arXiv subjects

R. Collina

Publications and source records attributed to R. Collina.

4 recordsLinked to original sources

arXiv2004

Large Deviation Approach to the Randomly Forced Navier-Stokes Equation

The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure yields the dimensional scaling predicted by K41 theory at the lowest perturbative order, where the perturbation parameter is the inverse Reynolds number. Moreover, an explicit expression of the prefactor of the scaling law is obtained.

physics.flu-dyn↗

arXiv2003

Self-similar behavior of pre-turbulent fluctuations

The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. In virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure yields the dimensional scaling predicted by K41 theory at the lowest perturbative order, where the perturbation parameter is the inverse Reynolds number. This result is valid over a finite spatio-temporal domain, where the physical solution can be considered as stationary.

physics.flu-dyn↗

arXiv1994

A Functional and Lagrangian Formulation of Two-Dimensional Topological Gravity

We reconsider two-dimensional topological gravity in a functional and lagrangian framework. We derive its Slavnov-Taylor identities and discuss its (in)dependence on the background gauge. Correlators of reparamerization invariant observables are shown to be globally defined forms on moduli space. The potential obstruction to their gauge-independence is the non-triviality of the line bundle on moduli space ${\cal L}_x$, whose first Chern-class is associated to the topological invariants of Mumford, Morita and Miller. Based on talks given at the Fubini Fest, Torino, 24-26 February 1994, and at the Workshop on String Theory, Trieste, 20-22 April 1994.

hep-th↗

arXiv1993

On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings

We provide a simple lagrangian interpretation of the meaning of the $b_0^-$ semi-relative condition in closed string theory. Namely, we show how the semi-relative condition is equivalent to the requirement that physical operators be cohomology classes of the BRS operators acting on the space of local fields {\it covariant} under world-sheet reparametrizations. States trivial in the absolute BRS cohomology but not in the semi-relative one are explicitly seen to correspond to BRS variations of operators which are not globally defined world-sheet tensors. We derive the covariant expressions for the observables of topological gravity. We use them to prove a formula that equates the expectation value of the gravitational descendant of ghost number 4 to the integral over the moduli space of the Weil-Peterson Kähler form.

hep-th↗