Growth Rate Equation Research Articles

Calculation and Empirical Analysis on the Contributions of R&D Spending and Patents to China’s Economic Growth

Based on the national data from 1995 to 2014, we develop an extended C-D production function model alongside with the Solow growth rate equation to investigate contributions of RD 2) comparing to patents granted, RD 3) the output elasticity of labor is significantly higher than other factors, signaling capital saving technical progress in China. The elasticity coefficient of scientific-technical progress to GDP is small. Nevertheless, its influence is gradually increasing and the intensive economic growth transformation has formed. Some policy implications are distilled after empirical analysis. R&D application, transformation and related incentive mechanism should be improved. Besides, the fields of R&D funding should be adjusted to further coordinate the relationship between the structure of R&D expenditures and the industrial structure.

P79] New features implemented in the Open Calphad software project

In this paper the interdiffusion process and Frenkel effect (Kirkendall porosity) are studied in Ni-Cu and NiAl-Cu systems at 1273 K. The generalized Boltzmann-Matano method is used for calculation of the intrinsic diffusion coefficients as a polynomial function in the whole composition range. The calculated interdiffusion coefficient in Cu-Ni diffusion couple decrease with increasing Ni content. The total decrease of interdiffusion coefficient exceeds two orders of magnitude. The equation for the void growth rate is obtained. The experimental results of diffusion and voids formation are analyzed. The voids radii is estimated and compared with experiments.

Modeling C-Curves for the Growth Rate of Widmanstätten and Bainitic Ferrite in Fe-C Alloys

When Zener formulated his maximum growth rate criterion for predicting the coarseness of various metallographic objects, he simplified the growth rate equations and predicted that the optimum coarseness should be twice the critical value for which all the driving force would be absorbed by interfacial energy. It is now emphasized that a composition dependence of the diffusion coefficient has a considerable influence and can result in a ratio much larger than two. Various approximations have now been removed from the growth rate equation. When applied to acicular ferrite in the Fe-C system, a C-curve for the growth rate is obtained that resembles the unusually wide C-curve obtained experimentally when information on Widmanstatten ferrite and bainite is combined. It is not necessary to explain that shape as a combination of separate curves for Widmanstatten ferrite and bainite. The main reason for the wide C-curve is the direct effect of the composition dependence of the diffusivity of carbon in austenite.

Kinetics of fatigue crack growth and crack paths in the old puddled steel after 100-years operating time

The goal of the authors’ investigations was determination of the fatigue crack growth in fragments of steel structures (of the puddled steel) and its cyclic behavior. Tested steel elements coming from the turn of the 19th and 20th were gained from still operating ancient steel construction (a main hall of Railway Station, bridges etc.). This work is a part of investigations devoted to the phenomenon of microstructural degradation and its potential influence on their strength properties. The analysis of the obtained results indicated that those long operating steels subject to microstructure degradation processes consisting mainly in precipitation of carbides and nitrides inside ferrite grains, precipitation of carbides at ferrite grain boundaries and degeneration of pearlite areas [1, 2]. It is worth noticing that resistance of the puddled steel to fatigue crack propagation in the normalized state was higher. The authors proposed the new kinetic equation of fatigue crack growth rate in such a steel. Thus the relationship between the kinetics of degradation processes and the fatigue crack growth rate also have been shown. It is also confirmed by the materials research of the viaduct from 1885, which has not shown any significant changes in microstructure. The non-classical kinetic fatigue fracture diagrams (KFFD) based on deformation (??) or energy (?W) approach was also considered. In conjunction with the results of low- and high-cycle fatigue and gradual loss of ductility as a consequence (due to the microstructural degradation processes) - it seems to be a promising construction of the new kinetics fatigue fracture diagrams with the energy approach.

Dynamic Modeling of the Microalgae Cultivation Phase for Energy Production in Open Raceway Ponds and Flat Panel Photobioreactors

A dynamic model of microalgae cultivation phase is presented in this work. Two cultivation technologies are taken into account: the open raceway pond and the flat panel photobioreactor. For each technology, the model is able to evaluate the microalgae areal and volumetric productivity and the energy production and consumption. Differently from the most common existing models in literature, which deal with a specific part of the overall cultivation process, the model presented here includes all physical and chemical quantities that mostly affect microalgae growth: the equation of the specific growth rate for the microalgae is influenced by CO2 and nutrients concentration in the water, light intensity, temperature of the water in the reactor and by the microalgae species being considered. All these input parameters can be tuned to obtain reliable predictions. A comparison with experimental data taken from the literature shows that the predictions are consistent, slightly overestimating the productivity in case of closed photobioreactor. The results obtained by the simulation runs are consistent with those found in literature, being the areal productivity for the open raceway pond between 50 and 70 t/(ha*year) in Southern Spain (Sevilla) and Brazil (Petrolina) and between 250 and 350 t/(ha*year) for the flat panel photobioreactor in the same locations.

Zigzag faceting and width refinement of graphene nanoribbons and nanoperforations via catalyzed edge-annealing on Cu(111)

Abstract Top-down subtractive lithography has previously been used to pattern graphene nanostructures which lack ideal properties due to (1) limited resolution and (2) disordered edges. Here, we introduce a method to convert such disordered edges into relatively smooth zigzag edges via annealing on a Cu(111) substrate at ~950 °C. The Cu catalyzes the re-arrangement of graphene edge atoms to energetically favorable sites, inducing zigzag edge faceting. The dimensions of the graphene nanostructures can be increased, decreased, or held constant during the annealing by tuning the relative balance between growth and etching reactions, described by a fundamental growth rate equation. To demonstrate the flexibility of this method, we lithographically pattern graphene nanoribbons with zigzag or armchair orientations, or alternatively perforate graphene with circular holes, and then anneal these nanostructures to realize zigzag edge termination in each case, with nanostructure feature size tailored from 8 to 80 nm. The annealed nanostructures have smoother zigzag edges (~40% reduction in 1σ line edge roughness), and Raman spectroscopy confirms that they have lower edge disorder than top-down patterned samples.

Band Propagation, Scaling Laws, and Phase Transition in a Precipitate System. 2. Computational Study.

In this second paper, we introduce a chemical kinetic model that investigates the dynamics of the experimental Ni(2+)/NH3-OH(-) Liesegang system characterized by a pattern of β-nickel hydroxide bands led by a growing pulse of α-nickel hydroxide. The model is based on a system of reaction-diffusion equations describing the precipitation reaction and dissolution of the nickel hydroxide polymorphs by ammonia. The hydroxide ions are assumed to be static whereas ammonia serves as a diffusing "vehicle" that supplies the hydroxide ions along the precipitation zone, and these ions in turn react with the static Ni(2+) ions. The precipitation-diffusion equations are coupled to nucleation, polymorphic transition, and growth rate equations, each of which is characterized by a critical constant specific to the solid phase dynamics. In the proposed model, priority is given to polymorphic transition rather than nucleation. This implies that the critical constants must be subject to a constraint different than that derived for the Lifshitz-Slyozov instability encountered in classical Liesegang patterns. Numerical simulations confirm the validity of our model and the derived constraint. The pulse position and width are found to scale in time as t(α) with α ≃ 0.5, in agreement with the experimental results. Finally, the mass of the bands is shown to oscillate in time, suggesting competition between growth and polymorphic transition on one side and dissolution on the other.

Experimental and simulation study of the physical foaming process using high-pressure CO2

The simultaneous simulation of nucleation and growth of multiple bubbles was performed for a batch foaming process of low-density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) using CO2 as a foaming agent. The simulation model involved a Blander–Katz bubble nucleation rate equation and a set of bubble growth rate equations that account for the momentum balance across the bubble interface, the diffusion of dissolved gas molecules in a polymer, and the overall mass balance of the gas in bubbles and in the polymer. The present study considered the overlapping of the concentration boundary layers. The simulation results could predict the experimental results of the bubble nucleation and bubble growth behaviors of the polymers in a fairly quantitative manner. Moreover, the effects of the physical properties on bubble nucleation and bubble growth dynamics were demonstrated in a series of sensitivity studies. The effect of interfacial tension and the diffusion coefficient strongly affected the bubble nucleation and growth rates, respectively.

The mechanical properties and the microstructural degradation effect in an old low carbon steels after 100-years operating time

The paper presents the results of historical types of steel after over 100 years of operating. The object of interest were parts of steel structure of the hall historic 19th-century Main Railway Station in Wroclaw. The study has shown the presence of the microstructural degradation processes in puddled steel. In all the analysed steels (low carbon puddled steel) microstructure degradation processes were related to: presence of numerous precipitations of carbides and nitrides (or the carbides–nitrides) of iron inside the ferrite grains, presence of continuous precipitations of cementite at ferrite grain boundaries. In order to restore the initial state of the microstructure, all tests were carried out in two stages of heat treatment; as-received state and after the normalisation (950°C, 2h, cooled in air) state. The microstructures degradation significantly influenced the mechanical properties. Its influence is most strongly emphasized in the impact resistance test results. It has been shown that the presence of degradation processes significantly changes the type of fracture; from ductile to the cleavage. This fact is well illustrated by the SEM-images of crack path. Results of the fatigue crack growth rate test indicate for worsening of resistance to the fatigue crack propagation of the material depending on the degree of degradation processes intensity in tested steel. The differences in the kinetics of fatigue cracking are also well illustrated by the SEM-images along the fatigue crack path. The authors have proposed a new kinetic equation of the fatigue crack growth rate for puddled steel.

(Olin Palladium Award) Some Critical Issues in the Breakdown of Passive Films

Passivity breakdown is the precursor to most forms of localized corrosion, including pitting, stress corrosion cracking, corrosion fatigue, and crevice corrosion, and also results in the phenomenon of depassivation, including electrochemical polishing and trans-passive dissolution, corresponding to passivity breakdown over macroscopic dimensions. In this OLIN Palladium Medal address, I will review my work in this area in terms of developing the Point Defect Model (PDM) for passivity and passivity breakdown and will identify principal challenges, as I see them. Starting with the rate equation for barrier layer growth, as predicted by the PDM, and by using phase-space analysis, I derive the condition that must be met for passivity to exist; the rate of growth of the barrier layer at the metal/barrier layer interface, due to the generation of oxygen vacancies at zero barrier layer thickness, must exceed the dissolution rate of the barrier layer. If this condition is met, the barrier layer may exist as a meta-stable phase and passivate the surface. In this regard, it is important to note that passivity is a kinetic state, not a equilibrium thermodynamic phenomenon, as has been so often assumed in the past. This fact has been used to resolve Faraday’s famous paradox arising from his iron-in-nitric acid experiments of 1833. Violation of this condition implies that the barrier layer cannot exist on the surface, even as a meta-stable phase and, hence, that the surface depassivates (loss of the barrier layer). If depassivation occurs over a macroscopic area, this phenomenon accounts for acid depassivation, transpassive dissolution, resistive depassivation, and electrochemical polishing. However, if depassivation occurs on a microscopic area, localized corrosion phenomena, including pitting, stress corrosion cracking, corrosion fatigue, and crevice corrosion occur, resulting in rapid penetration of a cavity into the metal. This unified theory of corrosion (UTC) accounts for all known forms of corrosion, except for hydrogen embrittlement, which lies outside of the realm of the PDM. After having established the basis of the UTC, I will then proceed to discuss the mechanism by which both general and localized depassivation occurs, which has been identified as being due to cation vacancy condensation at the m/bl interface, such that the barrier layer separates from the metal and film growth into the metal via oxygen vacancy generation cannot occur. This condition assures the depassivation inequality stated above, because the rate of growth of the barrier layer into the metal is reduced to zero and because all oxides exhibit a finite dissolution rate. The lecture will then proceed to show how the UTC predicts the critical breakdown voltage and induction time for a single breakdown site, as a function of the chloride activity, pH, and potential. It will then be shown that, by postulating that the breakdown sites are normally distributed with respect to the cation vacancy diffusivity, it is possible to derive the distribution functions for the breakdown voltage and the induction time for a large population of potential breakdown sites on the surface and to identify the critical characteristic of a breakdown site (high cation vacancy diffusivity). From there, I will demonstrate a variety of phenomena, including photo-inhibition of passivity breakdown, the impact of other halides (F-, Br-, I-), anion inhibition via competitive absorption into surface oxygen vacancies, the role of the precipitated outer layer, and the predicted impact of alloying elements on passivity breakdown. Where possible and appropriate, these predictions will be compared with experiment. As expected the PDM contains many model parameters that are poorly-known. However, values for all of the parameters may be obtained by optimizing the expressions for the impedance of the barrier layer as a function of frequency and film formation potential, as derived from the PDM, on experimental electrochemical impedance spectroscopic (EIS) data and optimization of the expressions for passivity breakdown (potential and induction time) on the corresponding experimental data. Finally, I will demonstrate how the PDM has led to the development of a deterministic protocol, Damage Function Analysis (DFA), for predicting the evolution of localized corrosion damage on metal and alloy surfaces, as a system evolves along a pre-determined corrosion evolutionary path, which is defined as the path taken by the system in terms of those properties of the system (temperature, potential, pH, [Cl-], etc) that have a significant impact of the damage accumulation rate. Time permitting, I will demonstrate how DFA may be used to predict the evolution of general and localized corrosion damage in practical systems.

Effect of stocking density on key growth traits of a fast-growing and heat-resistant strain of sea cucumber (Apostichopus japonicus)

We evaluated the effect of rearing density on the yield of a fast-growing and heat-resistant strain of Apostichopus japonicus using a full-sib family. We analysed the relationship between density and key growth parameters during factory seedling of A. japonicus and developed a model to explain the variation in growth. From 130 to 220 days, the rearing density of A. japonicus had a significant effect on body weight, specific growth rate, coefficient of variation and survival rate (P < 0.05). We obtained predicted integral regression equations for yield and growth rate, density fluctuation, variable coefficient fluctuation and survival rate. Specific growth rate had a significant effect on the yield of A. japonicus and, therefore, can be used as a primary indicator of yield. We recommend that stocking density should be adjusted from age 130–166 days to avoid frequent seedling separation to different pools of different seedling sizes during the fast growth period of A. japonicus seedlings, a procedure that causes yield decline. The optimal initial stocking density was 24.4 g m−2 (0.2 g L−1).

Analytic scaling function for island-size distributions.

We obtain an explicit solution for the island-size distribution described by the rate equations for irreversible growth with the simplified capture rates of the form σ(s)(Θ)∝Θ(p)(a+s-1) for all s≥1, where s is the size and Θ is the time-dependent coverage. The intrinsic property of this solution is its scaling form in the continuum limit. The analytic scaling function depends on the two parameters a and p and is capable of describing very dissimilar distribution shapes, both monomodal and monotonically decreasing. The obtained results suggest that the scaling features of the size distributions are closely related to the size linearity of the capture rates. A simple analytic scaling is obtained rigorously here and helps to gain a better theoretical understanding of possible origins of the scaling behavior of the island-size distributions.

Kinetics of the Reduction of Hematite Concentrate Particles by Carbon Monoxide Relevant to a Novel Flash Ironmaking Process

A novel ironmaking process is under development at the University of Utah to produce iron directly from iron oxides concentrates by the gas–solid flash reaction using gaseous fuels and reductants. This process will reduce energy consumption and minimize carbon dioxide emissions. Having investigated the hydrogen reduction kinetics of magnetite and hematite concentrate particles relevant to the novel flash ironmaking process, the carbon monoxide reduction kinetics of hematite concentrate particles (average particle size 21 µm) was determined in the temperature range 1473 K to 1623 K (1200 °C to 1350 °C) under various carbon monoxide partial pressures. At 1623 K (1350 °C) and residence time 5 seconds, the reduction degree of hematite concentrate particles was more than 90 pct under a pure carbon monoxide. This is slower than reduction by hydrogen but still significant, indicating that CO will contribute to the reduction of hematite concentrate in the flash process. The kinetics of CO reduction separately from hydrogen is important for understanding and analyzing the complex kinetics of hematite reduction by the H2 + CO mixtures. The nucleation and growth rate equation with the Avrami parameter n = 1.0 adequately described the carbon monoxide reduction kinetics of hematite concentrate particles. The reduction rate is of 1st order with respect to the partial pressure of carbon monoxide and the activation energy of the reaction was 231 kJ/mol, indicating strong temperature dependence. The following complete rate equation was developed that can satisfactorily predict the carbon monoxide reduction kinetics of hematite concentrate particles and is suitable for the design of a flash reactor $$ \frac{{{\text{d}}X}}{{{\text{d}}t}} = 1.91 \times 10^{7} \times e^{{\frac{ - 231000}{\text{RT}}}} \times \left( {p{\text{CO}} - \frac{{p{\text{CO}}_{2} }}{K}} \right) \times (1 - X), $$ where X is the fraction of oxygen removed from iron oxide, R is 8.314 J/mol K, T is in K, p is in atm, and t is in seconds.

150 fs~10 ps脉宽下熔石英激光损伤的仿真与分析

Based on the reduced growth rate equation of electron density, a theoretical model is established to describe the change of the conduction band electron density of fused silica with the laser pulse duration. Using the concept of the critical electron density, a scope of the laser-induced damage of fused silica is calculated with the pulse width from 150 fs to 10 ps. The analysis shows that the avalanche ionization still takes a leading role from 5 ps to 10 ps. Instead of electrons provided by the fused silica itself, the initial electrons produced by the photoionization make a contribution to the impact ionization. It reaches a balance between avalanche ionization and photoionization when the pulse width shrinks to 4 ps. After that, the photoionization plays a main role in the growth of the conduction band electron density. Through the fitting curve, a new pulse width law is obtained to satisfy the laser-induced damage threshold changing from 150 fs to 10 ps. The results demonstrate that the threshold is proportional to tp0.38(tp is the pulse width), and changes to tp0.34 when the temperature dependence is concerned.

Stochastic stability of systems with semi-Markovian switching

This paper examines stochastic stability of switched dynamics in continuous time. The time evolution of the so called continuous state is at all times, determined by the dynamics indexed by the switching process or discrete state. The main contribution of this paper appears as stochastic stability results for switched dynamics with semi-Markovian switching. The notion of moment stability in the wide sense (MSWS) is applied as a generalization of ϵ-moment stability. A sufficient criterion for MSWS is presented for the above class of systems, where each subsystem is assumed to be characterized by a Lyapunov function candidate together with an associated growth rate equation. For the set of Lyapunov functions, a compatibility criterion is assumed to be fulfilled, bounding the ratio between pairs of Lyapunov functions.

The Effect of Gravity on the Stability of an Evaporating Liquid Film

Evaporation of a Dichloromethane liquid film is explored with an evolution equation describing film dynamics. The film is subject to different initial conditions, smooth and uniform random perturbation. Two different gravity environments (Earth and zero gravity) and two different domain shapes (square and rectangular) have been used. The occurrence of long wave instabilities affecting film dynamics is noted in each of these cases. The evaporating Dicholormethane liquid film is destabilized via long wave instabilities in zero gravity. The thermocapillary patterns formed due to long wave destabilization show a coupling to the initial conditions and domain shape. A criterion for the occurrence of long wave instabilities based on the growth rate of perturbations is described. This equation considers a non-stationary film thickness. It predicts that long wave instabilities are always present in zero gravity environments with a growth rate that increases as the film thickness decreases due to evaporation. Our equation for growth rate of long wave instabilities may be used as an engineering design tool to confine operating parameters of zero gravity heat transfer equipment, that include or harness phase change, to safe limits.

Juvenile growth rate equation for the freshwater gammarid Gammarus roeseli

Juvenile growth rate equation for the freshwater gammarid Gammarus roeseli

Crystal shape and size control using a plug flow crystallization configuration

This work focuses on modeling and control of a continuous plug flow crystallizer (PFC) used to produce tetragonal hen-egg-white (HEW) lysozyme crystals and proposes an optimization-based control scheme to produce crystals with desired size and shape distributions in the presence of disturbances. Initially, a kinetic Monte Carlo (kMC) model is developed to simulate the crystal growth in a seeded PFC, which consists of five distinct segments. The crystal growth rate equations taken from (Durbin and Feher, 1986) are used in the kMC simulations for the modeling of the crystal growth in the direction of (110) and (101) faces. Then, a population balance equation (PBE) is presented to describe the spatio-temporal evolution of the crystal volume distribution of the entire crystal population, and the method of moments is applied to derive a reduced-order moment model. Along with the mass and energy balance equations, the leading moments that describe the dominant dynamic behavior of the crystal volume distribution are used in the optimization-based controller to compute optimal jacket temperatures for each segment of the PFC and the optimal superficial velocity, in order to minimize the squared deviation of the average crystal size and shape from the set-points throughout the PFC. Furthermore, a feed-forward control (FFC) strategy is proposed to deal with feed flow disturbances that occur during the operation of the PFC. Using the proposed optimization and control schemes, crystals with desired size and shape distributions are produced in the presence of significant disturbances in the inflow solute concentration and size distribution of seed crystals.

Size distributions, scaling properties, and Bartelt-Evans singularities in irreversible growth with size-dependent capture coefficients

We present a theoretical analysis of the rate equations for irreversible growth with a monomer influx, desorption, and a power-law dependence of the capture coefficients on the number of monomers $s$. Special emphasis is given to the size distribution shapes and their time invariance in terms of a new variable which is distinctly different from the conventional $s/{s}_{*}$ ratio, with ${s}_{*}$ being a representative size in the distribution. Our results can be briefly formulated as follows. First, we generalize the earlier results to systems with desorption. Second, the analytical size distributions are obtained by applying the transformation to a certain invariant size variable ($\ensuremath{\rho}$) for which the regular growth rate is independent of the cluster size, and the Green function in the form of Gaussian with a spreading dispersion. Third, the size distribution shapes reflect the time dependence of the monomer concentration inverted in terms of the $z\ensuremath{-}\ensuremath{\rho}$ variable, with $z$ as a representative invariant size. Fourth, the fluctuation-induced broadening of these spectra depends critically on the growth law. Fifth, the obtained distributions show a refined time-invariant scaling in the appropriate variables for a broad range of conditions and for all but very small $z$, while the scaling in terms of $\ensuremath{\rho}/z$ works only in the formal limit $z\ensuremath{\rightarrow}\ensuremath{\infty}$.

Economic Growth Model Based on Six Basic Factors of Production&amp;boxh;Xu Growth Rate Equation

This paper proposes an economic growth model based on the Six Basic Factors of Production and Xu Growth Rate Equation for the first time, which fills-in the deficits of the New Classical Economic Growth Model based on the Solow Model. The empirical analysis indicates that over the past three decades, the consumption of six basic factors of production had complicated relations with economic growth. In some years, the consumption rate of the basic factors of production was meager, but the economy witnessed relative- ly rocketing growth rate; in some years, the factors of pro- duction consumption rate was very high, but the economy growth rate slowed down. In general, economy grows at the expenses of huge consumption of four factors. There is an obvious characteristic of huge input and low efficiency. The average contribution rate of technological advance peaks in the middle, while it drops down at two ends. Noticeably, since 2004, the technology contribution rate generally shows a downward trend, reasons of which should be explored sys- tematically in aspects like economic policy and industry structure with a view to boost further transformation of the macro-economy scientific growth model. profound researches, by now, there is no single theory of- fering an effective enough prescription to the economy of countries. Currently, some countries possess great wealth, but some countries are still stuck in poverty. This is an obje- ctive portrait of the dilemma of theory. Therefore, economic growth is still a difficult economic problem to be settled. Ev - ery year, a large number of research papers emerge about it. Just like a master once put it:as long as people begin to think about this problem,it's hard for them to think about other is- sues (Robert, 1988). However, we must keep the warning of Solow in mind:If there are not new ideas proposed,we will have no reason to return to this old problem (Robert, 1991). This article will propose a new economic growth model— economic growth model based on Six Basic Factors of Pro- duction,and build a corresponding growth rate equation ① . This new attempt might uncover a thread and observation. 2 The evolution of the economic growth the- ory