Homogenization of lateral diffusion on a random surface

We study the problem of lateral diffusion on a static, quasi-planar surface generated by a stationary, ergodic random field possessing rapid small-scale spatial fluctuations. The aim is to study the effective behaviour of a particle undergoing Brownian motion on the surface viewed as a projection on the underlying plane. By formulating the problem as a diffusion in a random medium, we are able to use known results from the theory of stochastic homogenization of SDEs to show that, in the limit of small scale fluctuations, the diffusion process behaves quantitatively like a Brownian motion with constant diffusion tensor $D$. While $D$ will not have a closed-form expression in general, we are able to derive variational bounds for the effective diffusion tensor, and using a duality transformation argument, obtain a closed form expression for $D$ in the special case where $D$ is isotropic. We also describe a numerical scheme for approximating the effective diffusion tensor and illustrate this scheme with two examples.Comment: 25 pages, 7 figure

Ancestry versus ethnicity: the complexity and selectivity of Mexican identification in the United States

Using microdata from the 2000 U.S. Census, we analyze the responses of Mexican Americans to questions that independently elicit their “ethnicity” (or Hispanic origin) and their “ancestry.” We investigate whether different patterns of responses to these questions reflect varying degrees of ethnic attachment. For example, those identified as “Mexican” in both the Hispanic origin and the ancestry questions might have stronger ethnic ties than those identified as Mexican only in the ancestry question. How U.S.-born Mexicans report their ethnicity/ancestry is strongly associated with measures of human capital and labor market performance. In particular, educational attainment, English proficiency, and earnings are especially high for men and women who claim a Mexican ancestry but report their ethnicity as “not Hispanic.” Further, intermarriage and the Mexican identification of children are also strongly related to how U.S.-born Mexican adults report their ethnicity/ancestry, revealing a possible link between the intergenerational transmission of Mexican identification and economic status

Intermarriage and the intergenerational transmission of ethnic identity and human capital for Mexican Americans

Using microdata from the 2000 U.S. Census and from recent years of the Current Population Survey (CPS), we investigate whether selective intermarriage and endogenous ethnic identification interact to hide some of the intergenerational progress achieved by the Mexican-origin population in the United States. First, using Census data for U.S.-born youth ages 16-17 who have at least one Mexican parent, we estimate how the Mexican identification, high school dropout rates, and English proficiency of these youth depend on whether they are the product of endogamous or exogamous marriages. Second, we analyze the extent and selectivity of ethnic attrition among second-generation Mexican-American adults and among U.S.-born Mexican-American youth. Using CPS data, we directly assess the influence of endogenous ethnicity by comparing an “objective” indicator of Mexican descent (based on the countries of birth of the respondent and his parents and grandparents) with the standard “subjective” measure of Mexican self-identification (based on the respondent’s answer to the Hispanic origin question). For third-generation Mexican-American youth, we show that ethnic attrition is substantial and could produce significant downward bias in standard measures of attainment which rely on ethnic self-identification rather than objective indicators of Mexican ancestry

Ethnic Identification, Intermarriage, and Unmeasured Progress by Mexican Americans

Using Census and CPS data, we show that U.S.-born Mexican Americans who marry non- Mexicans are substantially more educated and English proficient, on average, than are Mexican Americans who marry co-ethnics (whether they be Mexican Americans or Mexican immigrants). In addition, the non-Mexican spouses of intermarried Mexican Americans possess relatively high levels of schooling and English proficiency, compared to the spouses of endogamously married Mexican Americans. The human capital selectivity of Mexican intermarriage generates corresponding differences in the employment and earnings of Mexican Americans and their spouses. Moreover, the children of intermarried Mexican Americans are much less likely to be identified as Mexican than are the children of endogamous Mexican marriages. These forces combine to produce strong negative correlations between the education, English proficiency, employment, and earnings of Mexican-American parents and the chances that their children retain a Mexican ethnicity. Such findings raise the possibility that selective ethnic “attrition” might bias observed measures of intergenerational progress for Mexican Americans

Immigration and the U.S. labour market

Over the last several decades, two of the most significant developments in the U.S. labor market have been: (1) rising inequality, and (2) growth in both the size and the diversity of immigration flows. Because a large share of new immigrants arrive with very low levels of schooling, English proficiency, and other skills that have become increasingly important determinants of success in the U.S. labor market, an obvious concern is that such immigrants are a poor fit for the restructured American economy. In this chapter, we evaluate this concern by discussing evidence for the United States on two relevant topics: the labor market integration of immigrants, and the impact of immigration on the wages and employment opportunities of native workers. In these dimensions, the overall labor market performance of U.S. immigrants seems quite favorable. U.S. immigrants have little trouble finding jobs, and this is particularly true of unskilled immigrants. Most U.S. immigrants experience substantial earnings growth as they adapt to the American labor market. For most immigrant groups, the U.S.-born second generation has achieved socioeconomic parity with mainstream society; for some Hispanic groups, however, this is not the case. On the whole, immigration to the United States has not had large adverse consequences for the labor market opportunities of native workers. Therefore, with regard to the economic integration and labor market impacts of immigration, it is not obvious that the seemingly haphazard nature of U.S. immigration policy has led to unfavorable outcomes

An examination of the fraud liability shift in consumer card-based payment systems

Identity theft ; Fraud ; Payment systems

Lumley's energy cascade dissipation rate model for boundary-free turbulent shear flows

True dissipation occurs mainly at the highest wavenumbers where the eddy sizes are comparatively small. These high wavenumbers receive their energy through the spectral cascade of energy starting with the largest eddies spilling energy into the smaller eddies, passing through each wavenumber until it is dissipated at the microscopic scale. However, a small percentage of the energy does not spill continuously through the cascade but is instantly passed to the higher wavenumbers. Consequently, the smallest eddies receive a certain amount of energy almost immediately. As the spectral energy cascade continues, the highest wavenumber needs a certain time to receive all the energy which has been transferred from the largest eddies. As such, there is a time delay, of the order of tau, between the generation of energy by the largest eddies and the eventual dissipation of this energy. For equilibrium turbulence at high Reynolds numbers, there is a wide range where energy is neither produced by the large eddies nor dissipated by viscosity, but is conserved and passed from wavenumber to higher wavenumbers. The rate at which energy cascades from one wavenumber to another is proportional to the energy contained within that wavenumber. This rate is constant and has been used in the past as a dissipation rate of turbulent kinetic energy. However, this is true only in steady, equilibrium turbulence. Most dissipation models contend that the production of dissipation is proportional to the production of energy and that the destruction of dissipation is proportional to the destruction of energy. In essence, these models state that the change in the dissipation rate is proportional to the change in the kinetic energy. This assumption is obviously incorrect for the case where there is no production of turbulent energy, yet energy continues to cascade from large to small eddies. If the time lag between the onset on the energy cascade to the destruction of energy at the microscale can be modeled, then there will be a better representation of the dissipation process. Development of an energy cascade time scale equation is discussed

Treaty Self-Execution as “Foreign” Foreign Relations Law?

This contribution to the Oxford Handbook on Comparative Foreign Relations considers how a state’s approach to foreign relations problems may have an external origin, or what we call “foreign” Foreign Relations Law (FFRL). Using the distinction between self-executing and non-self-executing treaties as a case study, we find close parallels between manifestations of this distinction in various states and how it evolved in the United States, where the distinction was first articulated. The chapter explores whether these parallels reflect the distinction’s transplantation from one legal system to another or the organic development of similar doctrines to address similar problems within the states involved. The chapter then addresses the utility of differentiating the exogenous/endogenous origins of particular foreign relations doctrines. We argue that consideration of a doctrine’s exogenous origins raises questions that can deepen and develop the nascent field of comparative foreign relations law. Why do states accept (or reject) FFRL? How does FFRL enter a state’s system? Who is doing the transporting? What happens to FFRL in its new site(s) – i.e., how static or dynamic does the concept prove in different settings? Further research on such questions may, in turn, set the table for more normative questions such as when states should seek (or resist) the importation of foreign relations law