scholarly journals Lipschitz stability for the growth rate coefficients in a nonlinear Fisher-KPP equation

2021 ◽  
Vol 14 (2) ◽  
pp. 695-721
Author(s):  
Patrick Martinez ◽  
◽  
Judith Vancostenoble
Keyword(s):  
Growth Rate ◽  
Rate Coefficients ◽  
Lipschitz Stability ◽  
Kpp Equation

Influence of Growth Rate Coefficients of Microorganisms on Microcosm Stability

2003 ◽  
Vol 2003.16 (0) ◽  
pp. 43-44
Author(s):  
Atsumi MURAKAMI ◽  
Hiroaki YOSHIDA ◽  
Yoshio ISHIKAWA ◽  
Katsura SUGIURA
Keyword(s):  
Growth Rate ◽  
Rate Coefficients

Distribution of Imported Glyphosate in Quackgrass (Elytrigia repens) Rhizomes in Relation to Assimilate Accumulation

Weed Science ◽  
1993 ◽  
Vol 41 (1) ◽  
pp. 7-11 ◽  
Author(s):  
Wen-Jang Shieh ◽  
Donald R. Geiger ◽  
Stephen R. Buczynski
Keyword(s):  
Growth Rate ◽  
Light Period ◽  
Rate Coefficients ◽  
Elytrigia Repens ◽  
Wide Range ◽  
Whole Plants ◽  
Rhizome Buds ◽  
Rhizome Development ◽  
Rhizome Age ◽  
Herbicide Glyphosate

The fact that quackgrass may occasionally escape control by the herbicide glyphosate is thought to result from the wide range in growth rate and sink activity among rhizome buds, especially in older portions of the rhizome. To study growth of rhizome structures, we supplied whole plants with14CO2throughout a 10-h light period and determined the amount of labeled carbon accumulated by the end of the subsequent 14-h night. Growth of rhizome structures during this 24-h period was estimated by determining their growth rate coefficients: the amount of labeled carbon accumulated per unit of carbon present in the structure. Growth rate coefficients generally were high for the rhizome tip that is enclosed in a sheath and the adjacent bud and rhizome segment, with values decreasing rapidly in a basipetal direction. However, extensive differences in the level and pattern of assimilate accumulation among rhizome structures were observed as rhizome development continued. Glyphosate accumulation generally paralleled the level of assimilate accumulation even though the range among rhizome structures for both increased with rhizome age. As a result of the increased variability among buds, some of the older buds will accumulate only a small, perhaps sublethal, amount of glyphosate and this may explain the tendency of the buds in older regions to escape control by glyphosate.

EXISTENCE AND SURVIVAL OF TWO COMPETING SPECIES IN A POLLUTED ENVIRONMENT: A MATHEMATICAL MODEL

2001 ◽  
Vol 09 (02) ◽  
pp. 89-103 ◽  
Author(s):  
J. B. SHUKLA ◽  
A. K. AGRAWAL ◽  
B. DUBEY ◽  
P. SINHA
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Emission Rate ◽  
Biological Species ◽  
Rate Coefficients ◽  
Washout Rate ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Model Study ◽  
External Sources

In this paper, a nonlinear mathematical model to study the effect of a toxicant emitted into the environment from external sources on two competing biological species is proposed and analyzed. The cases of constant emission and instantaneous spill of a toxicant are considered in the model study. In the case of constant emission, it is shown that four usual outcomes of competition between two species may be altered under appropriate conditions which are mainly dependent on emission rate of toxicant into the environment, uptake concentrations of toxicant by the two species and their growth rate coefficients and carrying capacities. However, in the case of instantaneous spill, it is found that if the washout rate of toxicant is large, then the four outcomes of competition exist under usual conditions. It is also pointed out that the survival of the competitors, coexisting in absence of the toxicant, may be threatened if the constant emission of toxicant into their environment continues unabatedly.

Contribution of floating macrophytes (Lemna sp.) to pond modelization

2005 ◽  
Vol 51 (12) ◽  
pp. 283-289
Author(s):  
H. Jupsin ◽  
H. Richard ◽  
J.L. Vasel
Keyword(s):  
Growth Rate ◽  
Oxygen Transfer ◽  
Digital Image Analysis ◽  
Surface Coverage ◽  
Deterministic Model ◽  
Rate Coefficients ◽  
Oxygen Balance ◽  
Nitrogen And Phosphorus ◽  
Experimental Conditions ◽  
Floating Macrophytes

The objective of the present study was to develop a methodology for the quantification of the growth rate of Lemnaceae biomass by digital image analysis. The effect of biomass surface coverage on the oxygen transfer coefficient (Kla) was also quantified. Contribution of Lemnaceae to oxygen balance was evaluated by closed respirometry. Monod-like equations could be derived from growth rate coefficients in various experimental conditions. This opens the way to a deterministic model of Lemnaceae ponds where uptake of nitrogen and phosphorus (even heavy metals) can be calculated.

A New AID for Interpolating and Assessing Collision Strengths and Rate Coefficients

1988 ◽  
Vol 102 ◽  
pp. 107-110
Author(s):  
A. Burgess ◽  
H.E. Mason ◽  
J.A. Tully
Keyword(s):  
Significant Loss ◽  
Impact Excitation ◽  
Rate Coefficients ◽  
Electron Impact Excitation ◽  
Graphical Display ◽  
Practical Procedure ◽  
Positive Ions ◽  
Allowed Transition ◽  
Computational Errors ◽  
Existing Data

AbstractA new way of critically assessing and compacting data for electron impact excitation of positive ions is proposed. This method allows one (i) to detect possible printing and computational errors in the published tables, (ii) to interpolate and extrapolate the existing data as a function of energy or temperature, and (iii) to simplify considerably the storage and transfer of data without significant loss of information. Theoretical or experimental collision strengths Ω(E) are scaled and then plotted as functions of the colliding electron energy, the entire range of which is conveniently mapped onto the interval (0,1). For a given transition the scaled Ω can be accurately represented - usually to within a fraction of a percent - by a 5 point least squares spline. Further details are given in (2). Similar techniques enable thermally averaged collision strengths upsilon (T) to be obtained at arbitrary temperatures in the interval 0 < T < ∞. Application of the method is possible by means of an interactive program with graphical display (2). To illustrate this practical procedure we use the program to treat Ω for the optically allowed transition 2s → 2p in ArXVI.

The threshold energy for atom displacement in fcc metals

1990 ◽  
Vol 48 (4) ◽  
pp. 530-531
Author(s):  
Wilfried Sigle ◽  
Matthias Hohenstein ◽  
Alfred Seeger
Keyword(s):  
Growth Rate ◽  
Elevated Temperatures ◽  
Threshold Energy ◽  
Dislocation Loops ◽  
Absolute Minimum ◽  
Voltage Electron ◽  
Atom Displacement ◽  
Electron Microscopes ◽  
Fcc Metal

Prolonged electron irradiation of metals at elevated temperatures usually leads to the formation of large interstitial-type dislocation loops. The growth rate of the loops is proportional to the total cross-section for atom displacement,which is implicitly connected with the threshold energy for atom displacement, Ed . Thus, by measuring the growth rate as a function of the electron energy and the orientation of the specimen with respect to the electron beam, the anisotropy of Ed can be determined rather precisely. We have performed such experiments in situ in high-voltage electron microscopes on Ag and Au at 473K as a function of the orientation and on Au as a function of temperature at several fixed orientations.Whereas in Ag minima of Ed are found close to <100>,<110>, and <210> (13-18eV), (Fig.1) atom displacement in Au requires least energy along <100>(15-19eV) (Fig.2). Au is thus the first fcc metal in which the absolute minimum of the threshold energy has been established not to lie in or close to the <110> direction.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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