton panel cointegration tests validate the long-run equilibrium relationship among the outlined variables. Further empirical results indicate that the share of exports is negatively significant with economic growth in countries such as Kuwait, Lebanon, Tunisia, and Jordan. Additionally, savings and labor force participation have a positive relationship with economic growth in individual countries such as Algeria and Bahrain. As per the panel, there is no significant relationship between labor force participation and economic growth. This indicates that the skilled labor force enhanced economic growth.ConclusionsThese findings come with inherent far-reaching policy suggestions for economies and panels. Further details on country-specific policy actions are presented in the concluding section.Graphical

ПОБУДОВА ТРЬОХСЕКТОРНОЇ МОДЕЛІ ЕКОНОМІЧНОГО ЗРОСТАННЯ З ЕНДОГЕННИМ ПОКАЗНИКОМ ТЕХНОЛОГІЧНОГО ПРОГРЕСУ

The purpose of this article is to build a three-sectoral model of economic growth with an endogenous indicator of technological progress, taking into account the economic and geopolitical conditions of modern Ukraine. Classical models of economic growth can hardly be called universal and adaptive to the conditions of functioning of countries that develop non-linearly and under the influence of many external shocks, such as Ukraine. Therefore, at this stage, it is relevant to build a modified model that will take into account the latest achievements of economic scientists and the specific, crisis conditions of Ukraine's functioning: the problem of low technological structure of Ukrainian products, the crisis in the raw materials sector and significant destruction of energy infrastructure caused by shelling and missile attacks by Russian troops. In the process of building the model, were used methods of statistical analysis, regression analysis, economic and mathematical modeling, and mathematical programming. Based on the modification of the Solow exogenous growth model and the Romer endogenous growth model, was built a model that takes into account the research, raw materials, and final production sectors, which allowed to take into account a number of features of the Ukrainian economy and the current geopolitical situation. The model was specified using the principles of regression analysis, which allowed to demonstrate the feasibility of its practical application. Using the appropriate software, the model was optimized, i.e., was found the optimal distribution of investments and labor resources between sectors and capital, which maximizes total output for the next three years, namely 2023, 2024 and 2025. The model was also tested, which made it possible to characterize this one as adequate and valid, and therefore suitable for use. The results of the optimization allowed us to draw conclusions about the expediency of an even distribution of investments between sectors and capitals and the need for a slightly higher concentration of the economically active population in the raw materials sector.

Calcite Kinks Grow via a Multistep Mechanism.

The classical model of crystal growth assumes that kinks grow via a sequence of independent adsorption events where each solute transitions from the solution directly to the crystal lattice site. Here, we challenge this view by showing that some calcite kinks grow via a multistep mechanism where the solute adsorbs to an intermediate site and only transitions to the lattice site upon the adsorption of a second solute. We compute the free energy curves for Ca and CO3 ions adsorbing to a large selection of kink types, and we identify kinks terminated both by Ca ions and by CO3 ions that grow in this multistep way.

Deconvolution of main hydration kinetic peaks in properly sulfated Portland cements with boundary nucleation and growth models and relation to early-age concrete strength development

When the hydration kinetics of properly sulfated Portland cements is monitored by heat flow calorimetry, the initial dissolution peak and the dormant period is followed by the main hydration peak – formation of calcium-silicate-hydrates and portlandite, the so-called silicate peak. This main peak is superimposed by a peak associated to further tricalcium aluminate dissolution and a surge in precipitation of sulfoaluminates (the so-called sulfate depletion peak) right after sulfate added for setting control is depleted in the material system. In this paper strategies for the deconvolution of silicate peak and sulfate depletion peak are presented. Hereby, the boundary nucleation and growth model and the classical bulk nucleation and growth model serve as tools for deconvolution of calorimetric data. We discuss obtained kinetic parameters and their temperature dependency. The boundary nucleation and growth model for constant nucleation rate emerged as the most suitable model for the silicate reaction, the bulk nucleation and growth model with an order of three, indicating site saturation, as adequate for the sulfate depletion peak. The reaction enthalpy for tricalcium silicate hydration was obtained as 503 J/g, remarkably close to literature values. Calorimetric data related to the sulfate depletion peak is corroborated by X-ray diffraction analysis of formation history of crystalline hydration products. Furthermore, the history of the (silicate) degree of reaction as predicted by the boundary nucleation and growth model for different temperature histories is related to experimentally obtained early-age strength histories. • Investigation of hydration kinetics of commercial, well-sulfated Portland cement. • Main peak (C-S-H and portlandite formation) superimposed by sulfate depletion peak. • Strategies for deconvolution of peaks with Avrami–Cahn models as tools for analysis. • Degree of silicate reaction history is linked to early-age strength gain.

(Invited) The Impact of Interface Layer on Li Plating and Stripping Morphology

Li metal is the preferred anode material for high energy Li batteries. However, a stable plating and stripping of Li metal at the anode−solid electrolyte interface (SEI) remains a significant challenge, particularly at practically feasible current densities. The formation of the SEI layer can significantly change the Li-nucleation density and growth morphology. With multiscale modeling, these factors can be investigated in more detail. Upon, lithiation, while a classical nucleation and growth model can describe the nucleation density of Li clusters and the charging rates in ultrahigh vacuum, a trace amount of reactive gas (oxygen for example) can change Li growth morphology. Reactive molecular dynamics simulations revealed that the fine balance between Li growth rate and the reaction rate of the thin lithium-oxide shell on the surface of the metallic Li can lead to Li nanowire formation. During delithiation, the accumulation of Li vacancies can lead to void generation and interface delamination. A DFT-informed kinetic Monte Carlo (KMC) model was developed to investigate the impact of the SEI layer, stack pressure, and alloying effects. The contact area is then incorporated into a 1D Newman battery model to simulate the impact of the contact area on the battery performance.

Exploring the impacts of energy and environmental constraints on China’s urbanization process

China's urbanization has brought great economic prosperity, but the process has gradually slowed down due to energy and environmental constraints, which implies the growth drag effects. Exploring the relationship among energy consumption, environmental pollution and urbanization is of great practical significance for policymakers. This study extends the classical Solow growth model by introducing energy and environmental constraints. An empirical analysis was conducted using spatial econometric methods and geographically and temporally weighted regression (GTWR). The results show that the urbanization of direct and indirect growth drag effects under the dual constraints of energy and environment are 0.288% and 0.122%, respectively. The restriction of energy consumption in a province inhibits the urbanization development of local and surrounding provinces at the same time. The spatial distribution characteristics of urbanization growth drag effect in 30 provinces of China evolve dynamically with time. After 2005, the growth drag effect of China’s overall urbanization growth has not been effectively alleviated. This study not only establishes a theoretical model of the growth drag effect of urbanization process, but also investigates the spatial interaction and temporal-spatial evolution characteristics of the growth drag effect of urbanization in China. These findings will be useful for policymakers to reduce energy consumption and carbon emissions when pursuing national urbanization.