Explaining the Law of Equilibrium in the Gravity Model of Rural-Urban Flows: A Case Study of Bushehr County

Introduction
Development inflation and growth density in some regions of the country, including big cities and provincial centers, have caused regional inequalities. Therefore, knowing the components and effective factors in creating regional balance can manage and control the challenges facing the regional planning system at the national level as well as at the local level. This research seeks to provide a model and structure that can explain and evaluate the law of balance in the Center of Gravity model of rural-urban flows in the direction of regional equilibrium. Therefore, the state of rural-urban linkages is analyzed at the level of the Bushehr district, and the distance vector of the force of each region from the point of view of the Center of gravity, as the spatial vector of rural-urban flows, is analyzed and evaluated. Considering that in the research model, the city and the rural areas under study are considered multi-particle devices, as a result, the Center of Gravity mechanism is applied in such a way that all the elements and components of this model behave in a coordinated manner. When the Center of gravity model calculates the rural-urban flows, the force vectors in different axes and dimensions must be equal to each other so that they can neutralize each other and the condition of balance is established. The meaning of this statement is that the result of the force vector of rural-urban flows in economic, socio-cultural, and infrastructure dimensions in different regions is equal to each other and the final force vector in each of these dimensions is equal to zero. In other words, the areas where the rural-urban flow force vector value is lower than the center of gravity value act as opposite force vectors of the areas where the rural-urban flow value is higher than the center of gravity value.
 
Methodology
According to the purpose, the present research is of an applied type, and according to the nature of the study, it is descriptive-analytical. The study process in this research was based on two documentary-library methods and field surveys based on questionnaires. The questionnaire related to the components and indicators of regional balance in city-rural relations in three economic, socio-cultural, and infrastructural-environmental sectors was completed by official statistics. The method of sampling and obtaining the sample (households living in the studied rural areas) in the present study is a multi-stage random stratified method. In this way, first, according to the size of the population and the distance of the rural areas from the city center, two categories were determined - from 10 to 25 km and from 25 to 40 km - according to the distance from the city center. After classification, appropriate samples of 380 questionnaires, which included 71 items, were assigned to them.
 
Findings
The findings of the research indicated that the internal balance of the rural-urban flows can be explained with great accuracy in such a way that the total value of the vector of the economic flows of the two village groups is equal to (0.89), the result of the socio-cultural flows is equal to (1.26) and the result of the infrastructure flow force vector (4.28). According to the establishment of the law of balance in the three dimensions of the coordinate axes as follows:
 
 
It is clear that the desired function, which is the establishment of the equilibrium condition, is true in the case of the center gravity model. The interpretation of this issue shows that the research model has been able to measure rural-urban flows in economic, social-cultural, and infrastructural-environmental dimensions well. To investigate and analyze these currents, the position of each of the force vectors should be measured relative to the position of the center of gravity. The position of the force vector of rural-urban flows in the villages that are close to the location vector of the center of gravity indicates the lack or reduction of the force vector. In other words, the villages that are far from the location vector of the Center of gravity have a more favorable situation in terms of development because they contain a larger force vector and the location vector of rural-urban flows in such areas is further away from the Center of gravity.
 
Discussion and Conclusion
The results of the research proved that the value of the force vector of rural-urban flows in four villages is lower than that of the Center of gravity and is higher in six other villages. In other words, the force vector of rural-urban flows in some rural areas has a positive flow and some others have a negative flow compared to the location of the center of gravity. To check this issue, the balance law should be used. To determine the state of balance of the force vector of rural-urban flows in rural areas, the state of these vectors was evaluated on three axes (x, y, z). According to the findings of the research as well as the "law of balance"; the balance law formula was measured in three dimensions for economic, social-cultural, and infrastructural-environmental flows in all regions, and its accuracy was determined. So far, many studies have addressed the issue of rural-urban relations in the form of rural-urban flows and linkages, But considering this issue the balance law and the center of gravity model of rural-urban flows are new and, for the first time in this field a result, the views, and opinions of the researchers about it have not been evaluated in the form of a scientific article, so it is enough to say that it is hoped that the current research and especially the Center of gravity model will be used by other researchers soon so that it can be placed in the crucible of scientific criticism and its quality can be determined.