Lagrangian approximations and weak solutions of the Navier-Stokes equations

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.

Local Seafood Availability in San Diego, California Seafood Markets

Like many developed coastal cities, San Diego, California has strong geographic and recreational ties to the adjacent ocean, but weak culinary ones. Less than 10% of the seafood consumed in the U.S., and San Diego in particular, is domestic. The popularity and abundance of farmers’ markets and other local markets in San Diego indicates an interest among producers and the public alike in cultivating local, diverse food systems, but this trend has been slower to catch on for seafood. The goal of this project was, therefore, to define and begin to understand the influences on the patterns of locally sourced, domestic seafood availability in San Diego. This study focused on seafood availability in seafood markets including researching market websites and contacting seafood counter managers to determine the general frequency (consistent, occasional, none) at which the markets sold seafood produced by San Diego fishermen or aquafarmers. Seafood market locations were mapped, and demographic and spatial information was gathered for each market’s zip code. The results of the study revealed that only 8% of San Diego’s 86 seafood markets consistently carried San Diego-sourced seafood, and 14% of markets carried it on occasion. Increased density of these local seafood markets was correlated with proximity to the coast, with almost 80% of the markets located within 2 km of the coast. Neither per capita income nor racial diversity was correlated with local seafood market density, indicating that factors contributing to coastal isolation matter more than wealth or diversity in determining where local seafood is sold. The geographic disparity in local seafood availability may be due to a variety of factors, including a small fishing fleet, prevalence of imported seafood, limited waterfront and urban infrastructure needed to support a local seafood system, and a lack of public awareness about local fisheries. Information gleaned from this study can inform further investigation into the influences on local, equitable seafood systems, as well as help consumers, producers and marketers to make informed decisions about seafood purchases and marketing efforts.

Integrated soil fertility management in eastern and western Africa: The role of knowledge and innovation systems, its adoption and impact

The rise in population growth, as well as nutrient mining, has contributed to low agricultural productivity in Sub-Saharan Africa (SSA). A plethora of technologies to boost agricultural production have been developed but the dissemination of these agricultural innovations and subsequent uptake by smallholder farmers has remained a challenge. Scientists and philanthropists have adopted the Integrated Soil Fertility Management (ISFM) paradigm as a means to promote sustainable intensification of African farming systems. This comparative study aimed: 1) To assess the efficacy of Agricultural Knowledge and Innovation Systems (AKIS) in East (Kenya) and West (Ghana) Africa in the communication and dissemination of ISFM (Study I); 2) To investigate how specifically soil quality, and more broadly socio-economic status and institutional factors, influence farmer adoption of ISFM (Study II); and 3) To assess the effect of ISFM on maize yield and total household income of smallholder farmers (Study III). To address these aims, a mixed methodology approach was employed for study I. AKIS actors were subjected to social network analysis methods and in-depth interviews. Structured questionnaires were administered to 285 farming households in Tamale and 300 households in Kakamega selected using a stratified random sampling approach. There was a positive relationship between complete ISFM awareness among farmers and weak knowledge ties to both formal and informal actors at both research locations. The Kakamega AKIS revealed a relationship between complete ISFM awareness among farmers and them having strong knowledge ties to formal actors implying that further integration of formal actors with farmers’ local knowledge is crucial for the agricultural development progress. The structured questionnaire was also utilized to answer the query pertaining to study II. Soil samples (0-20 cm depth) were drawn from 322 (Tamale, Ghana) and 459 (Kakamega, Kenya) maize plots and analysed non-destructively for various soil fertility indicators. Ordinal regression modeling was applied to assess the cumulative adoption of ISFM. According to model estimates, soil carbon seemed to preclude farmers from intensifying input use in Tamale, whereas in Kakamega it spurred complete adoption. This varied response by farmers to soil quality conditions is multifaceted. From the Tamale perspective, it is consistent with farmers’ tendency to judiciously allocate scarce resources. Viewed from the Kakamega perspective, it points to a need for farmers here to intensify agricultural production in order to foster food security. In Kakamega, farmers with more acidic soils were more likely to adopt ISFM. Other household and farm-level factors necessary for ISFM adoption included off-farm income, livestock ownership, farmer associations, and market inter-linkages. Finally, in study III a counterfactual model was used to calculate the difference in outcomes (yield and household income) of the treatment (ISFM adoption) in order to estimate causal effects of ISFM adoption. Adoption of ISFM contributed to a yield increase of 16% in both Tamale and Kakamega. The innovation affected total household income only in Tamale, where ISFM adopters had an income gain of 20%. This may be attributable to the different policy contexts under which the two sets of farmers operate. The main recommendations underscored the need to: (1) improve the functioning of AKIS, (2) enhance farmer access to hybrid maize seed and credit, (3) and conduct additional multi-locational studies as farmers operate under varying contexts.