Spatial Aggregation in Gravity Models: 2. One-Dimensional Population Density Models

1982 ◽  
Vol 14 (4) ◽  
pp. 525-553 ◽  
Author(s):  
M Batty ◽  
P K Sikdarfl
Keyword(s):  
Population Density ◽  
Spatial Information ◽  
Interaction Model ◽  
Theoretical Models ◽  
Spatial Aggregation ◽  
Gravity Models ◽  
Model Parameters ◽  
One Dimensional ◽  
Dimensional Interaction ◽  
Population Density Model

This paper, the second of four, is concerned with applying a methodology for analysing the spatial aggregation problem in gravity models outlined in the first paper. The methodology is based on a consistent framework for linking measures of pattern in interaction data to the derivation and estimation of related interaction models using spatial information theory. In this quest, a link is forged between information in data and the parameters of an associated model, and in part 1 it was suggested that if this link could be formalised then a means would be available for predicting changes in model parameters from different aggregations of the data, prior to the actual estimation of the models themselves. This relationship can be formalised for the case of the continuous one-dimensional interaction model such as the population density model, and this paper is concerned with demonstrating such an application to aggregations of zones in the Reading region. The framework is first described and two continuous models are presented. Then, the discrete model is estimated by means both of regression and of entropy techniques applied to various aggregations of the region, and the resulting parameters are related to the predicted and observed informations. Finally, the parameters approximated from observed information by use of the theoretical models are compared with the estimated parameters, and the approximation is deemed good, thus providing some confidence in the general concepts developed to handle these types of problem.

Effects of Spatial System Design on Spatial Interaction Models. 1: The Spatial System Definition Problem

1989 ◽  
Vol 21 (1) ◽  
pp. 27-46 ◽  
Author(s):  
S H Putman ◽  
S-H Chung
Keyword(s):  
Goodness Of Fit ◽  
Spatial Interaction ◽  
Interaction Model ◽  
Spatial Aggregation ◽  
Model Parameters ◽  
Interaction Models ◽  
Spatial Interaction Models ◽  
Aggregation Methods ◽  
Future Paper ◽  
Spatial System

Rather little has been published about systematic empirical research on the problem of spatial aggregation and its effects on spatial interaction models. Of the work which has been published, all of it has dealt almost exclusively with single-parameter spatial interaction models. In this article five different aggregation procedures are examined. The experiments were based on the use of a multivariate multiparametric spatial interaction model. A first set of hypotheses tests was performed with respect to the sensitivity of model parameters to spatial aggregation methods. A second set was performed with respect to the sensitivity of model goodness-of-fit to the five spatial aggregation methods. Although questions remain, the results clearly show that the multiparametric model responds well to different aggregation algorithms. Some parameters showed substantial response, as they should, to different zonal aggregations, whereas others are shown to be much less responsive. Further, the results clearly indicate that systematic aggregation procedures generally produce better results than do random procedures. A future paper will continue with a discussion of zone definition criteria, and recommendations will be made with regard to aggregation algorithms.

SIMULATION OF THE DYNAMICS OF MYXOBACTERIA SWARMS BASED ON A ONE-DIMENSIONAL INTERACTION MODEL

1995 ◽  
Vol 03 (02) ◽  
pp. 579-588 ◽  
Author(s):  
BEATE PFISTNER
Keyword(s):  
Cell Density ◽  
Single Cells ◽  
Interaction Model ◽  
Time Dependent ◽  
One Dimensional ◽  
Front Tracking Method ◽  
Dimensional Interaction ◽  
Differential Integral Equation ◽  
Dependent Model ◽  
High Level

Myxobacteria have a high level of intercellular coordination. Their swarms show “streets” and “whirls” of parallel gliding cells as well as wave-like moving cell density fields, so called “rippling”. The dependence from two phenomenological parameters, gliding velocity and turning frequency, has turned out to be characteristic for cell behavior at the swarm edge. As cells at the swarm edge are mostly gliding parallel in one dimension, the behavior of single cells can be comprised in a one-dimensional model describing interactions between cells of the same species in a homogenous environment, where turning frequency determines the cell density distribution via a hyperbolic differential integral equation. After specifying the parameter functions appearing in the integral, it is examined how these parameters influence the turning behavior and therefore the edge development of swarms over time. Numerical simulations of this model are performed both for the stationary and the time dependent case. For the time dependent model a front tracking method is applied using a Lagrange interpolation at the swarm edge. The simulations show that perception of different gliding directions is significant for the dynamics of swarm expansion and retraction.

scholarly journals The KN Interaction in Higher Partial Waves

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1434
Author(s):  
Albert Feijoo ◽  
Daniel Gazda ◽  
Volodymyr Magas ◽  
Àngels Ramos
Keyword(s):  
Experimental Data ◽  
Cross Sections ◽  
Interaction Model ◽  
Theoretical Models ◽  
Reaction Cross ◽  
Chiral Expansion ◽  
Scattering Data ◽  
Model Parameters ◽  
Partial Waves ◽  
Coupled Channels

We present a chiral K¯N interaction model that has been developed and optimized in order to account for the experimental data of inelastic K¯N reaction channels that open at higher energies. In particular, we study the effect of the higher partial waves, which originate directly from the chiral Lagrangian, as they could supersede the role of high-spin resonances employed in earlier phenomenological models to describe meson-baryon cross sections in the 2 GeV region. We present a detailed derivation of the partial wave amplitudes that emerge from the chiral SU(3) meson-baryon Lagrangian up to the d-waves and next-to-leading order in the chiral expansion. We implement a nonperturbative unitarization in coupled channels and optimize the model parameters to a large pool of experimental data in the relevant energy range where these new contributions are expected to be important. The obtained results are encouraging. They indicate the ability of the chiral higher partial waves to extend the description of the scattering data to higher energies and to account for structures in the reaction cross-sections that cannot be accommodated by theoretical models limited to the s-waves.

Spatial Aggregation in Gravity Models. 1. An Information-Theoretic Framework

1982 ◽  
Vol 14 (3) ◽  
pp. 377-405 ◽  
Author(s):  
M Batty ◽  
P K Sikdar
Keyword(s):  
Spatial Interaction ◽  
Spatial Aggregation ◽  
Gravity Models ◽  
Model Parameters ◽  
Data Sets ◽  
Density Level ◽  
Information Theoretic ◽  
Spatial Interaction Models ◽  
Spatial Entropy ◽  
Information Components

This is the first of four papers concerned with developing a comprehensive approach to the spatial aggregation problem in gravity models. A framework for exploring the problem is outlined in this paper, and will be applied to one-dimensional and two-dimensional spatial interaction models in the subsequent papers. Appropriate statistics for measuring changes in spatial variation due to spatial aggregation in data sets and in model predictions of spatial interaction are derived by use of information theory; and these statistics, such as spatial entropy, have excellent decomposition properties which can be readily exploited in the study of aggregation effects in data and models. These properties involve information components associated with density, level of detail or average zone size, dimension, and level of resolution. Use of the spatial entropy function, in particular, enables consistent relationships to be developed between information components and model parameters, and these relationships are examined in detail in subsequent papers.

Spatial Aggregation in Gravity Models: 4. Generalisations and Large-Scale Applications

1982 ◽  
Vol 14 (6) ◽  
pp. 795-822 ◽  
Author(s):  
M Batty ◽  
P K Sikdar
Keyword(s):  
Large Scale ◽  
Spatial Information ◽  
Spatial Interaction ◽  
Model Performance ◽  
Spatial Aggregation ◽  
Gravity Models ◽  
Future Research ◽  
Data Set ◽  
Four Levels ◽  
Parameter Values

This paper is concerned with applying and extending a methodology for analysing spatial aggregation in gravity models developed in three earlier papers to a larger scale and hence more realistic example of spatial interaction than has been treated so far. Problems of model performance and the analysis of spatial aggregation effects identified in earlier papers are first described, and accordingly the spatial information (entropy) function used previously is then generalised to enable a wider set of models to be applied. Seven models are generated by means of spatial and generalised entropy functions subject to a standard set of model constraints, and the properties of the models in terms of their canonical forms are presented. The models are then applied to four levels of aggregation (234, 121, 58, and 22 zones) of the spatial interaction pattern in Edmonton, Alberta. As in previous papers, information in the data set at the four levels of aggregation is first measured and interpreted, the models are then fitted to these four levels, and relationships between information and parameter values sought. The approximation theory developed earlier is then used to predict parameter values of such models directly from observed spatial information. The results are only fair, better than those of part 3, but worse than those of part 2; although in terms of predicted parameter shift between levels of aggregation, the shifts associated with the doubly constrained model are accurately predicted. The various themes in these papers are then drawn together, conclusions with respect to the value of the insights gained are made, and speculations as to the most fruitful lines for future research outlined.

A Theoretical Analysis of CO2 Absorption in Sun Versus Shade Leaves

1978 ◽  
Vol 100 (1) ◽  
pp. 20-24 ◽  
Author(s):  
R. H. Rand
Keyword(s):  
Experimental Data ◽  
Quantitative Estimate ◽  
Geometric Model ◽  
Model Parameters ◽  
Co2 Absorption ◽  
Temperature Model ◽  
Spongy Mesophyll ◽  
One Dimensional ◽  
Mesophyll Tissue ◽  
Shade Leaves

A one-dimensional, steady-state, constant temperature model of diffusion and absorption of CO2 in the intercellular air spaces of a leaf is presented. The model includes two geometrically distinct regions of the leaf interior, corresponding to palisade and spongy mesophyll tissue, respectively. Sun, shade, and intermediate light leaves are modeled by varying the thicknesses of these two regions. Values of the geometric model parameters are obtained by comparing geometric properties of the model with experimental data of other investigators found from dissection of real leaves. The model provides a quantitative estimate of the extent to which the concentration of gaseous CO2 varies locally within the leaf interior.

scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

scholarly journals Evaluation of the Vertical Producing Degree of Commingled Production via Waterflooding for Multilayer Offshore Heavy Oil Reservoirs

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2428 ◽  
Author(s):  
Fei Shen ◽  
Linsong Cheng ◽  
Qiang Sun ◽  
Shijun Huang
Keyword(s):  
Heavy Oil ◽  
Flow Model ◽  
Dynamic Method ◽  
Theoretical Models ◽  
Oil Reservoirs ◽  
Sweep Efficiency ◽  
One Dimensional ◽  
Heavy Oil Reservoirs ◽  
The Difference ◽  
Important Form

Recently, commingling production has been widely used for the development of offshore heavy oil reservoirs with multilayers. However, the differences between layers in terms of reservoir physical properties, oil properties and pressure have always resulted in interlayer interference, which makes it more difficult to evaluate the producing degree of commingled production. Based on the Buckley–Leverett theory, this paper presents two theoretical models, a one-dimensional linear flow model and a planar radial flow model, for water-flooded multilayer reservoirs. Through the models, this paper establishes a dynamic method to evaluate seepage resistance, sweep efficiency and recovery percent and then conducts an analysis with field data. The result indicates the following: (1) the dynamic difference in seepage resistance is an important form of interlayer interference during the commingled production of an offshore multilayer reservoir; (2) the difference between commingled production and separated production is small within a certain range of permeability ratio or viscosity ratio, but separated production should be adopted when the ratio exceeds a certain value.

Experimental Validation of a Volumetric Planetary Rover Wheel/Soil Interaction Model

2013 ◽  
Author(s):  
Willem Petersen ◽  
John McPhee
Keyword(s):  
Contact Force ◽  
Interaction Model ◽  
Contact Model ◽  
Soil Parameters ◽  
Model Parameters ◽  
Force Model ◽  
Normal Contact ◽  
Planetary Rover ◽  
Normal Contact Force ◽  
Contact Force Model

For the multibody simulation of planetary rover operations, a wheel-soil contact model is necessary to represent the forces and moments between the tire and the soft soil. A novel nonlinear contact modelling approach based on the properties of the hypervolume of interpenetration is validated in this paper. This normal contact force model is based on the Winkler foundation model with nonlinear spring properties. To fully define the proposed normal contact force model for this application, seven parameters are required. Besides the geometry parameters that can be easily measured, three soil parameters representing the hyperelastic and plastic properties of the soil have to be identified. Since it is very difficult to directly measure the latter set of soil parameters, they are identified by comparing computer simulations with experimental results of drawbar pull tests performed under different slip conditions on the Juno rover of the Canadian Space Agency (CSA). A multibody dynamics model of the Juno rover including the new wheel/soil interaction model was developed and simulated in MapleSim. To identify the wheel/soil contact model parameters, the cost function of the model residuals of the kinematic data is minimized. The volumetric contact model is then tested by using the identified contact model parameters in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain and compared against experiments.

scholarly journals Resource-Driven Encounters and the Induction of Disease Among Consumers

2016 ◽  
Author(s):  
Rebecca K. Borchering ◽  
Steve E. Bellan ◽  
Jason M. Flynn ◽  
Juliet R.C. Pulliam ◽  
Scott A. McKinley
Keyword(s):  
National Park ◽  
Interaction Model ◽  
Spatially Explicit ◽  
Encounter Rate ◽  
Model Parameters ◽  
Expected Number ◽  
Spatially Explicit Model ◽  
Consumer Population ◽  
Using Data ◽  
The Relationship

AbstractSubmitted Manuscript 2016. Territorial animals share a variety of common resources, which can be a major driver of conspecific encounter rates. We examine how changes in resource availability influence the rate of encounters among individuals in a consumer population by implementing a spatially explicit model for resource visitation behavior by consumers. Using data from 2009 and 2010 in Etosha National Park, we verify our model's prediction that there is a saturation effect in the expected number of jackals that visit a given carcass site as carcasses become abundant. However, this does not directly imply that the overall resource-driven encounter rate among jackals decreases. This is because the increase in available carcasses is accompanied by an increase in the number of jackals that detect and potentially visit carcasses. Using simulations and mathematical analysis of our consumer-resource interaction model, we characterize key features of the relationship between resource-driven encounter rate and model parameters. These results are used to investigate a standing hypothesis that the outbreak of a fatal disease among zebras can potentially lead to an outbreak of an entirely different disease in the jackal population, a process we refer to as indirect induction of disease.

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