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## Pipe Poiseuille flow of viscously anisotropic, partially molten rock (2014)

Citations: | 1 - 0 self |

### Citations

281 | PETSc users manual - Balay, Buschelman, et al. - 2011 |

146 |
The generation and compaction of partially molten rock.
- McKenzie
- 1984
(Show Context)
Citation Context ...pectively, for the rest of the manuscript. In writing the non-dimensional equations, it is convenient to define a ratio of the compaction length, an inherent length scale of magma/mantle interaction [=-=McKenzie, 1984-=-], to the system 5 size H, R = 1 H √ (rξ + 4 3 )η0K0 ηL . (8) Dynamic pressure perturbations cause variations in melt flux (and hence (de)compaction) over a length scale that is less than or equal to ... |

56 |
Some remarks on the movement of small melt fractions in the mantle,
- McKenzie
- 1989
(Show Context)
Citation Context ...ce appropriate at small porosity, K(φ) = K0 (φ/φ0) n , (4) where n is a constant, usually taken as two or three, and φ0 is a reference porosity at which the permeability takes its reference value K0 [=-=McKenzie, 1989-=-, Riley and Kohlstedt, 1991, Faul, 1997, Wark and Watson, 1998]. Following on the work of Takei and Katz [2013], we can relate the second-order stress tensor to the second-order strain-rate tensor via... |

48 | Approximation Theory and Approximation Practice
- Trefethen
- 2012
(Show Context)
Citation Context .... Solutions of equations (12) incorporating radial variation in anisotropy are obtained numerically, to a tolerance of 10−10, using the Chebfun package [Driscoll et al., 2008, Trefethen et al., 2011, =-=Trefethen, 2013-=-] for Matlab. Figure 1a–b show the components of base-state velocity under an imposed, radially variable anisotropy (coloured curves). These differ quantitatively from the uniform anisotropy case, but... |

39 | The dynamics of melt and shear localization in partially molten aggregates, - Katz, Spiegelman, et al. - 2006 |

36 | Spontaneous small-scale melt segregation in partial melts undergoing deformation. - Stevenson - 1989 |

28 | A method of reducing dispersion in convective difference scheme - Fromm - 1968 |

25 | Stress-driven melt segregation in partially molten rocks. - HOLTZMAN, GROEBNER, et al. - 2003 |

25 |
Grain-scale permeability of texturally equilibrated, monomineralic rocks:
- Wark, Watson
- 1998
(Show Context)
Citation Context ...(4) where n is a constant, usually taken as two or three, and φ0 is a reference porosity at which the permeability takes its reference value K0 [McKenzie, 1989, Riley and Kohlstedt, 1991, Faul, 1997, =-=Wark and Watson, 1998-=-]. Following on the work of Takei and Katz [2013], we can relate the second-order stress tensor to the second-order strain-rate tensor via a fourth-order viscosity tensor, σij + p Lδij = cijklε̇kl, (5... |

24 |
Permeability of partially molten upper mantle rocks from experiments and percolation theory:
- Faul
- 1997
(Show Context)
Citation Context ... (φ/φ0) n , (4) where n is a constant, usually taken as two or three, and φ0 is a reference porosity at which the permeability takes its reference value K0 [McKenzie, 1989, Riley and Kohlstedt, 1991, =-=Faul, 1997-=-, Wark and Watson, 1998]. Following on the work of Takei and Katz [2013], we can relate the second-order stress tensor to the second-order strain-rate tensor via a fourth-order viscosity tensor, σij +... |

22 | Linear analysis of melt band formation by simple shear. - Spiegelman - 2003 |

19 | The chebop system for automatic solution of differential equations - DRISCOLL, BORNEMANN, et al. - 2008 |

18 | Viscous constitutive relations of solid-liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model. - Takei, Holtzman - 1978 |

16 | Stress-driven melt segregation and strain partitioning in partially molten rocks: effects of stress and strain. - HOLTZMAN, KOHLSTEDT - 2007 |

15 |
Kinetics of melt migration in upper mantle-type rocks, Earth Planet.
- Riley, Kohlstedt
- 1991
(Show Context)
Citation Context ...t small porosity, K(φ) = K0 (φ/φ0) n , (4) where n is a constant, usually taken as two or three, and φ0 is a reference porosity at which the permeability takes its reference value K0 [McKenzie, 1989, =-=Riley and Kohlstedt, 1991-=-, Faul, 1997, Wark and Watson, 1998]. Following on the work of Takei and Katz [2013], we can relate the second-order stress tensor to the second-order strain-rate tensor via a fourth-order viscosity t... |

13 | Stress-driven melt segregation in partially molten olivine-rich rocks deformed in torsion. 51:21–42, - King, Zimmerman, et al. - 2010 |

8 |
The Effect of Heating Rate on the Stability of Stationary Fluids,"
- Currie
- 1967
(Show Context)
Citation Context ...versally accepted method for analysing the linear stability of a time-dependent base state [Doumenc et al., 2010]. Following Takei and Katz [2013], we adopt the frozen-time approximation [Lick, 1965, =-=Currie, 1967-=-], whereby we assume that the perturbation grows at a rate that is faster than the rate-of-change of the base state. We therefore take φ0 to be constant and uniform in solving for the evolution of per... |

6 |
The instability of a fluid layer with time-dependent heating.
- LICK
- 1965
(Show Context)
Citation Context ...re is no universally accepted method for analysing the linear stability of a time-dependent base state [Doumenc et al., 2010]. Following Takei and Katz [2013], we adopt the frozen-time approximation [=-=Lick, 1965-=-, Currie, 1967], whereby we assume that the perturbation grows at a rate that is faster than the rate-of-change of the base state. We therefore take φ0 to be constant and uniform in solving for the ev... |

4 | Numerical models of shear-induced melt band formation with anisotropic matrix viscosity. - BUTLER - 2012 |

4 | Transient Rayleigh–Benard–Marangoni convection due to evaporation: a linear non-normal stability analysis. - DOUMENC, BOECK, et al. - 2010 |

4 | Stress-induced anisotropy of partially molten rock analogue deformed under quasi-static loading test. - TAKEI - 2010 |

4 | et al.: Chebfun Version 4.2. The Chebfun Development Team - Trefethen - 2011 |

3 | Consequences of viscous anisotropy in a deforming, two-phase aggregate: 1. governing equations and linearised analysis. - Katz, Takei - 2013 |

3 | Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust - Keller, May, et al. |

3 | Experimental quantification of permeability of partially molten mantle rock. Earth Plan. - Miller, Zhu, et al. - 2013 |

2 | An experimental study of pressure shadows in partially molten rocks - Qi, Zhao, et al. |

2 | Disequilibrium melting of a two phase multicomponent mantle. Geophys - Rudge, Bercovici, et al. |

1 | Generalized Bessel Functions of the First - Baricz |

1 | Viscous anisotropy of the partially molten mantle: theory and evidence from laboratory experiments. 2013. Abstract T42D-06 presented at 2013 Fall Meeting - Katz, Qi, et al. |

1 | Base-state stress-driven melt segregation in torsion and extrusion experiments on partially molten rocks - Qi, Kohlstedt, et al. |

1 |
Flow in deformable porous-media. Part 1. Simple analysis
- Spiegelman
- 1993
(Show Context)
Citation Context ... H, R = 1 H √ (rξ + 4 3 )η0K0 ηL . (8) Dynamic pressure perturbations cause variations in melt flux (and hence (de)compaction) over a length scale that is less than or equal to the compaction length [=-=Spiegelman, 1993-=-]. Hence we expect the compaction length to influence the scale of emergent features in the solution. The governing equations, expressed in terms of non-dimensional quantities, are ∂φ ∂τ = ∇ · [(1− φ)... |