Accuracy of equations describing diameter growth

1989 ◽  
Vol 19 (10) ◽  
pp. 1283-1286 ◽  
Author(s):  
Boris Zeide
Keyword(s):  
Power Function ◽  
Exponential Function ◽  
Diameter Growth ◽  
Negative Exponential Function ◽  
Growth Decline ◽  
Growth Equations ◽  
Negative Exponential

The investigation of the structure of growth equations shows that most of them describe the growth decline by a negative exponential function. This decline can also be described by a power function. It was found that the equation based on this assumption is the best available model of diameter growth. Some applications of this equation are discussed.

scholarly journals Response to fertilizer nitrogen and water of post-rainy season sorghum on a Vertisol. 2. Biomass and water extraction

1998 ◽  
Vol 131 (4) ◽  
pp. 429-438 ◽  
Author(s):  
PIARA SINGH ◽  
J. L. MONTEITH ◽  
K. K. LEE ◽  
T. J. REGO ◽  
S. P. WANI
Keyword(s):  
Water Content ◽  
Exponential Function ◽  
Root Length ◽  
Dry Matter ◽  
Root Length Density ◽  
Vapour Pressure Deficit ◽  
Negative Exponential Function ◽  
Neutron Probe ◽  
Negative Exponential ◽  
N Rates

During rainless weather following a monsoon, sorghum (Sorghum bicolor cv. SPH–280) was grown on a Vertisol either unirrigated throughout growth or irrigated for 7 weeks after emergence and rainfed thereafter. Before sowing, ammonium sulphate was applied at six rates from 0 to 150 kg/ha N. Roots were sampled every 2 weeks to determine biomass and root length density as a function of depth. Every week, soil water content in all treatments was measured gravimetrically to a depth of 0·23 m and with a neutron probe from 0·3 to 1·5 m.Below 0·45 m, volumetric water content was a negative exponential function of time after roots arrived and the maximum depth of extraction moved downwards at 2–5 cm per day. In the dry treatment, the extraction ‘front’ lagged behind the deepest roots by c. 12 days initially but the two fronts eventually converged. Irrigation delayed the descent of the extraction front by c. 20 days but thereafter it appeared to descend faster than without irrigation. Averaged over N rates, the time constant of the exponential function was inversely related to the root length density, lv, decreasing with depth from about 20 to 10 days as lv increased from 2·5 to 4·0 km/m3.The biomass[ratio ]water ratio was almost independent of N but increased from a mean of 5·3 g dry matter per kg water in the dry treatments to 6·9 g/kg with irrigation. When normalized by the seasonal mean difference in vapour pressure deficit within irrigated and unirrigated plots, the ratios were 13·1 and 13·3 kPa g per kg water, respectively.

Waveforms and velocities for non-nearest-neighbour contact distributions

1979 ◽  
Vol 16 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Exponential Function ◽  
The Other ◽  
Nearest Neighbour ◽  
Negative Exponential Function ◽  
Specific Contact ◽  
Negative Exponential

This paper examines a model for ecological and epidemiological spread. Expressions are derived for mean waveforms and expectation velocities for two specific contact distributions. Whilst one distribution may be bounded above by a negative exponential function the other may not, and these two situations respectively give rise to finite and infinite asymptotic expectation velocities.

scholarly journals A New Mathematical Approach for the Estimation of epidemic Model Parameters with Demonstration on COVID-19 Pandemic in Libya

2020 ◽  
Author(s):  
Mohamed E Saleh ◽  
Zeinab Elmehdi Saleh
Keyword(s):  
Exponential Function ◽  
Epidemic Model ◽  
Model Parameters ◽  
Cumulative Number ◽  
Epidemic Spread ◽  
Exponential Distributions ◽  
Negative Exponential Function ◽  
Seir Model ◽  
Start Date ◽  
Negative Exponential

Background: The SEIR model or a variation of it is commonly used to study epidemic spread and make predictions on how it evolves. It is used to guide officials in their response to an epidemic. This research demonstrates an effective and simple approach that estimates the parameters of any variations of the SEIR model. This new technique will be demonstrated on the spread of COVID-19 in Libya. Methods: A five compartmental epidemic model is used to model the COVID-19 pandemic in Libya. Two sets of data are needed to evaluate the model parameters, the cumulative number of symptomatic cases and the total number of active cases. This data along with the assumption that the cumulative number of symptomatic cases grows exponentially, to determine most of the model parameters. Results: Libya epidemic start-date was estimated as t_o=-18.5 days, corresponding to May 5th. We mathematically demonstrated that the number of active cases follows two competing exponential distributions: a positive exponential function, measuring how many new cases are added, and a negative exponential function, measuring how many cases recovered. From this distribution we showed that the average recovery time is 48 days, and the incubation period is 15.2 days. Finally, the productive number was estimated as R0 = 7.6. Conclusions: With only the cumulative number of cases and the total number of active cases of COVID19, several important SEIR model parameters can be measured effectively. This approach can be applied for any infectious disease epidemic anywhere in the world.

Waveforms and velocities for non-nearest-neighbour contact distributions

1979 ◽  
Vol 16 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Eric Renshaw
Keyword(s):  
Exponential Function ◽  
The Other ◽  
Nearest Neighbour ◽  
Negative Exponential Function ◽  
Specific Contact ◽  
Negative Exponential

This paper examines a model for ecological and epidemiological spread. Expressions are derived for mean waveforms and expectation velocities for two specific contact distributions. Whilst one distribution may be bounded above by a negative exponential function the other may not, and these two situations respectively give rise to finite and infinite asymptotic expectation velocities.

Calculating Thornthwaite and Mather's actual evapotranspiration using an approximating function

1984 ◽  
Vol 14 (3) ◽  
pp. 466-467 ◽  
Author(s):  
J. Pastor ◽  
W. M. Post
Keyword(s):  
Soil Water ◽  
Exponential Function ◽  
Water Loss ◽  
Water Storage ◽  
Field Capacity ◽  
Actual Evapotranspiration ◽  
Soil Water Storage ◽  
Negative Exponential Function ◽  
Negative Exponential

A simple negative exponential function is presented which relates soil water storage to a maximum storage value (field capacity) and accumulated potential water loss. This formula summarizes 10 tables from Thornthwaite and Mather (Publications in Climatology, 10: 183–311, 1957) needed to calculate actual evapotranspiration (AET). Comparisons are presented for values predicted by this formula and Thornthwaite and Mather's tabulated values.

Sense of Effort and the Effects of Fatigue in the Tongue and Hand

1996 ◽  
Vol 39 (1) ◽  
pp. 114-125 ◽  
Author(s):  
Nancy Pearl Solomon ◽  
Donald A. Robin ◽  
Sara I. Mitchinson ◽  
Douglas J. VanDaele ◽  
Erich S. Luschei
Keyword(s):  
Exponential Function ◽  
Pressure Transducer ◽  
Central Fatigue ◽  
Negative Exponential Function ◽  
Effort Level ◽  
Before And After ◽  
Negative Exponential ◽  
Disordered Speech ◽  
Over Time ◽  
Meaningful Measure

Fatigue and increased effort are common symptoms for people with movement disorders and dysarthria, but they are rarely quantified. In an attempt to develop a clinically useful and physiologically meaningful measure of fatigue, we used a task that involves sustaining a target effort level without visual feedback while squeezing a bulb connected to a pressure transducer. In the first experiment, 12 healthy young adults performed the constant-effort task with the tongue and the preferred hand at 3 submaximal levels of effort. The resulting pressure declined over time as a negative exponential function with a nonzero asymptote. In the second experiment, 6 subjects performed the constant-effort task before and after acutely fatiguing the tongue and hand. The rate of pressure decline was significantly greater after fatigue. One possible mechanism for the characteristic negative exponential function is that It reflects a constant descending drive from higher centers in the CNS to the appropriate motoneuron pools. Thus, this technique may elucidate the contribution of central fatigue to normal and disordered speech.

Physical modeling of the full acoustic waveform in a fractured, fluid‐filled borehole

Geophysics ◽  
1988 ◽  
Vol 53 (9) ◽  
pp. 1219-1224
Author(s):  
Petko Zlatev ◽  
Eileen Poeter ◽  
Jerry Higgins
Keyword(s):  
Exponential Function ◽  
Physical Modeling ◽  
Wave Amplitude ◽  
Crystalline Rock ◽  
Wave Mode ◽  
Fracture Aperture ◽  
Negative Exponential Function ◽  
Tube Wave ◽  
Fracture Apertures ◽  
Negative Exponential

Three concrete models were constructed, one each with a fracture oriented at 90, 45, and 10 degrees to the axis of the borehole. These were used to simulate physically the propagation of the full acoustic waveform through a fluid‐filled borehole in crystalline rock and to ascertain the effects of fracture aperture and orientation of fluid‐filled fractures on the waveform. The tube‐wave mode of the waveform was most indicative of the magnitude of fracture aperture. Normalized tube‐wave amplitude decreased as a negative exponential function of aperture over the range of fracture apertures studied (closed to 0.66 cm). The 90 degree fracture orientation caused greater tube‐wave amplitude reduction than the 45 degree fracture. We hypothesize that this reduction can be attributed to the borehole wall’s guiding the wave across the 45 degree fracture. However, the 10 degree model gave ambiguous results, which are believed to be related to the low ratio of tube‐wave wavelength to aperture as measured parallel to the borehole axis, i.e., axial aperture.

scholarly journals Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou, China: 1964–2010

2021 ◽  
Vol 13 (2) ◽  
pp. 463
Author(s):  
Jian Feng ◽  
Yanguang Chen
Keyword(s):  
Exponential Function ◽  
Urban Growth ◽  
Spatial Information ◽  
Population Distribution ◽  
Spatial Dynamics ◽  
Exponential Model ◽  
Model Parameters ◽  
Urban Density ◽  
Negative Exponential Function ◽  
Negative Exponential

Urban population density provides a good perspective for understanding urban growth and socio-spatial dynamics. Based on sub-district data of the five national censuses in 1964, 1982, 1990, 2000, and 2010, this paper is devoted to analyzing of urban growth and the spatial restructuring of the population in the city of Hangzhou, China. Research methods are based on mathematical modeling and field investigation. The modeling result shows that the negative exponential function and the power-exponential function can be well fitted to Hangzhou’s observational data of urban density. The negative exponential model reflects the expected state, while the power-exponential model reflects the real state of urban density distribution. The parameters of these models are linearly correlated to the spatial information entropy of population distribution. The fact that the density gradient in the negative exponential function flattened in the 1990s and 2000s is closely related to the development of suburbanization. In terms of investigation materials and the changing trend of model parameters, we can reveal the spatio-temporal features of Hangzhou’s urban growth. The main conclusions can be reached as follows. The policy of reformation and opening-up and the establishment of a market economy improved the development mode of Hangzhou. As long as a city has a good social and economic environment, it will automatically tend to the optimal state through self-organization.

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