Cotton flow

Using the conformally-invariant Cotton tensor, we define a geometric flow, the Cotton flow, which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an entropy functional, and study the flow of nine homogeneous spaces both numerically and analytically. In particular, we show that the arbitrarily deformed homogeneous 3-sphere flows into the round 3-sphere. Two of the nine homogeneous geometries, which are degenerated by the Ricci flow, are left intact by the Cotton flow.
Classical and Quantum Gravity


Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow
Sellier, A.; AYDIN, SELÇUK HAN; Tezer, Münevver (2014-12-01)
The fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x(0) in an unbounded conducting Newtonian liquid with uniform viscosity mu and conductivity sigma > 0 subject to a prescribed uniform ambient magnetic field B = Be-1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field sigma are expressed at any observation point x not equal x(0) in...
Pipe flow of a magnetizable fluid in rectangular cavities under magnetic sources
Senel, P.; Tezer, Münevver (2017-10-01)
In this paper, the fully developed flow of an electrically non-conducting, viscous, incompressible, magnetizable fluid is investigated in rectangular pipes with square or rectangular cross-sections under the effect of spatially varying magnetic field. Magnetic field is generated by multiple wires carrying electric current that pass below and above along the pipe. Thus, the problem is reduced to the 2D flow of a magnetizable fluid in the cross-section of the pipe (cavity). Governing equations are solved in t...
Stress behavioursof viscoelastic flowaround square cylinder
Tezel Tanrısever, Güler Bengüsu; Yapıcı, Kerim; Uludağ, Yusuf (2019-06-01)
In this study, it is aimed the numerically investigation of the flow of liner PTT (Phan-Thien-Tanner) fluid, which is a viscoelastic fluid model over limited square obstacle by finite volume method. The finite volume method has been used for simultaneous solution of continuity, momentum and fluid model equations with appropriate boundary conditions. The effects of the inertia in terms of Reynolds number, Re, (0 < Re < 20) and the of elasticity in terms of Weissenberg number, We, (1 < We < 15) of PTT flow ...
Flexible multibody analysis using absolute nodal coordinate formulation
Çiftçi, Muhammed Ali; Darendeliler, Haluk; İder, S. Kemal; Department of Mechanical Engineering (2014)
The motion of the planar flexible multibody system with large deformation is analyzed by using the absolute nodal coordinate formulation (ANCF). For this purpose, flexible multibody systems consisting of beams are considered. In the conventional planar ANCF beam elements, there are two nodes located at the ends. Each element has eight degrees of freedom which consist of four global coordinates and four global slopes. In this study, a planar beam element is developed with quadratic shape functions and new no...
Hasanlı, Nızamı; ELLIALTIOGLU, S; LAIHO, R; BAKHYSHOV, AE (1993-12-01)
The compositional variation of the elastic coefficients C-11 and C33 for TlGa(S1-xSex) and TlInxGa1-xS2 layer mixed crystals are discussed using Brillouin scattering measurements. Clear anomalies are observed for the longitudinal phonons propagating parallel to the (00 1) plane (elastic coefficient C-11) at x(c) congruent-to 0.8 and x(c) congruent-to 0.3 in TlInxGa1-xS2 and TlGa(S1-xSex)2, respectively. These anomalies are explained by the formation of infinite clusters. A considerable difference in the rat...
Citation Formats
A. U. Ö. Kişisel, B. Ö. Sarıoğlu, and B. Tekin, “Cotton flow,” Classical and Quantum Gravity, 2008, Accessed: 00, 2020. [Online]. Available: