Finite time singularities in a class of hydrodynamic models

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant, $0<\alpha< 1$. Unlike the case $\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\alpha$ results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of anti-parallel vortex filaments and an analog of the Crow instability is found at small wave-numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like $(t^*-t)^{1/(2-\alpha)}$, where $t^*$ is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal pape

Investigating web-based recruitment sources: Employee testimonials vs word-of-mouse

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Tenure or permanent contracts in North American higher education?:A critical assessment

This article offers a critical perspective on the academic tenure system in the USA. Academic tenure is most frequently defended for the protection it affords freedom of speech in higher education, and it is attacked for its cost and lack of flexibility in a rapidly changing sector. The paper makes a third argument, that tenure sustains an unhealthy divide between tenured, untenured, and non-tenure-track staff members. It leads to differences in status, income, and job satisfaction that are inimical to basic principles of social justice. While financial considerations are a powerful factor in university efforts to constrain or challenge tenure, the maintenance of the tenure system and its use to control entry to permanent employment needs further examination. The author explores the system of ‘permanent’ contracts common in British and Australasian universities as an alternative for the USA – not because it benefits entrepreneurial university managers and administrators, but for its potential to offer a greater range of career positions for actual and potential staff members