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

Modeling water waves beyond perturbations

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein-Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.Comment: 15 pages, 1 figure, 39 references. This document is a contributed chapter to an upcoming volume to be published by Springer in Lecture Notes in Physics Series. Other author's papers can be downloaded at http://www.denys-dutykh.com

N-body simulations of gravitational dynamics

We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N-body simulations and their most important results.Comment: invited review (28 pages), to appear in European Physics Journal Plu

Gendering the careers of young professionals: some early findings from a longitudinal study. in Organizing/theorizing: developments in organization theory and practice

Wonders whether companies actually have employees best interests at heart across physical, mental and spiritual spheres. Posits that most organizations ignore their workforce – not even, in many cases, describing workers as assets! Describes many studies to back up this claim in theis work based on the 2002 Employment Research Unit Annual Conference, in Cardiff, Wales

Formation of vitisin A during red wine fermentation and maturation

The definitive version is available at www.blackwell-synergy.comDuring alcoholic fermentation the formation of vitisin A occurred mainly in the period between 20% and 85% glucose utilisation, when the concentrations of the precursors, malvidin-3-glucoside and pyruvic acid were at a maximum. The maximum rate of vitisin A synthesis of 11 mg/Lh occurred when 57% of glucose had been utilised and 440 mg/L malvidin-3-glucoside, 114 mg/L pyruvic acid and 3.1 mg/L measured oxygen were present. During maturation, production of vitisin A appeared to be linked with the availability of a suitable oxidant. Synthesis of vitisin A continued for approximately 6 months of maturation in air-tight bottles while the precursors were available. In wines that underwent malolactic fermentation, the malolactic bacteria consumed pyruvic acid and thereby limited the production of vitisin A. At the end of a 12 month maturation period, the concentration of vitisin A declined in wines made without any malolactic fermentation, even though malvidin-3-glucoside and pyruvic acid were still present. This indicated that there was a shortage of a suitable oxidant required to complete the reaction.Robert E. Asenstorfer, Andrew J. Markides, Patrick G. Iland and Graham P. Jone