Related papers: Functional renormalization-group approach to decay…
The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the…
In this work we consider the problem of constructing initial conditions for a flow model such that the resulting flow evolution leads to a self-similar energy cascade consistent with Kolmogorov's statistical theory of turbulence. As a first…
We investigate the phase diagram of a one-dimensional dissipative Bose-Hubbard model using the nonperturbative functional renormalization group (FRG). Each lattice site is coupled to an independent bath, generating long-range temporal…
We explore one-point and two-point statistics of the Navier-Stokes-alpha-beta regularization model at moderate Reynolds number in homogeneous isotropic turbulence. The results are compared to the limit cases of the Navier-Stokes-alpha model…
Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension $d$) at finite temperature $T>0$ are reviewed and reexamined in this much expanded version of [Europhys. Lett. {\bf 76} 457 (2006)]. The…
We study the time evolution of velocity and pressure gradients in isotropic turbulence, by quantifying their decorrelation time scales as one follows fluid particles in the flow. The Lagrangian analysis uses data in a public database…
We develop a new functional renormalization group (FRG) approach for the two-dimensional XY-model by combining the lattice FRG proposed by Machado and Dupuis [Phys. Rev. E 82, 041128 (2010)] with a duality transformation which explicitly…
The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this…
A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy…
The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by…
We compute the Functional Renormalization Group (FRG) disorder- correlator function R(v) for d-dimensional elastic manifolds pinned by a random potential in the limit of infinite embedding space dimension N. It measures the equilibrium…
We here exploit a rigorous mathematical theory of vorticity dynamics for Navier-Stokes solutions in terms of stochastic Lagrangian flows and their stochastic Cauchy invariants, that are conserved on average backward in time. This theory…
In this article we consider a damped version of the incompressible Navier-Stokes equations in the whole three-dimensional space with a divergence-free and time-independent external force. Within the framework of a well-prepared force and…
We study the replica field theory which describes the pinning of elastic manifolds of arbitrary internal dimension d in a random potential, with the aim of bridging the gap between mean field and renormalization theory. The full effective…
In Lagrangian turbulence one is faced with the puzzle that 2D Navier-Stokes flows are nearly as intermittent as in three dimensions although no intermittency is present in the inverse cascade in 2D Eulerian turbulence. In addition, an…
We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both…
Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs--Runge oscillations that…
Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We…
Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight opens new possibilities for applying FRG methods to…
The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates $\mathcal{O}(N^4)$ independent variables, where $N$ is the number of interacting states (e.g.…