Exact results for the Kardar--Parisi--Zhang equation with spatially correlated noise

We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by means of dynamic field theory and the renormalization group. Using a stochastic Cole--Hopf transformation we derive {\em exact} exponents and scaling functions for the roughening transition and the smooth phase above the lower critical dimension $d_c = 2 (1+\rho)$. Below the lower critical dimension, there is a line $\rho_*(d)$ marking the stability boundary between the short-range and long-range noise fixed points. For $\rho \geq \rho_*(d)$, the general structure of the renormalization-group equations fixes the values of the dynamic and roughness exponents exactly, whereas above $\rho_*(d)$, one has to rely on some perturbational techniques. We discuss the location of this stability boundary $\rho_* (d)$ in light of the exact results derived in this paper, and from results known in the literature. In particular, we conjecture that there might be two qualitatively different strong-coupling phases above and below the lower critical dimension, respectively.Comment: 21 pages, 15 figure

Toward ending segregation in the 1980s

The conflict concerning desegregation in the 1970s has roots and implications that extend beyond schooling to all aspects of life in metropolitan America. The issue is whether the ghettoization of blacks in areas distinct and separate from protected white enclaves will continue as the vehicle for imposing caste inequality. The challenge for the 1980s is to develop constructive policies and practices in education and training, jobs and housing, and urban development and taxation that will work to end the mutually destructive process of racial segregation across the national landscape. This article explores a number of control, incentive, market, and cooperative approaches to breaching the color line of racial ghettoization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43868/1/11256_2005_Article_BF01956009.pd

A Multigenerational View of Inequality

The study of intergenerational mobility and most population research are governed by a two-generation (parent-to-offspring) view of intergenerational influence, to the neglect of the effects of grandparents and other ancestors and nonresident contemporary kin. While appropriate for some populations in some periods, this perspective may omit important sources of intergenerational continuity of family-based social inequality. Social institutions, which transcend individual lives, help support multigenerational influence, particularly at the extreme top and bottom of the social hierarchy, but to some extent in the middle as well. Multigenerational influence also works through demographic processes because families influence subsequent generations through differential fertility and survival, migration, and marriage patterns, as well as through direct transmission of socioeconomic rewards, statuses, and positions. Future research should attend more closely to multigenerational effects; to the tandem nature of demographic and socioeconomic reproduction; and to data, measures, and models that transcend coresident nuclear families

Social change and the family: Comparative perspectives from the west, China, and South Asia

This paper examines the influence of social and economic change on family structure and relationships: How do such economic and social transformations as industrialization, urbanization, demographic change, the expansion of education, and the long-term growth of income influence the family? We take a comparative and historical approach, reviewing the experiences of three major sociocultural regions: the West, China, and South Asia. Many of the changes that have occurred in family life have been remarkably similar in the three settings—the separation of the workplace from the home, increased training of children in nonfamilial institutions, the development of living arrangements outside the family household, increased access of children to financial and other productive resources, and increased participation by children in the selection of a mate. While the similarities of family change in diverse cultural settings are striking, specific aspects of change have varied across settings because of significant pre-existing differences in family structure, residential patterns of marriage, autonomy of children, and the role of marriage within kinship systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45661/1/11206_2005_Article_BF01124383.pd