Non-monotonic Growth Research Articles

Simultaneous Selective-Area and Vapor-Liquid-Solid Growth of InP Nanowire Arrays.

Selective-area epitaxy is highly successful in producing application-ready size-homogeneous arrays of III-V nanowires without the need to use metal catalysts. Previous works have demonstrated excellent control of nanowire properties but the growth mechanisms remain rather unclear. Herein, we report a detailed growth study revealing that fundamental growth mechanisms of pure wurtzite InP ⟨111⟩A nanowires can indeed differ significantly from the simple picture of a facet-limited selective-area growth process. A dual growth regime with and without metallic droplet is found to coexist under the same growth conditions for different diameter nanowires. Incubation times and highly nonmonotonous growth rate behaviors are revealed and explained within a dedicated kinetic model.

Optical properties of ZnO-based step quantum wells

The MgxZn1−xO/ZnO and MgxZn1−xO/CdyZn1−yO step quantum well structures have been produced by the pulsed laser deposition method. It has been established that the increase of the barrier height ratio for charge carriers in the conduction and valence bands upon transition from the active ZnO layers in the MgxZn1−xO/ZnO system to the active layers of CdyZn1−yO in a low-dimensional MgxZn1−xO/CdyZn1−yO system is associated with the fact that the electron concentration in CdyZn1−yO films rises with an increase in the cadmium content. As the result, the Fermi level is displaced to the bottom of the conduction band. In the range of quantum well widths from 1 to 12 nm the nonmonotonous growth of exciton and defect-related intensities in photoluminescence spectra is observed.

Emergence of coexistence and limit cycles in the chemostat model with flocculation for a general class of functional responses

We consider a model of two microbial species in a chemostat competing for a single-resource, involving the flocculation of the most competitive species which is present in two forms: isolated and attached. We first show that the model with one species and a non-monotonic growth rate of isolated bacteria may exhibit bi-stability and allows the appearance of unstable limit cycles through a sub-critical Hopf bifurcations due to the joined effect of inhibition and flocculation. We then show that the model with two species presents an even richer set of possible behaviors: coexistence, bi-stability and occurrence of stable limit cycles through a super-critical Hopf bifurcations. All these features cannot occur in the classical chemostat model, where generically at most one competitor can survive on a single resource.

Land acquisition and industrial growth

Purpose – This paper aims to understand the impact of land acquisition and the provision of rehabilitation and remuneration (R & R) transfers included in it, toward the short-run and the long-run growth of an economy as well as on the welfare of farmers and industrialists over time. Design/methodology/approach – The authors develop a two-sector model of growth with agriculture and manufacturing in which land is an essential input to production in both sectors. Industrialists buy land from farmers and deals include R & R payments. Individuals live for one period and at its end, bequeath land and capital assets to their child. There is Hicks-neutral technical progress in each sector. Findings – The R & R policy has no effect on the long-run sectoral growth or land allocation. While such a policy benefits the farmers initially, after a certain period, it reduces their welfare. The R & R scheme makes the industrialist worse-off in all periods. It was found that besides the standard convergence effect, land acquisition by the industrial sector increases the growth rate of capital. This may lead to non-monotonic growth rate of capital. Research limitations/implications – The two-sector model abstracts from labor and labor markets. Hence, sectoral employment mobility or changes in the skill-wage premium over time are not captured. Originality/value – First, this paper developed a two-sector growth model with land as a factor of production and an asset. Second, it examined growth and distributive impacts of the R & R package embodied in land transactions.

Dimensional effects in exciton and defect-related luminescence of ZnO-based step quantum wells

The /ZnO and / step quantum well structures have been produced by the pulsed laser deposition method. It has been established that the increase of the barrier height ratio for charge carriers in the conduction and valence bands upon transition from the active ZnO layers in the /ZnO system to the active layers of in a low-dimensional / system is associated with the fact that the electron concentration in films rises with an increase in the cadmium content. As a result, the Fermi level is displaced to the bottom of the conduction band. In the range of quantum well widths from 1 nm to 12 nm the nonmonotonous growth of exciton and defect-related intensities in photoluminescence spectra is observed.

Somatic growth of juvenile green turtle (Chelonia mydas) morphotypes in the Colombian Pacific

Somatic growth rates of green turtles (Cheloniamydas) are affected by foraging success and influence their survival and reproduction. Gorgona National Park (GNP) in the Colombian Pacific (2°58′03″N, 78°10′49″W) is an insular foraging site that offers a unique opportunity to study the black (occurring only in the eastern Pacific) and yellow (with western Pacific nesting beach origins) morphotypes of green turtles during their juvenile phase. A total of 995 turtles were captured and marked between October 2003 and December 2012. Recapture rates were low (20 black morphotype and 13 yellow morphotype turtles) but suggested that at least some turtles remain in the area for extended periods (>5 years). Mean growth rate was slightly higher for black morphotype (mean 0.92 ± 0.24 cm y−1) than yellow morphotype turtles (mean 0.74 ± 0.26 cm y−1), and both morphotypes displayed a non-monotonic growth pattern. Black morphotype turtles grew faster at intermediate sizes, similar to black turtles at other locations in the eastern Pacific, whereas yellow morphotype turtles had slowest growth at intermediate sizes. Our data underscore the importance of GNP as a foraging habitat for C. mydas individuals from distinct nesting populations and indicate that these morphotypes have different growth patterns while residing at the same foraging site.

External and internal gelation of pectin solutions: microscopic dynamics versus macroscopic rheology

Pectin is a natural biopolymer that forms, in the presence of divalent cations, ionic-bound gels typifying a large class of biological gels stabilized by non-covalent cross-links. We investigate and compare the kinetics of formation and aging of pectin gels obtained either through external gelation via perfusion of free Ca2+ ions, or by internal gelation due to the supply of the same ions from the dissolution of CaCO3 nanoparticles. The microscopic dynamics obtained with photon correlation imaging, a novel optical technique that allows obtaining the microscopic dynamics of the sample while retaining the spatial resolution of imaging techniques, is contrasted with macroscopic rheological measurements at constant strain. Pectin gelation is found to display peculiar two-stage kinetics, highlighted by non-monotonic growth in time of both microscopic correlations and gel mechanical strength. These results are compared to those found for alginate, another biopolymer extensively used in food formulation.

The bit‐economy: An artificial model of open‐ended technology discovery

We describe and demonstrate an artificial model of technology discovery called the Bit‐Economy. The model is built from a minimal set of fundamental hallmarks of technology and develops under an open‐ended evolutionary operator which rewards new technology which is able to coordinate both spatially and temporally with the existing technology set. The Bit‐Economy, is able to replicate several features of real technology development including nonmonotonic growth, bunching of creation and destruction events, qualitative topologies of patent networks, and efficiency and waste‐management gains. In contrast to related works, we do not apply an exogenous fitness landscape and so are able to study the process of technology discovery as a self‐guided search toward more complex outcomes. © 2013 Wiley Periodicals, Inc. Complexity 18: 57–67, 2013

A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.

Influence of the Individual DPOAE Growth Behavior on DPOAE Level Variations Caused by Conductive Hearing Loss and Elevated Intracranial Pressure

Minor conductive hearing loss (CHL) can compromise the evaluation of the inner ear function with distortion product otoacoustic emissions (DPOAE). Elevation of the intracranial pressure (ICP) is also expected to alter the middle ear (ME) sound transmission. An impaired ME sound transmission leads to an attenuation of the DPOAE primary tone levels (L1 and L2) during forward transmission and of DPOAE levels (LDP) during backward transmission. The effect of the attenuation of L1 and L2 is complex and might have unexpected effects on DPOAE levels. In this work, CHL- and ICP-induced alterations of LDP versus L1 growth functions (constant L2 and increasing L1) are investigated. The first aim of this study is to explain how alterations of ME sound transmission can affect DPOAEs and to characterize the dependency of DPOAE level alterations on L2,L1 combinations and on the individual shape of LDP versus L1 growth functions. The second aim is to identify analogies between CHL- and ICP-induced alterations of DPOAEs and to discuss implications for a potential noninvasive ICP monitoring. This study focuses on general theoretical considerations, supported by selected experimental observations in different species and simulations. DPOAEs were measured in guinea pigs before and after induction of a CHL (1 ear) and during increased ICP (1 ear), and in humans during changes of the postural position to alter the ICP (4 ears). In both CHL and elevated ICP, DPOAE levels are not only reduced, but LDP versus L1 growth functions exhibit a shift to higher L1. The absolute DPOAE level alterations strongly depend on the L2,L1 combinations and the individual shape of the LDP versus L1 growth functions. In steeper LDP versus L1 growth functions, the DPOAE level alterations exhibit a larger variation. DPOAE levels can even increase. The largest variation can be found in ears with a nonmonotonic DPOAE growth behavior. An example of a guinea pig ear is presented with a nonmonotonic DPOAE growth behavior and a CHL of 4 dB, where the DPOAE level alterations varied between -32 and +9 dB depending on L1. The data enable a more comprehensive view of DPOAE level alterations during CHL and elevated ICP. The observations also explain the problem that DPOAE and ICP alterations do not correlate linearly. An evaluation of the shift of the LDP versus L1 growth function along the L1 axis provides a potential tool to improve both the assessment of the inner ear function in the presence of a CHL and noninvasive ICP monitoring with DPOAEs.

Extremum seeking via continuation techniques for optimizing biogas production in the chemostat

We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each of the two subproblems can be solved with relatively simple algorithms. We are then free to choose any numerical optimization algorithm. We give a demonstration for two choices: one is based on slow-fast dynamics and numerical continuation, the other is a combination of golden-section and Newton iteration. The method copes with non-monotonic growth functions.

U-shaped development: an old but unsolved problem.

Even today the investigation of U-shaped functions in human development is of considerable importance for different domains of Developmental Psychology. More and more scientific researchers focus their efforts on the challenge to describe and explain the phenomenon by identifying those skills and abilities being affected. The impact of U-shaped functions on diagnostic decision-making and on therapeutic treatment programs highlights the importance of understanding the nature of non-monotonic development. The present article therefore addresses the relevant questions of how U-shaped functions are defined in theory, in which developmental domains such non-monotonic growth curves are suggested to occur, and which implications there are for future methodology and diagnostic practice. Finally, it is recommended to clearly identify those interactions between proximal and distal subcomponents which are expected to contribute to a U-shaped development.

Photoluminescence peculiarities in InGaAs/GaAs structures with different InAs quantum dot densities

Emission peculiarities and X-ray diffraction (XRD) have been studied in GaAs/InGaAs/GaAs quantum wells (QWs) with different densities of embedded InAs quantum dots (QDs). The QD density decreased from 1.1×1011 to 1.3×1010cm−2 when the QD growth temperature was increased from 470 up to 535°C. The QD density changes are accompanied by the nonmonotonic variation of the photoluminescence (PL) intensity and peak positions: the highest PL intensity corresponds to lowest emission energy (1.3μm) in InAs QDs obtained at the QD density equal to 3.4×1010cm−2.PL temperature dependences have been studied in the range of 10–300K with the aim to analysis the QD band gap shrinkage. It revealed the process of In/Ga intermixing that is characterized by nonmonotonic behavior versus QD growth temperatures and QD densities.The XRD study has revealed high intensity peaks related to the diffraction of X-ray beam from (400) crystal planes in the cubic GaAs QW layers and GaAs substrates. It was shown that (400) diffraction peaks in GaAs QW layers shift to high angles, in comparison with the GaAs substrate, testifying the compression strain. The strain value in GaAs QW layers has been estimated and it is revealed that this value changes nonmonotonic with InAs QD density and its minimum corresponds to a QD density of 3.4×1010cm−2. It is shown that In/Ga intermixing is stimulated by the compression strains: higher level of strains provokes higher In/Ga intermixing.Therefore, the shift of PL peak positions in InAs QDs versus QD density and size is the result of the influence of three factors: the quantum confined effect in QDs of different sizes, In/Ga intermixing, and the compression strain. The value of PL peak shift owing to the compression strains in QWs has been estimated as well. Physical reasons for the nonmonotonic variation of PL and strains in InGaAs/GaAs QWs versus InAs QD density have been discussed.

Fuzzy servo controller for CSTB with substrate inhibition kinetics

Continuous stirred tank bioreactors with non-monotonic growth kinetics can exhibit bifurcation and multiple equilibrium points. Maximum productivity for this bioreactor is located at the limit of a bifurcation. Therefore, when the desired operating point is near optimal productivity, even small perturbations may drive the system from stability to an undesired, unstable condition. This work describes a fuzzy servo controller that was designed based on sector nonlinearities to force the bioreactor to stay near its optimal productivity point. The designed controller enables tracking of a reference signal that switches between stable and unstable nodes and finally stabilizes at the optimal operating point. Two reference signals were evaluated for the substrate and the biomass respectively. The performance of the proposed controller was compared to PID and LQ controllers. Linear matrix inequalities were used to prove the closed-loop stability.

Somatic growth rates of hawksbill turtles Eretmochelys imbricata in a northern Great Barrier Reef foraging area

An understanding of the rate at which long-lived species grow is essential for determining important life history parameters, including assessments of foraging habitat quality, the time taken to reach sexual maturity, and the age at which maturity is reached. The hawksbill sea turtle Eretmochelys imbricata is a Critically Endangered species that is typically associated with coral reefs throughout the tropical oceans. Little is known about its life history through most age-classes, especially in the western Pacific, one of the last strongholds for the species. We undertook annual surveys of a foraging population of hawksbill turtles on 13 reefs, within the far northern section of the Great Barrier Reef (GBR), from 1997 to 2008. We obtained growth rate data from 128 turtles that were recaptured once (n = 103), twice (n = 23), or 3 times (n = 2). The curved carapace length of recaptured turtles ranged from 61.3 to 91.4 cm (x= 79.8 ± 7.26 cm, mean ± SD). Recapture intervals spanned between 11 and 120 mo (mean: 59 mo; median: 72 mo). We show that mean annual growth rates did not differ between sexes and had a non-monotonic growth pattern, reaching peak growth for both sexes within the 65 to 70 cm curved carapace length size-class. Growth slowed thereafter at a linear rate, to negligible growth upon reaching an adult size of >80 cm. Hawksbill turtles grew faster in the southern GBR, compared to those found in the far north of the reef. Understanding spatial and temporal differences in growth rates, and thus age at maturity, is an important step towards resolving life history differences among sea turtle populations.

Analysis of a model for the effects of an external toxin on anaerobic digestion

Anaerobic digestion has been modeled as a two-stage process using coupled chemostat models with non-monotone growth functions, [9]. This study incorporates the effects of an external toxin. After reducing the model to a 3-dimensional system, global stability of boundary and interior equilibria is proved using differential inequalities and comparisons to the corresponding toxin-free model. Conditions are given under which the behavior of the toxin-free model is preserved. Introduction of the toxin results in additional patterns such as bistabilities of coexistence steady states or of a periodic orbit and an interior steady state.

Properties of traveling waves for integrodifference equations with nonmonotone growth functions

In this paper, we will establish some new properties of traveling waves for integrodifference equations with the nonmonotone growth functions. More precisely, for c ≥ c *, we show that either $${\lim\limits_{\xi\rightarrow+\infty} \phi(\xi)=u*}$$ or $${0 < \liminf\limits_{\xi \rightarrow + \infty} \phi(\xi) < u* < \limsup \limits_{\xi\rightarrow+\infty}\phi(\xi)\leq b,}$$ that is, the wave converges to the positive equilibrium or oscillates about it at +∞. Sufficient conditions can assure that both results will arise. We can also obtain that any traveling wave with wave speed c > c* possesses exponential decay at −∞. These results can be well applied to three types of growth functions arising from population biology. By choosing suitable parameter numbers, we can obtain the existence of oscillating waves. Our analytic results are consistent with some numerical simulations in Kot (J Math Biol 30:413–436, 1992), Li et al. (J Math Biol 58:323–338, 2009) and complement some known ones.

Correlation-Coefficient-Based Fast Template Matching Through Partial Elimination

Partial computation elimination techniques are often used for fast template matching. At a particular search location, computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location. Due to the nonmonotonic growth pattern of the correlation-based similarity measures, partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures. In this paper, we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation, and we propose basic-mode and extended-mode partial correlation elimination algorithms for fast template matching. The basic-mode algorithm is more efficient on small template sizes, whereas the extended mode is faster on medium and larger templates. We also propose a strategy to decide which algorithm to use for a given data set. To achieve a high speedup, elimination algorithms require an initial guess of the peak correlation value. We propose two initialization schemes including a coarse-to-fine scheme for larger templates and a two-stage technique for small- and medium-sized templates. Our proposed algorithms are exact, i.e., having exhaustive equivalent accuracy, and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes. While the actual speedups are data dependent, in most cases, our proposed algorithms have been found to be significantly faster than the other algorithms.

NOISE AND SEASONAL EFFECTS ON THE DYNAMICS OF PLANT–HERBIVORE MODELS WITH MONOTONIC PLANT GROWTH FUNCTIONS

We formulate general plant–herbivore interaction models with monotone plant growth functions (rates). We study the impact of monotone plant growth functions in general plant–herbivore models on their dynamics. Our study shows that all monotone plant growth models generate a unique interior equilibrium and they are uniform persistent under certain range of parameters values. However, if the attacking rate of herbivore is too small or the quantity of plant is not enough, then herbivore goes extinct. Moreover, these models lead to noise sensitive bursting which can be identified as a dynamical mechanism for almost periodic outbreaks of the herbivore infestation. Montone and non-monotone plant growth models are contrasted with respect to bistability and crises of chaotic attractors.

Atomically resolved nucleation and initial growth of a Ag three-dimensional island on Si(001) substrate

The initial growth of a Ag three-dimensional island on an atomically resolved Si(001) substrate was investigated in situ by scanning tunneling microscopy (STM) at room temperature. It took \ensuremath{\sim}20 min for the island to grow from nucleation to a final dimension of 25 nm \ifmmode\times\else\texttimes\fi{} 35 nm \ifmmode\times\else\texttimes\fi{} 22 monolayers (ML). Uniquely, the island growth occurred under no Ag deposition. The Ag atoms required for the growth were provided from the two-dimensional Ag layer and diffusing Ag atoms on the layer that was deposited before the observation. Thanks to this unique growth mechanism, it was allowed to observe the island growth under an isotropic supply of Ag atoms without the shadowing effect of metal deposition by a scanning probe. On the other hand, the STM measurement itself affected finite effects on the growth; attractive interaction between the probe and Ag atoms promoted nucleation of the island, and tunnel current injection may have increased the effective temperature of the system. Despite such a measurement effect, some growth processes that are characteristic of typical metal thin-film growth on silicon substrates were clearly visualized, such as anisotropic and nonmonotonic growth rates that were affected by atomic surface defects, and the growth mode transition from area oriented to height oriented due to an accumulation of stress arising from the lattice mismatch.