Dependence Of Growth Rate Research Articles

The Impact of Gravity Waves on the Evolution of Tropical Anvil Cirrus Microphysical Properties

AbstractAnvil cirrus generated by deep convection covers large fractions of the tropics and has important impacts on the Earth's radiation budget and climate. In situ measurements made with high‐altitude aircraft indicate a rapid transition in ice crystal size distributions and habits as anvil cirrus ages. We use numerical simulations to investigate the impact of high‐frequency gravity waves on the evolution of anvil cirrus microphysical properties. The impacts of both monochromatic gravity waves and ubiquitous stochastic mesoscale temperature fluctuations are simulated. In both cases, the interplay between wave‐driven temperature fluctuations, deposition growth/sublimation, and sedimentation causes accelerated removal of both small ice crystals (diameters less than about 10 μm) and large crystals (diameters larger than ≈30 μm). These changes are consistent with the observed evolution of anvil cirrus microphysical properties. The Kelvin effect (higher saturation vapor pressure over curved surfaces) is a critical factor in the anvil evolution, driving mass transfer from small to large ice crystals. The wave‐driven decrease in ice concentration is much faster for typical anvil cirrus detrained at ≃11.5–12.5 km than for less frequent anvils at 15.5–17.5 km because of the strong temperature dependence of deposition growth and sublimation rates. The simulations also show that waves, along with the Kelvin effect, drive growth of mid‐sized (5–20 μm) ice crystals, which is consistent with the observed transition to bullet rosette habits in aging anvil cirrus. We conclude that high‐frequency gravity waves, which are generally not resolved in large‐scale models, likely have important impacts on anvil cirrus microphysical properties and lifetimes.

Kinetics formulation for Two-Dimensional Growth Behavior of Water/Ice Interface on Si Substrate.

Sublimation drying is used in the drying process of semiconductor device manufacturing. However, the solidification behavior mechanics of sublimation agents on substrates has not been clarified. Therefore, the properties of solidified films within substrate surfaces can become nonuniform, leading to their collapse. This study aimed to analyze the interface growth behavior during the cooling and solidification of a water/ice system as a basic case and to clarify the dynamic mechanism of the solidification behavior of liquid films on Si substrates. The solidification behavior of a water/ice system on Si substrates was captured on a video at different cooling rates. The recorded video was subjected to a digital image analysis to examine the crystal morphology and quantify the interface growth rate. The least-squares method with kinetic formulas was used to evaluate the feasibility of fitting the temperature variation to the interface growth rate. A visual examination of the morphology of interfacial growth revealed that it can be classified into four morphologies. The proposed kinetic equation describes the experimental results regarding the temperature dependence of the interfacial growth rate. Through image analysis, the interface growth rate of water and ice was quantified, and an evaluation formula was proposed.

Parametric effects on Richtmyer–Meshkov instability of a V-shaped gaseous interface within linear stage

The Richtmyer–Meshkov instability of a V-shaped air/SF6 gaseous interface is numerically studied via a high-order finite difference scheme and a localized artificial diffusivity method. The oblique angle of the interface ranges from 20° to 75°, and the incident shock Mach number varies from 1.05 to 1.75. The wave patterns and the vortex structures are visualized during the interface evolution. A cavity is observed at the spike fingertip when the oblique angle decreases, which proves to be formed due to Mach reflection of the transmitted shock through velocity decomposition. By analyzing the linear growth rates of the interface, a modified empirical model for the reduction factor is suggested with model coefficients acquired by linear fitting for different Mach numbers. With shock polar analysis (SPA) method and visualization of the wave configuration, a criterion is proposed to explain the non-monotonic dependence of the linear growth rate on the oblique angle. In addition, Mach number effects on the linear growth rate are discussed by the SPA method, especially the anomalous behavior of the Mach 1.05 case.

Telephone cord blister formation in solvent swollen elastomer films.

Video imaging was used to study large-slope folded telephone cord blister formation in solvent swollen films of polydimethylsiloxane (PDMS) elastomers. Chlorobenzene, chloroform, heptane and toluene were used to swell PDMS films with thickness values in the range 15 μm < h < 223 μm supported on glass substrates. Measurements of the blister width, corrugation wavelength and blister growth speed were studied as a function of the film thickness for all four solvents. Modified theories of buckling were shown to accurately predict the film thickness dependence of the width and corrugation wavelength and a modified fracture mechanics approach was shown to reproduce the non-monotonic thickness dependence of the blister growth rates. Two critical thickness values were identified for telephone cord blisters formed on solvent swollen PDMS films-one corresponding to a lower critical thickness for blistering and the other corresponding to a peak in the thickness dependent blister growth rates. Blister formation is shown to be consistent with the existence of mixed modality in the growth of the crack tip at the film-substrate interface. Both critical thickness values are shown to depend upon the strength of the adhesive interactions between the film and the substrate and the Young's modulus of the films. A simple method of patterning surfaces with telephone cord blisters is also introduced.

Effect of Solution Stoichiometry on BaSO4 Crystallization from Turbidity Measurements and Modeling.

The impact of solution stoichiometry on the nucleation and growth of BaSO4 was studied by measuring solution transmittance and subsequent fitting to a crystallization model. Our results show that a large excess of either Ba2+ or SO42- ions inhibits both the nucleation and growth of BaSO4. However, for a small excess of Ba2+, the growth is enhanced. The dependence of nucleation and growth rates on supersaturation and solution stoichiometry was captured by a semiempirical rate model. Hence, the solution stoichiometry is a highly relevant parameter while studying all aspects of BaSO4 crystallization, and it could be worthwhile to examine other minerals similarly.

(Invited) Ru Selective Metal Deposition for Hybrid Metallization in Nano-Interconnect Applications

The connection of semiconductor devices happens through metal interconnects at the back end of line (BeOL) in integrated circuits. The BeOL consists of multiple metal levels that are vertically connected through small contact holes, or so-called vias. Especially at the lower metal levels, the vias are becoming much smaller in critical dimension, which increases their resistance significantly while more of these vias are needed to make the more complex connections in future device architectures. For these reasons, the vias resistance is becoming the dominating part of the total resistance of the stack and may become the limiting factor in keeping resistance-capacitance delay under control.In this work, the metal-on-metal area selective metal deposition is studied to make low resistive vias. The via is first prefilled with the Ru before performing the Cu metallization of the remainder of the vias and wires. Ru is chosen as the preferred metal [1] because it can be used without a metal barrier (it does not electromigrate) and this provides a large resistance benefit as compared to the Cu metallization which needs a TaN barrier combined with a Co liner. The combination of the different metals for the via (here Ru) and the metallization of wires (here Cu), is called a hybrid metallization scheme.We will discuss the challenges for the Ru selective deposition on the metal (growth area) towards different dielectrics as the non-growth area. The selectivity studies to optimize the Ru chemical vapour deposition (CVD) recipe and surface treatments are performed on blanket level (non-patterned wafers). A small molecule inhibitor dimethylamino-trimethylsilane (DMA-TMS) is used to passivate the dielectric surface which makes the dielectrics less reactive towards the Ru deposition improving thereby the selectivity of the CVD process (see also Fig.a).[2] We demonstrate that the growth rate and selectivity of Ru ASD depend on the CVD process conditions (type of co-reactant and process temperature) and the type of nanopattern (line spaces or via holes).[3]The most selective Ru process found with the line-space pattern (45/45nm line-space width) was also tested in nanoscale patterns with via holes of ~10.5nm.[4] It was found that the Ru growth rates in the patterned structures are enhanced as compared to the blanket substrates. The CVD Ru growth rates are ~ 1.3x higher in line-space nanopatterns as compared to flat metal substrates, and up to 3x higher in the small contact holes.[4] The growth enhancement of the CVD process is beneficial for the technological implementation of the process. The results show that the growth rate and the selectivity are different from the behavior on blankets and are also pattern dependent, which is consistent with a growth mechanism that is based on diffusion in addition to adsorption.[2] Therefore, the metal-on-metal selective deposition process may need to be optimized and adjusted to the patterned structure used in the interconnect application.[1] D. Gall et al, J. Appl. Phys. 2016, 119, p.085101.[2] F. Grillo and J. Soethoudt et al, Chem. Mater. 2020, 32, 22, 9560–9572.[3] A. Kumar Mandal et al, “Ruthenium Area-Selective Deposition for Nano-interconnect Structures: Process and nanopattern dependent selectivity and growth rate” Manuscript in submission 2023.[4] M.H. van der Veen et al, Proc. of the IITC 2021, S7-2.. Figure 1

Growth rate dependence on micronutrient provision in replacement heifers during the intrauterine period

According to the developmental origins of health and disease (DoHaD) hypothesis, the conditions during intrauterine development have a long-term effect on postnatal growth and animal health. This study aimed to determine the relationship between fetal micronutrient provision in the last three months of intrauterine development and growth intensity indicators in the first 180 days after birth. This study focused on 40 clinically healthy Simmental heifers. Samples of non-pigmented tail hair were collected from newborns before their first colostrum feeding. The micronutrient content (selenium, copper, zinc, manganese, cobalt, iron, chromium, and molybdenum) was analyzed using inductively coupled plasma mass spectrometry (Nexion 300D, Perkin Elmer, USA). Calf weight was measured on the first day of life and at 180 days, and average daily weight gain was calculated. The relationships between the variables were analyzed using Spearman’s rank correlation coefficient in IBM SPSS Statistics 20.0 (IBM Corp., USA). No significant correlations were found between the weights of the newborn calves and the micronutrient content in their hair samples. However, at 180 days of age, calf weight and average daily weight gain (in the first 180 days of life) correlated with the selenium (r = 0.349 and r = 0.408, p &lt; 0.05, respectively), copper (r = 0.378 and r = 0.440, p &lt; 0.01, respectively), zinc (r = 0.455 and r = 0.481, p &lt; 0.01, respectively), and cobalt (r = 0.304 and r = 0.344, p &lt; 0.05, respectively) contents in the hair samples of newborns. No correlations were found for manganese, iron, chromium, and molybdenum.

Linear perturbations of the Bloch type of space-periodic magnetohydrodynamic steady states. III. Asymptotics of branching

The previous paper of this series presented the results of a numerical investigation of the dependence of the dominant growth rates of Bloch eigenmodes on the diffusivity parameters (the molecular viscosity ν and molecular magnetic diffusivity η) in three linear stability problems: the kinematic dynamo problem, and the hydrodynamic and MHD stability problems for steady spaceperiodic flows and MHD states. The dominant eigenmodes (i.e., the stability modes, whose growth rates are maximum over the wave vector q of the planar wave involved in the Bloch modes) comprise branches. In some branches, the dominant growth rates are attained for constant half-integer q. In all the three stability problems for parity-invariant steady states, offshoot branches, stemming from the branches of this type, were found, in which the dominant growth rates are attained for q depending on ν and/or η. We consider now such a branching of the dominant magnetic modes in the kinematic dynamo problem, where an offshoot stems from a branch of neutral eigenmodes for q = 0, and construct power series expansions for the offshoots and the associated eigenvalues of the magnetic induction operator near the point of bifurcation. We show that the branching occurs for the molecular magnetic diffusivities, for which the two eigenvalues of the eddy diffusivity operator become imaginary, and magnetic field generation by the mechanism of the negative eddy diffusivity ceases. The details of branching in the other linear stability problems under consideration are distinct.

Assessing Memory in Convection Schemes Using Idealized Tests

AbstractTwo assumptions commonly applied in convection schemes—the diagnostic and quasi‐equilibrium assumptions—imply that convective activity (e.g., convective precipitation) is controlled only by the large‐scale (macrostate) environment at the time. In contrast, numerical experiments indicate a “memory” or dependence of convection also on its own previous activity whereby subgrid‐scale (microstate) structures boost but are also boosted by convection. In this study we investigated this memory by comparing single‐column model behavior in two idealized tests previously executed by a cloud‐resolving model (CRM). Conventional convection schemes that employ the diagnostic assumption fail to reproduce the CRM behavior. The memory‐capable org and Laboratoire de Météorologie Dynamique Zoom cold pool schemes partially capture the behavior, but fail to fully exhibit the strong reinforcing feedbacks implied by the CRM. Analysis of this failure suggests that it is because the CRM supports a linear (or superlinear) dependence of the subgrid structure growth rate on the precipitation rate, while the org scheme assumes a sublinear dependence. Among varying versions of the org scheme, the growth rate of the org variable representing subgrid structure is strongly associated with memory strength. These results demonstrate the importance of parameterizing convective memory, and the ability of idealized tests to reveal shortcomings of convection schemes and constrain model structural assumptions.

VLF chorus emissions modeling using EPOCH PIC code: Generation regimes and comparison with a backward wave oscillator theory

We present the results of a numerical model for VLF chorus emissions generation based on the EPOCH PIC code. The initial distribution function of energetic elections is assumed to have a finite-width step-like deformation in the velocities parallel to the geomagnetic field. This allows us to verify and generalize the analytical and numerical results obtained earlier within the framework of a backward wave oscillator model in which a sharp step feature is assumed. We show that in the presence of a sharp or smooth step, chorus emissions can be generated for realistic flux of energetic electrons even if the initial velocity distribution (without the step) is isotropic. Simulated chorus emissions behave very similarly for both sharp and finite-width steps. In particular, the generation of repetitive chirping chorus elements occurs if the coupling parameter exceeds the linear generation threshold several times. For smaller threshold excess, quasi-stationary or relaxation oscillation regimes take place. For the first time, we systematically study the dependence of the chorus emissions properties on the energetic electron distribution parameters, in particular, on the step width and the effective wave-particle coupling parameter proportional to the energetic electron flux and step height. We show that the functional dependences of the linear growth rate on the coupling parameter is the same for a smooth step gradient as those obtained for the sharp step within the framework of the backward wave oscillator model. The threshold flux of energetic electrons, above which whistler mode waves are generated, increases very fast with increasing step width. With a fixed relative step height, the threshold flux is about an order of magnitude higher for a step width of 8% than for a sharp step.

Growth-rate dependency of ribosome abundance and translation elongation rate in Corynebacterium glutamicum differs from that in Escherichia coli

Bacterial growth rate (µ) depends on the protein synthesis capacity of the cell and thus on the number of active ribosomes and their translation elongation rate. The relationship between these fundamental growth parameters have only been described for few bacterial species, in particular Escherichia coli. Here, we analyse the growth-rate dependency of ribosome abundance and translation elongation rate for Corynebacterium glutamicum, a gram-positive model species differing from E. coli by a lower growth temperature optimum and a lower maximal growth rate. We show that, unlike in E. coli, there is little change in ribosome abundance for µ <0.4 h−1 in C. glutamicum and the fraction of active ribosomes is kept above 70% while the translation elongation rate declines 5-fold. Mathematical modelling indicates that the decrease in the translation elongation rate can be explained by a depletion of translation precursors.

Individual-Based Modelling for Predicting Dry Matter Accumulation in Juveniles of Indian Olive Raised under Different Soil Treatments

Dry matter accumulation data for juvenile Indian Olive saplings was modelled using linear and non- linear regression models. The data was gathered bimonthly and for two years i.e., twelve readings. Linear, Quadratic, Power, Sigmoid, and Exponential models performed quite well for cumulative growth data (Adj. R2 &gt; 0.93). The Sigmoid model (Chapman- Richard) demonstrated upper asymptotic values ranged between 179.96- 334.49 grams for all treatments (T0 – T4) suggesting that olive saplings responded positively to different soil treatments. Both, age and size dependent relative growth rates (RGRs) manifested low values and decrease in RGR curve. Age- dependent RGR displayed a smooth decline in function, indicating extended longevity. Low RGR (along with low Specific Leaf Area), is a characteristic feature of slow growing and evergreen species and this trait was observed in Indian Olive growth too. Size- standardized RGR revealed that due to the low rate of decline, T4 had the superior RGR (and maximum dry matter accumulation) followed by other treatments. Moreover, T0 had the sharpest decrease and the lowest dry matter accumulation. Cross- validation of model parameters exhibited statistical stability.

Modeling of environmentally assisted intergranular crack propagation in polycrystals

AbstractPolycrystalline nickel‐based superalloys experience accelerated intergranular crack growth when exposed to dwell times in oxygen‐rich environments and a combination of high temperature and tensile mechanical loading. Increasing crack growth rates are observed for increasing amounts of environmental oxygen in a certain oxygen concentration range, while below and above that range crack growth rates remain approximately constant. A fully coupled chemo‐mechanical modeling framework accounting for the degradation of grain boundaries by oxygen has been presented by the authors. In this work, we expand the framework by a moving boundary condition to capture a realistic oxygen flux in grain boundary cracks for both edge cracks connected to the environment and interior cracks. In numerical simulation results, the behavior of the moving boundary condition is shown for intergranular crack propagation through a polycrystal subjected to cyclic loading. Finally, the capabilities of the modeling framework to qualitatively predict the dependence of the average crack growth rate on the environmental oxygen content, load level, and dwell time are evaluated and it is shown that predictions qualitatively agree with experimental observations for intergranular fracture.

Testing growth rate dependence in cosmological perturbation theory using scale-free models

Testing growth rate dependence in cosmological perturbation theory using scale-free models

Thermal dependence of Daphnia life history reveals asymmetries between key vital rates

Temperature variation affects virtually every aspect of ectotherms' ecological performance, such as their foraging rate, reproduction, and survival. Although these changes influence what happens at higher levels of organizations, such as populations and communities, qualitative changes in dynamics usually require some degree of asymmetry between key vital rates, i.e. that different vital rates, such as growth, development, fecundity and mortality rates, respond differently to temperature. In order to identify possible asymmetries among vital rates and/or life stages, we characterized the thermal response of individuals a clone of Daphnia sinensis, drawn from a high-mountain environment in Taiwan, and examined the temperature dependence of growth, maturation, reproduction, and mortality rates, as well as fitness measures (r and R0) at eight temperatures. Daphnia sinensis was able to maintain reproductive success over a broad range of temperatures, much wider than the one experienced in its environment. However, negative effects of temperature were perceptible at temperatures much lower than the highest one at which they can achieve reproductive success. Adult mortality greatly increased for temperatures above 23 °C, and other vital rates started to decelerate, resulting in a large drop in lifetime reproductive success. This finding implies that D. sinensis may be able to persist over a wide range of temperatures, but also that it may become more sensitive to the detrimental effect of species interactions at increased temperatures. Different vital rates responded relatively similarly at low temperatures, but the degree of asymmetry among these rates was much more pronounced at higher temperatures. In particular, rates associated with adult performance decelerated more strongly than juveniles’ rates. These findings indicate that elevated temperatures affect the balance between juvenile and adult performance, which is known to have a crucial role in Daphnia population dynamics. We discuss the implications of these results for the dynamics of structured populations.

Particle pump-out induced by trapped electron mode turbulence in electron cyclotron heated plasmas on XuanLong-50 spherical torus

Particle pump-out effects induced by low-frequency (<200 kHz) density fluctuations were observed in solely electron cyclotron wave (ECW)-heated plasmas on the spherical torus XuanLong-50 (EXL-50) without a central solenoid. The intensity of the relative density fluctuations increases with increasing ECW power and decays when the ECW is turned off while sustaining the plasma current. The electron densities are maintained relatively high and steady when the density fluctuations are completely absent, indicating that the outward transport of electrons is dominated by the particle pump-out effect of the ECW. The density fluctuations are modulated by a supersonic molecular beam injection pulse and the modulation amplitude decreases with increasing electron density at the same ECW injection power and decreasing ECW power at the same electron density, respectively. Analysis revealed that a critical value of electron temperature gradient (ETG) triggers the density fluctuations, and the intensity of the relative density fluctuations is positively correlated with the ETG and approximately inversely proportional to the effective collision frequency. With plasma parameters similar to those of EXL-50 experiments, the HD7 code simulations demonstrate that trapped electron mode (TEM) turbulence can be excited by ETG higher than the critical value observed in the experiment. In addition, the dependence of the mode growth rate (supposed to be proportional to the saturation level of fluctuations in quasi-linear theory) and the measured intensity of the density fluctuations is comparable. The simulated outward particle flux integrated over the poloidal wave number spectrum is significant and proportional to ETG. These observations demonstrate that the density fluctuation is TEM turbulence, which is driven by ETG and induces particle pump-out when the electron density/effective electron collision frequency is low. The potential relevance of this work with the controls of plasma profiles, impurities, helium ash, and heat transport in future reactors of similar low effective collision frequency is also discussed.

Double-lamella phenomenon of once-folding polymer crystallization raised by chain-end hydrogen-bonding interactions

Poly (ethylene glycol) (PEG) holding molecular weights around 7000 Da exhibits a double-lamella phenomenon on the surface replicas of bulk once-folding crystallization, whose mechanism is still unclear. Concerning to its specific hydrogen-bonding interactions at chain-ends, we performed dynamic Monte Carlo simulations to investigate the effects of specific chain-end interactions on once-folding crystallization of 16-mers. The results showed that the chain-end hydrogen-bonding interactions bring little effects to both kinetics of primary nucleation and lateral growth of chain-folded lamellar crystals but make a more significant terrace at the lateral growth front with a step of metastable once-folding towards the next step of stable chain-extending, raising the double-lamella phenomenon of their surface replicas. We found that the chain-end hydrogen-bonding interactions are rich at the surfaces of once-folded lamellar crystals, which thus enhance their metastability and retard their thickening into the chain-extended crystals. In addition, intra- and inter-molecular secondary nucleation at corresponding chain-folded and extended growth fronts show different growth rate dependences on the specific interaction strengths. Our results revealed the role of specific chain-end interactions in PEG crystallization.

A KdV-SIR equation and its analytical solutions: An application for COVID-19 data analysis

To describe the time evolution of infected persons associated with an epidemic wave, we recently derived the KdV-SIR equation that is mathematically identical to the Kortewegde Vries (KdV) equation in the traveling wave coordinate and that represents the classical SIR model under a weakly nonlinear assumption. This study further discusses the feasibility of applying the KdV-SIR equation and its analytical solutions together with COVID-19 data in order to estimate a peak time for a maximum number of infected persons. To propose a prediction method and to verify its performance, three types of data were generated based on COVID-19 raw data, using the following procedures: (1) a curve fitting package, (2) the empirical mode decomposition (EMD) method, and (3) the 28-day running mean method. Using the produced data and our derived formulas for ensemble forecasts, we determined various estimates for growth rates, providing outcomes for possible peak times. Compared to other methods, our method mainly relies on one parameter, σo (i.e., a time independent growth rate), which represents the collective impact of a transmission rate (β) and a recovery rate (ν). Utilizing an energy equation that describes the relationship between the time dependent and independent growth rates, our method offers a straightforward alternative for estimating peak times in ensemble predictions.

Growth and passivation of individual carbon nanoparticles by C2H2 addition at high temperatures: Dependence of growth rate and evolution on material and size.

Absolute kinetics for reactions of C2H2 with a series of ∼60 individual carbon nanoparticles (NPs) from graphite, graphene, graphene oxide, carbon black, diamond, and nano-onion feedstocks were measured for temperatures (TNP) ranging from 1200 to 1700K. All the NPs were observed to gain mass by carbon addition under conditions that varied with feedstock but with large variations in initial growth rate. Long reaction periods were studied to allow the evolution of growth rates over time to be observed. Diamond NPs were found to passivate against C2H2 addition if heated above ∼1400K, and the highly variable initial reactivity for carbon nano-onions was found to depend on the presence of non-onion-structure surface carbon. For graphitic and carbon black NPs, three distinct growth modes were observed, correlated with the initial NP mass (Minitial). Smallest graphitic and carbon black NPs, with masses <∼25 MDa, initially grew rapidly but also passivated quickly after adding <4% of Minitial. NPs in the 20-50 MDa range also passivated but only after multiple waves of fast growth separated by periods of low reactivity, with up to ∼11% total mass gain before passivation. The largest carbon black and graphitic NPs, with Minitial >50 MDa, grew rapidly and continuously, adding up to ∼300% of Minitial with no signof rate slowing as long as C2H2 was present. The efficiencies for C2H2 addition and etching by O2 are strongly correlated, but the correlation changes as the NPs passivate. Growth and passivation mechanisms are discussed.

Cosmological perturbation theory using generalized Einstein–de Sitter cosmologies

The separable analytical solution in standard perturbation theory for an Einstein--de Sitter (EdS) universe can be generalized to the wider class of such cosmologies (``generalized EdS,'' or gEdS) in which a fraction of the pressureless fluid does not cluster. We derive the corresponding kernels in both Eulerian perturbation theory (EPT) and Lagrangian perturbation theory, generalizing the canonical EdS expressions to a one-parameter family where the parameter can be taken to be the exponent $\ensuremath{\alpha}$ of the growing mode linear amplification $D(a)\ensuremath{\propto}{a}^{\ensuremath{\alpha}}$. For the power spectrum (PS) at one loop in EPT, the contribution additional to standard EdS is given, for each of the ``13'' and ``22'' terms, as a function of two infrared safe integrals. In the second part of the paper we show that the calculation of cosmology-dependent corrections in perturbation theory in standard [e.g., Lambda cold dark matter (LCDM)] models can be simplified, and their magnitude and parameter dependence better understood, by relating them to our analytic results for gEdS models. At second order the time dependent kernels are equivalent to the analytic kernels of the gEdS model with $\ensuremath{\alpha}$ replaced by a single redshift dependent effective growth rate ${\ensuremath{\alpha}}_{2}(z)$. At third order the time evolution can be conveniently parametrized in terms of two additional such effective growth rates. For the PS calculated at one-loop order, the correction to the PS relative to the EdS limit can be expressed in terms of just ${\ensuremath{\alpha}}_{2}(z)$, one additional effective growth rate function, and the four infrared safe integrals of the gEdS limit. This is much simplified compared to expressions in the literature that use six or eight redshift dependent functions and are not explicitly infrared safe. Using the analytic gEdS expression for the PS with $\ensuremath{\alpha}={\ensuremath{\alpha}}_{2}(z)$ gives a good approximation (to $\ensuremath{\sim}25%$) for the exact result.