|12. Migration, Gender, and Labor Force in Hubei Province, 1985–1990|
|图书名称：Re-Drawing Boundaries: Work, Households, and Gender in China|
图书作者：Barbara Entwisle and Gail E. Henderson ISBN：
出版社：Berkeley: University of California Press 出版日期：2000年
Sidney Goldstein, Zai Liang, and Alice Goldstein
Although China has a policy of gender equality inscribed in its constitution (People's Republic of China, Quanguo Renmin Daibiao Dahui 1983, 27), in reality women's roles often continue to be circumscribed by traditional patriarchal norms (Emerson 1982; Parish 1984b). This situation is reinforced if women move under strict family auspices (e.g., marriage migration to join a husband's family) or if their movement is in connection with job assignments that perpetuate gender differences in the workplace (see Tinker 1990). On the other hand, migration may provide a vehicle for change that allows women to break out of traditional family controls and achieve some economic independence (Rodenburg 1993, 282–83). This may be especially true for women who, as short-term and unofficial migrants, are separated from families and enter into situations of relative autonomy (see also chap. 10).
While increased spatial mobility for women and men has thus become an important aspect of the transition from a socialist to a market economy in China, limited opportunities have been available to assess who moves, what kind of mobility is chosen, and what the impact is on origin and destination. Particularly important is the question of how men and women differ in their participation in official, permanent migration and unofficial, temporary movement with respect to volume of mobility and socio-demographic and economic characteristics. The situation for China is not unlike that for many other developing countries, especially as it relates to the study of female migration (Bilsborrow 1993; Pedraza 1991).
Our analyses attempt to gain insights into these relations. Data from China's 1990 census and from a migration survey conducted in Hubei province in 1988 are used in complementary fashion to assess the inter relations among migrations, gender, and labor force patterns in the period of transition from a command to a market economy. The census analysis begins with an overview of how men and women differ in their rates and direction of migration between rural and urban places, with major emphasis on how these patterns differ between men and women who move as official migrants and those who move unofficially (defined later). The reasons for movement associated with the two types of migration are also explored. The gender/migration status groups are further compared in terms of their socioeconomic differentials, including age, labor force status, and occupation, and by rural-urban migration streams. The Hubei survey is also used to gain fuller understanding of the differing adjustments of official and temporary movers (defined later) at their destination and the possible factors involved in their attitudes.
SOURCES OF DATA
The 1990 census was the first to include questions on migration. For all persons living in a given location for more than one year, and for those who lived there less than one year and had officially changed their registration, the census ascertained whether they lived in a different county or city five years earlier. Among those identified as migrants in this way, distinction is possible between those who have changed their official registration to current residence (official migrants) and those who have not made such a change, but who have been away from their official place of residence for at least a year (unofficial migrants). Much of our analysis focuses on these unofficial migrants. The 1990 census does not include at their current place of residence persons who have been away from their place of registration for less than one year, unless they have officially changed their registration. Such short-term migrants are counted as residents where they are registered. Thus, census data provide an incomplete picture of the overall “temporary” migrant population, which includes all migrants living in a location who are not registered there.
Surveys in several cities of China have indicated that a high proportion of temporary migrants have been resident there for less than a year. In Shanghai, for example, in 1984, only half of the temporary migrants had lived in the municipality for a year or more; of those who came specifically to seek work, some 71 percent had been there for less than a year (unpublished-tabulations of the Shanghai Temporary Migration Survey, Brown University 1986). The Beijing Survey of Temporary Migrants of 1985 showed similar patterns: Of the temporary migrants who came to Beijing to work or live, only 40 percent had been living there for a year or more (unpublished tabulations, Brown University 1986).
The volume of temporary migrants identified by the census is therefore an undercount, making it impossible to obtain a full profile of the socioeconomic characteristics of temporary migrants with census data. Within the constraints of the census definitions, our analysis distinguishes among nonmigrants, official migrants, and unofficial migrants. We focus mainly on those aged 15–59, the age range largely encompassing those still in or eligible to participate in the labor force, reflecting the fact that in China women retire in their 50s and men in their 60s. To fully distinguish types of migrants and their characteristics, survey data are necessary. The 1988 Survey of Migration, Fertility, and Economic Change in Hubei Province provides some of the needed information. It encompassed 4,070 households containing 18,178 individuals living in cities (including the provincial capital), towns, and villages in three regions of the province. Its temporal proximity to the 1990 census facilitates integrated use with the census data. Located in central China, Hubei's population size and level of development place it among the top third of all provinces; its considerable mix of industrial and agricultural production make developments there sensitive to those occurring in the country as a whole as part of the transition to a market economy (see chap. 2, table 2.1).
Like the census, the survey identified as an official migrant anyone who had changed the location of the household registration. Unlike the census, however, the survey identified as temporary migrants anyone who was living away from place of registration, regardless of the length of time since the move or whether a county boundary had been crossed. Anyone changing village, town, or city of residence was identified as a migrant. To clarify this important difference between the census and the survey, and to facilitate comparisons with patterns in other provinces (e.g., chap. 11), we will distinguish between census counts of “unofficial migrants,” who have lived in the destination for more than a year or been away from place of registration for at least that long, and survey data on “temporary migrants,” who have lived in the destination for short as well as long periods of time.
Better coverage of short-term and short-distance migration is provided by the survey. Coverage is not complete, however. The survey did not sample persons living in group quarters. Those official migrants who moved to enroll in higher education programs and live in dormitories are therefore not included, nor are the relatively small number of people living in group quarters provided by state enterprises.
One other limitation of the survey should be noted. Since the survey used purposive sampling to ensure adequate numbers of official and temporary migrants, it does not provide weights to allow the relative approximation of each migration status category in the province. The survey therefore does not lend itself to estimation of the relative size of the various migrant categories within the total population.
MIGRATION IN HUBEI
As shown in Table 12.1, the 1990 census indicates that of the total Hubei population aged 15–59, 2.6 percent had moved there since 1985 as official migrants and 1.5 percent as unofficial migrants. This pattern held for both men and women, although slightly more men than women were migrants. Women constituted 48 percent of the province's entire population age 15–59, but they made up fewer of both migrant groups—44 percent of the official migrants and 43 percent of the unofficial movers. In Hubei's adult population as a whole, women engaged in unofficial movement to about the same extent as in officially sanctioned migration, although in both cases they did so somewhat less than men. The two types of migration together approximate the kind of movement that would be expected in a situation of uncontrolled mobility, although, as mentioned, census data exclude shortterm migrants.
Provincial and Regional Migration Streams
Of the official and unofficial migrants living in Hubei in 1990, most had moved within the province, indicating the importance of short-distance migration. This was especially true for women (data not shown). Some 70 percent of male official migrants and 55 percent of male unofficial migrants had moved intraprovincially, compared to 74 percent of the female official migrants and 80 percent of the female unofficial migrants. The higher proportion of women moving shorter distances stems in part from the greater constraints on women's activities and in part from the greater importance of marriage in female migration.
Rural-Urban Migration Streams
The heavy movement to Hubei's cities and towns by men and women is evidenced by comparison of the 1990 type of residence of the two migrant
This pattern especially characterizes migrants originating in rural areas. Among males, a higher percentage of official than unofficial rural-origin migrants moved to cities, but among females twice as high a proportion of rural-origin unofficial migrants as official migrants went to cities. The relative differences were as sharp for those going from villages to towns. By contrast, only 9 percent of female unofficial migrants from villages moved to other villages, compared to 52 percent of the official migrants. Marriage migration is a key explanatory factor: whereas it can lead to a change in permanent residence status for rural-to-rural migrants, it does not provide a legal basis for change to permanent residence in cities for those leaving rural
The data suggest that unofficial migration complements and substitutes for official migration. This interpretation is supported by the evidence on migration streams (Table 12.3). As mentioned, a majority of men and women moving from villages to cities and towns are temporary migrants. The importance of this migration stream is underscored when compared with the much smaller proportion of male and female intraurban migrants who are temporary movers. Migrants between urban locations have less need to rely on temporary movement because persons with urban registration can move more easily to another urban location. The desirability of urban locations also explains why such a high percentage of men moving to villages from cities and towns are temporary movers. Women are not characterized by the same pattern (very few are temporary migrants going from cities to villages) because they are much less likely than men to be assigned jobs in villages in connection with rural development (cf. S. Goldstein and A. Goldstein 1991).
Census Compared to Survey
As we have pointed out, the census definitions of official and unofficial migration are circumscribed temporally and spatially. Some insights into the impact of definition is provided by data from the Hubei survey (data not in table). For men and women, it shows (1) a higher percentage of temporary movement between cities and (2) a much higher proportion of movement between towns and from villages to towns among permanent and temporary migrants of both genders. However, the gender differentials identified by the census data are consistent with the differentials apparent from the survey.
In examining patterns of official migration, for example, according to the survey, 57 percent of city-origin male official migrants went to other cities, whereas this was true of 66 percent according to the census. For females, the comparable percentages are 70 and 80. Even greater discrepancies characterize movement from towns and villages to cities, showing the impact that enrollment in programs of higher education has on official migration rates to cities. In sharp contrast, the survey data show movement to towns to be substantially higher among city-origin official migrants.
When temporary migration is considered, the survey shows much higher percentages than the census for moving between cities for both men and women. Many of these persons may have moved for less than a year in connection with a business venture or to visit relatives. The survey also shows that half of the movement from towns is to other towns among both men and women, whereas the census identified much higher levels of towncity movement. Again, much of the temporary movement captured in the survey may be intracounty and of relatively short duration and therefore not identified by the census.
Finally, the survey showed much higher rates of rural-rural temporary migration than the census. Whereas the census levels for men were 14 percent and for women only 9 percent, the survey found that among temporary migrants about 40 percent each of the men and women moved between rural places. Many men participated in rural industrialization efforts, bringing skills with them that were unavailable at their destination. Women were more likely to move in connection with marriage and simply not change their registration at the time. In both cases, moves were likely to have been within the same county and thus measured in the survey but not defined as migration by the census.
REASONS FOR MIGR ATION
The reasons for migration recorded by the census vary between official and unofficial migrants as well as between men and women in Hubei. Among males, one-third of the official migrants but only a small percentage (4%) of the unofficial movers changed location because of job relocation or assignment. An official residence change was even more common in conjunction with schooling or training (46%), but exceedingly rare among male unofficial migrants (?1%). Among male unofficial migrants, by far the largest number (79%) moved because of business, which for most probably meant trying to take advantage of the new economic opportunities in sales and service work outside government-owned enterprises. Only 3 percent of official migrants gave business as a reason for their move. Marriage or other family reasons accounted for 12 percent of the moves made by male official migrants, 9 percent of male unofficial migrants.
Many fewer female than male official migrants moved in conjunction with job relocation or assignment—only 11 percent. Only 2 percent of female unofficial migrants moved for this reason. Women apparently are selected less often than men for official relocation in conjunction with work. In large part, this pattern reflects China's policy of moving children with their mother and the consequent reluctance to relocate women who are likely to bring children along and thereby add to urban growth and demands on urban infrastructure. Far more female official migrants(28%) moved in connection with schooling than for economic reasons, but their proportion was well below that of men (46%). Hardly any female unofficial movers gave education as a reason for migration, which was also true for male temporary migration. Like men, female unofficial migrants most frequently cited business as their reason for moving, although the 54 percent who did so was well below the 79 percent for men. Female unofficial migrants were much more likely than males to cite marriage and other family reasons for migration. Because legal restrictions of ten preclude family reasons as a justification for official change in registration, many women may rely on temporary movement as a way of maintaining or achieving family residential unity. Results of the Hubei survey strongly corroborate the census findings.
DIFFERENTIAL CHAR ACTERISTICS BY MIGR ATION STATUS
The impact of migration on origin and destination varies not only by number of migrants but also by the degree of selectivity selected on demographic and socioeconomic characteristics. Such selectivity may operate differently for official and unofficial migrants. The analysis be low uses census data to focus on gender, age, labor for cestatus, and occupation differentials in Hubei.
Male and female migrants are younger than nonmigrants. Official migrants are disproportionately concentrated in the youngest age group (15–24). Many are students or just initiating their careers through government assignments. Women in this age group migrate in connection with marriage as well. The age distributions are quite similar for males and females who are official migrants. Among unofficial migrants, however, women are more concentrated than the men in the youngest group, possibly because this movement is more likely to occur before marriage. These young women may take up activities like child care and housekeeping for pay, or even jobs in the industrial sector (e.g., textiles or electronics) as a way to enhance the skills that make them more marriageable, allow them to send remittances to their family, or help them save money for a dowry (chap. 10). Married and older women are more tied to their place of residence by family duties, and by additional economic responsibilities when their husbands have moved away temporarily. As temporary migrants, married women are more likely to engage in market or other activities that allow regular return to place of origin; they would thus be less likely to be identified as migrants under the census definitions.
Differences in Labor Force Status and Occupation
The labor force status of persons age 15–59 differs considerably by migration status, official or not, again reflecting in part the legal restrictions on permanent changes in registration in China. More than nine in ten male nonmigrants and almost as many female nonmigrants are employed. Male unofficial movers are even more concentrated in the labor force because so much of their movement is economically motivated. A much lower proportion of the female unofficial migrants are labor force participants. Marriage and accompanying a spouse explain the considerable number engaged as homemakers, although it may be that this work is just not visible (see chaps. 2 and 10). Official migrants provide a strikingly different profile. Just half of the men and four in ten of the women are in the labor force.
Among men, regardless of migration status, all but a small number of those not in the labor force are students in technical schools or universities. Nevertheless, the proportion of students among official migrants is sharply higher than among nonmigrants and unofficial migrants. Enrolling in higher education is clearly a major mechanism for obtaining a change in registration. For women, too, students account for almost all of those not in the labor force. The small proportion who are homemakers indicates the high level of labor force participation among women in China and also suggests that official migration for marriage and family factors does not lead to withdrawal from the labor force.
For those in the labor force, legal constraints on changing registration from rural to urban help explain occupational differences among migration types (Table 12.4). Large percentages of male government officials and
The Multiple Determinants of Migration Status
Several multinomial regression models were estimated to evaluate the differential importance of age, gender, education, current residence, and occupation on the likelihood of becoming an official or temporary migrant. We include education in the model, even though it is not discussed in our analysis of characteristics, because previous research has shown sharp educational differences between men and women and among migration categories (A. Goldstein, S. Goldstein, and Gu 1993). We limit the analysis to those aged 18–59 in the labor force to focus on migrants who are economically active. Note that doing so excludes some students, who made up a substantial fraction of these official migrants. Table 12.5 presents the results separately, comparing official migrants with nonmigrants (column 1), unofficial migrants with nonmigrants (column 2), and unofficial with official migrants (column 3).
Age has a strong effect on official and unofficial migration, with younger persons more likely to be migrants than older individuals. In addition, other things being equal, younger people are more likely to be unofficial than official migrants. Education has a positive effect on being an official migrant, but a negative effect on unofficial migration. Those with higher education, especially university education, are more likely to be official than unofficial migrants. These findings document the impact of government policies with respect to the transfer of skilled persons.
Surprisingly, when other variables such as education are controlled, men are less likely than women to be official migrants compared to nonmigrants; men are much more likely to be unofficial migrants than either official ones or nonmigrants. This suggests that gender roles play an important part in determining who becomes an unofficial migrant. The high level of female migration in relation to marriage also helps explain the relatively small gender differences in official migration once socio-demographic variables are controlled. The strong probability of being an unofficial rather than an official migrant in urban places indicates the effectiveness of government policy in controlling official migration to cities and the great attraction of urban places to those who move in response to economic opportunities but without a change in household registration.
Compared to those in agriculture, persons in every occupational category are more likely to be either official or unofficial migrants than nonmigrants,
Because of the complexity of the interplay between type of move, place of residence, and gender, we also specified a series of models that controlled separately for gender and current residence (available on request from authors). In general, these data confirm the patterns suggested by our analysis presented in Table 12.5. Life-cycle or life-stage effects and government policy have a strong impact on women; they are likely to be official migrants in rural locations at those ages associated with marriage, but in urban places also more likely than men to be unofficial as opposed to official migrants. Higher levels of education are directly related to obtaining a change in household registration for men and women in all locations. Therefore, increasing the education of women would clearly enhance their status. As more women obtain higher levels of education, they are more likely to migrate to take advantage of opportunities in urban places.
These logistic regressions using 1990 census data for Hubei present results similar to those obtained from a multinomial logistic model using the Hubei survey (A. Goldstein, S. Goldstein and Gu 1993). The major differences are the higher likelihoods of mobility indicated for temporary migrants who are sales/service/other workers in the Hubei survey. Since this occupational category especially encompasses migrants who have been at their destination for less than one year, the discrepancy in findings can be attributed at least in part to the differential coverage of our two datasources. It underscores the importance of considering short-term migration in any assessment of temporary mobility, since such migration is particularly selective of persons in the tertiary sector.
BEYOND THE CENSUS: ISSUES OF ADJUSTMENT
While the census provides valuable information on levels and streams of movement and on the characteristics of migrants, it does not enable the researcher to obtain any insights on a variety of issues pertaining to migrant adjustment. For such purposes we turn to the 1988 Hubei survey. Several questions in the survey dealt with the networks that the official and temporary migrants used for acquiring information and support at their destination; other questions ascertained migrants' relative satisfaction with their new circumstances. Such areas of inquiry may be especially important in analysis of gender differences among migrants. A brief review of the survey findings follows.
Networks are a central feature of life in China; for persons planning a move they may be especially useful as sources of information about opportunities and as support once the move has been made. For official migrants, formal agencies, including employers, were instrumental in providing information for many (60–80%) of the men and women moving to cities. However, because so many women moving to towns and especially to rural areas did so in connection with marriage, agencies were less important sources of information for these migrants. Friends and relatives were sources of information in a minority of cases, regardless of gender or residence, although ruralward migrants tended to rely on them somewhat more than others.
Men and women migrating temporarily to cities and towns were much more likely to turn to relatives or friends. Many temporary migrants, especially men, simply moved to establish their own business. Strikingly, one in four of the temporary migrant women to cities also moved in connection with their own business. Since temporary migrants moved outside the official channels, it is not surprising that they also did not use formal connections for finding work. Only in towns, where government policy has encouraged temporary movement, did some 30–40 percent of the temporary migrant men and women use agencies. Those moving to rural places used a variety of sources to obtain information.
Because so many official migrants move to urban places under state auspices, only one-quarter had friends or relatives at their destination. The percentage was even lower for women in rural places because so many moved for marriage. The temporary migrants form a sharp contrast to official migrants—those moving to cities had an especially high level (some, 60%) of connections and half or more of these provided help in obtaining jobs and housing. Women were especially likely to receive help with obtaining jobs and housing, perhaps because many became temporary migrants to take positions as household workers in cities. Temporary migrants to towns and rural areas had fewer contacts and received less help. In part this is because they maintain closer ties to their places of origin; this is again partly due to the high percentage of women who move in connection with marriage.
A large majority (70–80%) of official and temporary migrants—both men and women—reported that they experienced some difficulties in adjusting to their new place of residence. In general, men were more likely to indicate economic problems while women were more likely to cite cultural problems. Economic problems were most pronounced among temporary migrants who had gone to cities.
Despite these problems, some 80 percent of the migrants indicated that they were better off in their new place of residence than their origin. Among official migrants, this was most true of men; among unofficial temporary migrants, more women indicated satisfaction with the move. A regression analysis (not shown) taking into account a large variety of factors explored the determinants of levels of satisfaction with the destination. While occupational skills and economic opportunities, as well as level of development at the destination and type of migration, all contributed to whether an individual was satisfied with the change of residence, other important considerations seem to be expectations about living conditions and how the move affected the traditional roles of women. For example, those women who moved as temporary migrants to engage in their own business and who received relatively little help from friends or relatives expressed greater levels of satisfaction than others who had more help or moved in connection with marriage.
Both men and women had their expectations raised by the economic changes of the 1980s and the perceived opportunities for many of them in cities. However, reality often failed to meet their expectations. Moreover, women are still discriminated against in many areas of the job market, and cultural norms continue to restrict their career options. As a result, women's mobility (especially temporary movement) does not result in the kinds of advancement that many of them had anticipated, and their levels of satisfaction are therefore lower than might be expected. Nonetheless, in those areas where women are able to exercise some degree of autonomy (for example, as temporary migrants who come to urban places independently and engage in market activities), satisfaction appears to be higher.
Economic reforms instituted in China since 1978, first in rural areas and then in urban locations, unleashed massive population flows. But because of the nation's continued policy of strictly limiting migration to cities, much of the mobility of the 1980s was outside the official system. The consequences are both positive and negative. Unofficial migration has allowed development of a much needed tertiary sector, and it has been responsible for a significant shift from agricultural to nonagricultural employment (S. J. Wang 1995). It has also been instrumental in the growth of Special Economic Zones and their joint-venture enterprises (Zai Liang 1996). On the negative side, temporary migration has placed great strains on the infrastructure of many cities. Beijing and Shanghai, for example, were each estimated to have one million temporary migrants in residence in 1988; the numbers have risen substantially since then (China Daily 1988b; Roberts and Wei 1996). Temporary migrants are also thought to cause a variety of social problems.
One area of particular concern is the effect of migration on the lives of the migrants, and particularly on the women. Because many women move by themselves, their dislocation from familiar support networks of family and friends, their employment in enterprises and households that provide no benefits, and their vulnerability to exploitation may all have serious detrimental consequences for the migrants (Peng Xizhe 1995). Women's own assessment of their situation may be quite different, however: many believe that migration has enabled them to benefit from the economic changes and that it has provided them with a degree of autonomy that was not possible at their place of origin (see also chap. 10).
Many of these conclusions remain speculative because few data have been available, especially on a large scale, either to provide a socio-demographic profile of the men and women who are temporary migrants in comparison to official migrants or nonmigrants, or to determine their own assessment of their circumstances. The 1990 census was the first in China to include questions on migration, and we have used those data to analyze levels and streams of migration in Hubei province and to delineate some of the characteristics of the various migrant types. Census coverage is, however, not as comprehensive as desirable because intracounty moves and temporary migration of less than a year's duration are not defined as migration. We therefore supplemented the census data with the fuller coverage provided by the 1988 Hubei survey.
Movement in China is clearly and strongly from rural to urban places. Official and unofficial migrants participate in these streams. Women, however, tend to moves horter distances. They apparently continue to have more constraints on their mobility than men, and a substantial fraction move in connection with marriage. Nonetheless, many women are economic migrants, moving from rural to urban areas to take advantage of the economic opportunities available in cities and towns.
Overall, the census and survey data suggest that temporary migration is a way for women to participate in the economic changes taking place in China. That the survey suggests this even more strongly than the census partly reflects the survey's fuller coverage of temporary migrants. For a variety of reasons—many related to government policy, some to culture— women are more tied to their places of origin than are men. The household registration system was a powerful means of perpetuating this situation. With the breakdown of the constraints inherent in the system, however, women have become increasingly mobile, using temporary migration as their vehicle for change. Moreover, those women who were able to take advantage of the new urban opportunities believe that their way of life has improved.
China has continued its rapid development into the 1990s, and despite occasional controls, temporary migrants are generally allowed to move freely. In the process, temporary migration has come to serve as a supplement and complement to official migration. As a result, migration patterns in China are increasingly similar to those of other developing nations. Whether China is able to avoid many of the negative consequences of rapid population redistribution, and especially of the unchecked growth of large cities, remains to be seen. Another open question is what kind of impact the economic and demographic changes that accompany development will have on the status and roles of women. Our data suggest that changes are indeed taking place and that some women are benefiting from them. The trajectory of change in the future deserves careful monitoring.
* The authors are grateful for the constructive comments of the organizers of the conference “Gender, Households, and the Boundaries of Work in Contemporary China,” and of the discussant, Dr. Wang Feng. Funds for undertaking the 1988 Survey of Migration, Fertility, and Economic Change in Hubei Province were provided by a grant from the Rockefeller Foundation to the Population Studies and Training Center of Brown University in collaboration with the Population Institute at Wuhan University. Professors Gu Shengzu, Wu Shinmu, and Zhu Nong were instrumental in the data collection and processing phase of the study. Also gratefully acknowledged is the support for Zai Liang from the National Institute of Health and Human Development (1R55HD/0D34870 and 1R29HD34878) and the Queens College Presidential Research Award.
1. “Official” migration/migrants is often termed “permanent” migration/ migrants. As used here, “official” refers only to permanent changes in residence that have received government approval.
2. For a fuller description of the survey and the characteristics of the sample, see A. Goldstein, S. Goldstein, and Gu Shengzu, 1993.
3. This observation is based on our conversations with registration authorities.
4. For occupational codes we use the coding scheme devised by the State Statistical Bureau of China to collapse the over 800 occupation codes detailed in the census into seven broad categories. The production/transport category is a heterogeneous one that includes transportation, skilled, semi-skilled, and unskilled laborers, and extraction and construction workers.
5. The discussion in this section is largely based on material contained in A. Goldstein and S. Goldstein (1996).
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