Related papers: RG Flows and Bifurcations
A dynamical system description of the transition process in shear flows with no linear instability starts with a knowledge of exact coherent solutions, among them travelling waves (TWs) and relative periodic orbits (RPOs). We describe a…
Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations…
In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present the modeling of gas flow and coupling conditions for flow…
We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are…
Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of…
We show that the exact RG-flow equation introduced recently in hep-th/0207134 can be obtained in the sharp cut-off limit of the well-known ERGE. This can be expected from the fact that in this limit the new scale-dependent effective action…
If the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new…
We present the hydrodynamic theory of active XY spins coupled with flow fields, for systems both having and or lacking number conservation in two dimensions (2D). For the latter, with strong activity or nonequilibrium drive, the system can…
We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…
Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network…
In the theory of hydrodynamic stability, the procedure to decompose an incompressible flow field into its basic motion and disturbances is imprecise and problematic because the disturbances, infinitesimal or finite, are ill-defined…
We calculate numerically the renormalization group (RG) flow of lattice QCD in two-coupling space, $(\beta_{1\times 1},\beta_{1\times 2})$. This is the first explicit calculation of the RG flow of SU(3) gauge theory. From the RG flow,a…
For certain families of fluid flow, a new conserved quantity -- stream-helicity -- has been established.Using examples of linked and knotted streamtubes, it has been shown that stream-helicity does, in certain cases, entertain itself with a…
In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of…
The seemingly simple problem of determining the drag on a body moving through a very viscous fluid has, for over 150 years, been a source of theoretical confusion, mathematical paradoxes, and experimental artifacts, primarily arising from…
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases.…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Recent topological tools offer a powerful way to classify how phases of nonlinear bosonic resonators are organized. Yet, they remain incomplete. In particular, self-sustained oscillations in the form of limit cycles act as robust organizing…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. Building on previous work by the author, in this paper we…