RESUMO
A recently proposed variational principle with a discontinuous Lagrangian for viscous flow is reinterpreted against the background of stochastic variational descriptions of dissipative systems, underpinning its physical basis from a different viewpoint. It is shown that additional non-classical contributions to the friction force occurring in the momentum balance vanish by time averaging. Accordingly, the discontinuous Lagrangian can alternatively be understood from the standpoint of an analogous deterministic model for irreversible processes of stochastic character. A comparison is made with established stochastic variational descriptions and an alternative deterministic approach based on a first integral of Navier-Stokes equations is undertaken. The applicability of the discontinuous Lagrangian approach for different Reynolds number regimes is discussed considering the Kolmogorov time scale. A generalization for compressible flow is elaborated and its use demonstrated for damped sound waves.
RESUMO
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
RESUMO
Defining the gene products that play an essential role in an organism's functional repertoire is vital to understanding the system level organization of living cells. We used a genetic footprinting technique for a genome-wide assessment of genes required for robust aerobic growth of Escherichia coli in rich media. We identified 620 genes as essential and 3,126 genes as dispensable for growth under these conditions. Functional context analysis of these data allows individual functional assignments to be refined. Evolutionary context analysis demonstrates a significant tendency of essential E. coli genes to be preserved throughout the bacterial kingdom. Projection of these data over metabolic subsystems reveals topologic modules with essential and evolutionarily preserved enzymes with reduced capacity for error tolerance.
