Non-monotonic Growth Research Articles

Global dynamics of the chemostat with different removal rates and variable yields

In this paper, we consider a competition model between n species in a chemostat including both monotone and non-monotone growth functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. We construct a Lyapunov function which reduces to the Lyapunov function used by S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growth functions are of Michaelis-Menten type and the yields are constant. Various applications are given including linear, quadratic and cubic yields.

Growth rates of juvenile green turtles Chelonia mydas from three ecologically distinct foraging habitats along the east central coast of Florida, USA

A generalized additive mixed modeling approach was used to assess somatic growth for juvenile green turtles Chelonia mydas at 4 sites in 3 ecologically distinct foraging habitats along the east central coast of Florida, USA. The 3 habitats were a man-made nuclear submarine turning basin (Trident Submarine Basin), an estuary (Indian River Lagoon), and oceanic sabellariid worm rock reefs (Sebastian Inlet and St. Lucie Power Plant). Turtles from the Indian River Lagoon site grew significantly faster than turtles from the Trident Submarine Basin and sabellariid worm rock reef sites. There were no significant differences in growth rates between the sabellariid worm rock reef and Trident Submarine Basin sites. Non-monotonic or dome-shaped growth rate functions reflecting an immature peak in growth rates were observed for all 3 habitats. Growth rates peaked in 1998 for turtles in the Trident Submarine Basin and sabellariid worm rock reef habitats; since then growth rates have declined. This temporal decline in growth rates may reflect density-dependent effects on growth as more juveniles recruit to Florida for aging grounds, a direct result of increases in nest production at the primary rookeries (Costa Rica, Florida and Mexico). Developmental habitats are important for the survival of juvenile marine turtles. This study illustrates the degree to which juvenile growth rates vary among developmental habitats, which ultimately can affect the rate of growth and recovery potential of nesting stocks.

Does Entrepreneurship Promote Growth? A Model of Occupational Choice with Risk-Attitude Heterogeneous Agents

This paper studies whether promoting entrepreneurship is always growth-enhancing under a dynamic general-equilibrium framework in which agents differ in their risk attitude. Less risk averse agents become entrepreneurs who contribute to economic growth through a product variety effect. Workers, who are net savers, also contribute to growth through a loanable fund supply effect. The working of these two effects results in a non-monotone entrepreneurship-economic growth relationship. Due to risk aversion and the presence of an intergenerational externality, both of the two effects are under-valued by individuals. As a result, there can be too less or too much entrepreneurship in the decentralized equilibrium. Although having some of the entrepreneurial risk insured away can be growth-enhancing, it is never optimal to provide full insurance. How changes in the distribution of risk attitude and the degree of uncertainty may affect occupational choice and balanced growth are also examined.

Minimal Time Sequential Batch Reactors with Bounded and Impulse Controls for One or More Species

We consider the optimal control problem of feeding in minimal time a tank where several species compete for a single resource, with the objective being to reach a given level of the resource. We allow controls to be bounded measurable functions of time plus possible impulses. For the one-species case, we show that the immediate one-impulse strategy (filling the whole reactor with one single impulse at the initial time) is optimal when the growth function is monotonic. For nonmonotonic growth functions with one maximum, we show that a particular singular arc strategy (precisely defined in section 3) is optimal. These results extend and improve former ones obtained for the class of measurable controls only. For the two-species case with monotonic growth functions, we give conditions under which the immediate one-impulse strategy is optimal. We also give optimality conditions for the singular arc strategy (at a level that depends on the initial condition) to be optimal. The possibility for the immediate one-impulse strategy to be nonoptimal while both growth functions are monotonic is a surprising result and is illustrated with the help of numerical simulations.

An integral approach for simulation of vapour film dynamics around a spherical surface

The dynamics of a thermally driven vapour film around a solid sphere has been investigated here with both the sphere and the annular film surrounded by a large water pool. Integral models based on constant and variable vapour-phase densities have been developed here for studying a spherico-symmetric phase change problem for two immiscible phases, vapour and liquid around a hot sphere. Governing equations for both liquid and vapour phases are converted into a set of non-linear ODEs. Effects of distinct density on interface condition and density variation of vapour phase are taken into account both in energy equation of vapour phase and also in interfacial mass and energy balance. The present models have been validated with available analytical, incompressible Volume of Fluid (VOF) and experimental results of growth and collapse of either bubble or vapour film. A simple model, based on scale analysis, was evolved that successfully captured the non-monotonic growth of the film, as observed by the more detailed models under certain degree of liquid subcooling. In addition, the case of very small thermal boundary layer in the liquid side has been successfully studied for which the VOF model required very fine grid. It has been observed that the effect of density variation in the integral model results in marginally higher film growth at higher temperature. However, the effect of radiation on the film growth was found to be quite substantial. The integral model not only incorporates the effects of vapour-phase temperature variation and radiation exchange of heat but also is computationally several-fold efficient with respect to the VOF model.

Existence of traveling waves for integral recursions with nonmonotone growth functions

A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with overcompensation which still have asymptotic spreading speeds can be found by using the ideas introduced by Thieme (J Reine Angew Math 306:94-121, 1979) for the study of space-time integral equation models for epidemics. The present work gives a large subclass of these models with overcompensation for which the spreading speed can still be characterized as the slowest speed of a non-constant traveling wave. To illustrate our results, we numerically simulate a series of traveling waves. The simulations indicate that, depending on the properties of the fecundity function, the tails of the waves may approach the carrying capacity monotonically, may approach the carrying capacity in an oscillatory manner, or may oscillate continually about the carrying capacity, with its values bounded above and below by computable positive numbers.

On “Feedback Stabilization of Fed-Batch Bioreactors: Non-Monotonic Growth Kinetics”

Fil: de Battista, Hernan. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ingenieria; Argentina

Effect of spin crossovers on the Mott-Hubbard transition at high pressures

The effect of spin crossovers in dn terms on the effective Hubbard parameter (Ueff) determining the gap between the lower and upper Hubbard bands is analyzed using a many-electron approach to describe the electron structure of Mott insulators. A new mechanism of the insulator-metal transition is established for d5 ions, which is related to a decrease in Ueff caused by spin crossover. For other ions, the Ueff value is either independent of pressure (d2, d4, d7) or it exhibits nonmonotonic growth (d3, d6, d8).

Raman characterization of hydrogen ion implanted silicon: “High-dose effect”?

The Raman spectra of nanostructures formed on silicon Si single-crystalline wafers by implantation with hydrogen ions of fluencies ranging within D∼2×10 16–3×10 17 cm −2 are reported. The presence of both crystalline and amorphous silicon phases were found in the spectra. A non-monotonic growth in the intensities of the peaks originating from the crystalline and the amorphous phases with a dose of the implantation was registered. A ratio of the intensities of the main peaks of the amorphous to the crystalline Si phases also demonstrated a non-monotonic behaviour (“high-dose effect”). Possible reasons and mechanisms of the non-monotonic dependence of a “degree” of amorphization on a dose of the implantation (or irradiation) are discussed.

Biological control of the chemostat with nonmonotonic response and different removal rates

We show the global stabilization of the chemostat with nonmonotonic growth, adding a new species as a "biological" control, in presence of different removal rates for each species. This result is obtained by an extension of the Competitive Exclusion Principle in the chemostat, for the case of two species with different removal rates and at least one nonmonotonic response.

Social security, public education and the growth–inequality relationship

We study how the relationship between economic growth and inequality depends upon the levels of funding of two of the largest government programs, public education and social security. We do this in the context of an overlapping generations economy with heterogeneous agents where the government collects a tax on labor income to finance these programs. We show that in our model an increase in government spending on social security reduces income inequality and can have a non-monotonic effect on growth. When the initial level of social security funding is low, as is the case in most poor economies, then its increase will enhance growth. When its funding level is high as is typical for developed countries, we show that its further increase can slow down growth while reducing income inequality. These results obtain regardless of whether the increase in social security funding is financed by a tax increase or by cutting the public education budget. We also find that the effects of increasing the level of public education expenditures or the overall size of the government budget (holding the budget composition fixed) are characterized by similar non-monotonic growth–inequality relationships.

Distortion product otoacoustic emissions and basilar membrane vibration in the 6–9kHz region of sensitive chinchilla cochleae

Distortion product otoacoustic emissions (DPOAEs) and basilar membrane (BM) vibration were measured simultaneously in the 6-9 kHz region of chinchilla cochleae. BM-Input-Output functions in a two-tone paradigm behaved similarly to DPOAEs for the 2f1-f2 component, nonmonotonic growth with the intensity of the lower frequency primary and a notch in the functions around 60 dB SPL. Ripples in frequency functions occur in both BM and OAE curves as a function of the distortion frequency. Optimum f2/f1 ratios for DPOAE generation are near 1.2. The slope of phase curves indicates that for low f2f1(<1.1) the emission source is the place location while for f2f1>1.1 the relative constancy of the phase function suggests that the place is the nonlinear region of f2, i.e., the wave location. Magnitudes of the DPOAEs increase rapidly above 60 dB SPL suggesting a different source or mechanism at high levels. This is supported by the observation that the high level DPOAE and BM-DP responses remain for a considerable period postmortem.

Uncertainty growth in Hypo-Elastic Material Models

The purpose of this note is to highlight a new point of concern in the use of hypo-elastic constitutive equations. In particular, it is shown that if there is any uncertainty in the material constants that appear in such equations, it can induce nonmonotone uncertainty growth in the resulting solutions.

Anisotropy of the temperature dependence of the lattice parameters of EuBa2Cu3O7−d in the quasiharmonic limit

An x-ray diffraction analysis of the compound EuBa2Cu3O7−δ is carried out in the temperature range 20–300K. At all temperatures of measurement the structure is described in the orthorhombic system. Nonmonotonic growth of the crystal lattice parameter c with decreasing temperature is observed in the interval 150–20K, and substantial features of the temperature dependence of the coefficient of linear thermal expansion appear below the Debye temperature. The results of the experiment are in complete agreement with the conclusions of a microscopic treatment of the vibrations of the atoms of the BaO and europium layers and also the Cu–O chains.

Two-compartment model for competitive hybridization on molecular biochips

During competitive hybridization the specific and non-specific fractions of tested biomolecules in solution bind jointly with the specific probes immobilized in a separate cell of a microchip. The application of two-compartment model to the two-component hybridization allows analytically investigating the underlying kinetics. It is shown that the behaviour with the non-monotonous growth of complexes formed by the non-specific fraction on a probe cell is a typical feature of competitive hybridization for both diffusion-limited and reaction-limited kinetics. The physical reason behind such an evolution consists in the fact that the characteristic hybridization time for the perfect complexes turns out longer with respect to that for the mismatch complexes. This behaviour should be taken into account for the choice of optimum hybridization and washing conditions for the analysis of specific fraction.

Intermittency Growth in Fluid Turbulence

Measurement and phenomenological analyses of intermittency growth inan experimental turbulent pipe flow and numerical turbulence areperformed, for which working definitions such as degree,increment, and growth rate of intermittencyare introduced with the help of quasiscaling theory.The logarithmic–normal inertial scaling model is extended toquasiscaling as the second-order truncation of the Taylor expansionand is used for studying the intermittency growth problem. The extended self-similarityproperties are shown to be not consistent with the monotonicity of thethird order local quasiscaling exponent and the nonmonotonic behaviour ofthe intermittency growth rate as a result of bottleneck. Digestionsof the results with scale-dependent multifractals are provided.

Accelerated recording of negative index gratings in Ge-doped optical fibers using 248-nm 500-fs laser radiation

The fabrication of Bragg gratings in commercial B-Ge and high-Ge optical fibers using 248-nm 500-fs laser radiation is demonstrated. The underlying photosensitivity process is that of Type IIA, where negative index change gratings are recorded, following a nonmonotonic index change growth. Refractive index evolution curves for both average and modulated index changes are presented. Index changes of the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> are obtained for the fibers exposed, under 2.4 kJ/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sup> accumulated energy density. For comparative purposes grating exposures using 248-nm nanosecond excimer laser radiation are also appended. Thermal annealing studies performed revealed that Type IIA negative index gratings fabricated using femtosecond pulses exhibit enhanced thermal stability, enduring temperatures up to 650degC

Film Growth and Surface Roughness with Effective Fluctuating Covalent Bonds in Evaporating Aqueous Solution of Reactive Hydrophobic and Polar Groups: A Computer Simulation Model

Summary: A computer simulation model is proposed to study film growth and surface roughness in aqueous (A) solution of hydrophobic (H) and hydrophilic (P) groups on a simple three dimensional lattice of size with an adsorbing substrate. Each group is represented by a particle with appropriate characteristics occupying a unit cube (i.e., eight sites). The Metropolis algorithm is used to move each particle stochastically. The aqueous constituents are allowed to evaporate while the concentration of H and P is constant. Reactions proceed from the substrate and bonded particles can hop within a fluctuating bond length. The film thickness () and its interface width () are examined for hardcore and interacting particles for a range of temperature (). Simulation data show a rapid increase in and followed by its non-monotonic growth and decay before reaching steady-state and near equilibrium () in asymptotic time step limit. The growth can be described by power laws, e.g., with a typical value of in initial time regime followed by at . For hardcore system, the equilibrium film thickness () and surface roughness () seem to scale linearly with the temperature, i.e., at low and at higher . For interacting functional groups in contrast, the long time (unsaturated) film thickness and surface roughness, and decay rapidly followed by a slow increase on raising the temperature. Growth of the average film thickness at a temperature .

Formation and decay of a longshore baroclinic jet associated with transient coastal upwelling and downwelling: A numerical study with applications to the Baltic Sea

A numerical study is undertaken on the formation and decay of a longshore baroclinic jet (LBJ) caused by a transient wind stress favorable for upwelling and downwelling. The two‐pycnocline type of stratification, typical for the Baltic Sea summertime, results in a nonmonotonic growth of the LBJ velocity with wind stress and time and a two‐branch structure of the jet, with domination of a branch related to the seasonal thermocline (permanent halocline) in the case of fully developed downwelling (upwelling). The LBJ associated with the fully developed upwelling (downwelling) is found to display baroclinic instability, and its decay is accompanied by selective formation of mostly cyclonic (anticyclonic) eddies. If upwelling or downwelling is not fully developed, the LBJ formed in a flat bottom basin does not display baroclinic instability unless the β effect is included. The β effect causes a detachment of the LBJ jet from the shoreline in the eastern half‐basin and thereby stimulates baroclinic instability. As a result, mesoscale eddies are generated only in the eastern half‐basin, and only if the basin diameter D is large enough to satisfy the inequality D &gt; , where RI is the baroclinic Rossby radius, f is the Coriolis parameter, and β = df/dy. Effect of topography on baroclinic instability makes it possible to develop eddies, even if the LBJ related to partially developed upwelling or downwelling is considered at β = 0.

Feedback control for nonmonotone competition models in the chemostat

This paper deals with the problem of feedback control of competition between two species with one substrate in the chemostat with nonmonotone growth functions. Without control, the generic behavior is competitive exclusion. The aim of this paper is to find a feedback control of the dilution rate, depending only on the total biomass, such that coexistence holds. We obtain a sufficient condition for the global asymptotic stability of a unique equilibrium point in the positive orthant for a three-dimensional differential system which arises from this controlled competition model. This paper generalizes the results obtained by De Leenheer and Smith in (J. Math. Biol. 46 (2003) 48).