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.

scholarly journals A Wave-Spectrum Analysis of Urban Population Density: Entropy, Fractal, and Spatial Localization

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Yanguang Chen
Keyword(s):  
Urban Population ◽  
Population Distribution ◽  
Wave Spectrum ◽  
Spatial Dynamics ◽  
Exponential Model ◽  
Urban Morphology ◽  
Wave Number ◽  
Entropy Maximization ◽  
Negative Exponential Model ◽  
Negative Exponential

The method of spectral analysis is employed to research the spatial dynamics of urban population distribution. First of all, the negative exponential model is derived in a new way by using an entropy-maximizing idea. Then an approximate scaling relation between wave number and spectral density is derived by Fourier transform of the negative exponential model. The theoretical results suggest the locality of urban population activities. So the principle of entropy maximization can be utilized to interpret the locality and localization of urban morphology. The wave-spectrum model is applied to the city in the real world, Hangzhou, China, and spectral exponents can give the dimension values of the fractal lines of urban population profiles. The changing trend of the fractal dimension does reflect the localization of urban population growth and diffusion. This research on spatial dynamics of urban evolvement is significant for modeling spatial complexity and simulating spatial complication of city systems by cellular automata.

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.

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.

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.

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.

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