Gravitational collapse: A case for thermal relaxation

Two relativistic models for collapsing spheres at different stages of evolution, which include pre-relaxation processes, are presented. The influence of relaxation time on the outcome of evolution in both cases is exhibited and established. It is shown that relaxation processes can drastically change the final state of the collapsing system. In particular, there are cases in which the value of the relaxation time determines the bounce or the collapse of the sphere.Comment: 33 pages, LaTex 2.09, 11 Postscript figures. To be published in General Relativity and Gravitatio

Integrable Quasiclassical Deformations of Algebraic Curves

A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of hydrodynamic type is characterized.Comment: 28 pages, no figure

Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described by Hamilton-Jacobi type equations associated with hierarchies of dispersionless integrable systems. These hierarchies are constructed by applying the quasiclassical $\bar{\partial}$-dressing method.Comment: 30 pages, tcilate

A Conversation with Dorothy Gilford

In 1946, Public Law 588 of the 79th Congress established the Office of Naval Research (ONR). Its mission was to plan, foster and encourage scientific research in support of Naval problems. The establishment of ONR predates the National Science Foundation and initiated the refocusing of scientific infrastructure in the United States following World War II. At the time, ONR was the only source for federal support of basic research in the United States. Dorothy Gilford was one of the first Heads of the Probability and Statistics program at the Office of Naval Research (1955 to 1962), and she went on to serve as Director of the Mathematical Sciences Division (1962 to 1968). During her time at ONR, Dorothy influenced many areas of statistics and mathematics and was ahead of her time in promoting interdisciplinary projects. Dorothy continued her career at the National Center for Education Statistics (1969 to 1974). She was active in starting international comparisons of education outcomes in different countries, which has influenced educational policy in the United States. Dorothy went on to serve in many capacities at the National Academy of Sciences, including Director of Human Resources Studies (1975 to 1978), Senior Statistician on the Committee on National Statistics (1978 to 1988) and Director of the Board on International Comparative Studies in Education (1988 to 1994). The following is a conversation we had with Dorothy Gilford in March of 2004. We found her to be an interesting person and a remarkable statistician. We hope you agree.Comment: Published in at http://dx.doi.org/10.1214/088342307000000023 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hydrodynamic reductions and solutions of a universal hierarchy

The diagonal hydrodynamic reductions of a hierarchy of integrable hydrodynamic chains are explicitly characterized. Their compatibility with previously introduced reductions of differential type is analyzed and their associated class of hodograph solutions is discussed.Comment: 19 page