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17 May 2006: 4Laboratoire de Physique Statistique, UMR 8550 CNRS, Ecole Normale Supérieure, 24,rue Lhomond, 75231 Paris cédex 05, France. ... 1. 2. –12. 3. 10. G. I. IG. (ν. /g2 ). 1/3. ̂. H(g/ν2)1/3 Ĥ. ̂ (Ĥ/)10/3Π15/9. Π15/24. Π15/96. Π1–1/6

9 Mar 2004: 0.9993 4.81 0 1.52 – –S3 0 45.8 79.80 0.574 1.375 1.0192 0.9996 19.24 0 1.36 – –S7 0 45.2 ... 19.24 0.0282 1.37 550 0.100R10 0.0500 46.3 79.97 0.579 1.390 1.0107 1.0007 9.80 0.0551 0.99 450

26 Mar 2023: 1r. rrp1r. n2. r2p1 = 0. (4.24). The solution, finite at r = 0, is p1(r, t) = k(t)rn, so that now p(r, θ, t) = p0(r, t)

7 Aug 2008: Uc ={. (3 2M)1/4β, for M 2D 3/24/3 3,(3/24/3 2D M.

11 Apr 2013: 2 2 2. 24/.467. 35.1 Introduction.

30 May 2006: Stability of a large gas bubble rising through liquid 417. 24. ... 1. oo 1.712 1.26 1.42 1.10 1.24. 13.61 1.200 0.79 1.06 1.

1 Jun 2006: 0.01 (for Ra, = lo@), convection continues in the melt until t = 0.24, by which time the system is about 40% solidified.

18 May 2017: on the y-axis,with τ of (a) 0.085, (b) 0.24, (c) 0.39, (d) 0.55, (e) 0.71, ( f ) 0.87, (g) 1.00 and ... mUmH. 3F10 , (4.23). q= UmH2. sin2/3 θE2/3eq D1F1/30 , (4.24).

10 Mar 2011: Hr XNn1. dhndx. dxnd1. XNn1. hn! 3XNn1. h3n. 24. 35, ð61aÞ.

26 Apr 2006: e-mail: grae@esc.cam.ac.uk; heh1@esc.cam.ac.uk. (Received 24 July and in revised form 27 March 1997). ... 24/3λRa1/3 (3.1). between the Nusselt number Nu for thermal convection in the liquid region and theRayleigh number.

14 Apr 2010: 6νq0g. )1/3 ( gg′. )2/3(2.24). and St = 2q0(. 6νq0g. )2/3 ( gg′.

5 Jan 2006: The experimentswere generally left to run for 24 hours, but heat loss to the laboratory became asignificant factor after roughly 10 hours. ... dy. dτ= (1 θ). (1 y)(1 Λθ). (3.24). y(τ = 0) = 1, (3.25).

15 Sep 2006: There is also. [Journal of Petrologf, Vol. 29, P t n 3, pp 599-«24, 1988] Oxford Umvcroty Prcu 19S8. ... FJH,. (24). We determined numerical solutions of (15)—(18) in addition to either (19)—(23) or merely (24).The differences were negligible.

30 May 2006: 24-2. 740 J. Y. Holyer and H. E. Huppert. model for energy dissipation. ... The wavelengths given by (6.3) and (6.4) are 6.1 cm on the lower interface and 24-1 cm on the upper interface.

1 Jun 2006: 24 M. G. Worster and R. C. Kerr. with most metals, it has a low entropy of fusion and forms highly branched, rather than prism-like, crystals.

24 Apr 2014: The approximate constancy of the late-time first-ordercorrection (E 1.38t1/2) 0.24 is due to the adjustment of the radial flow near thesource towards unidirectional flow over a

26 Mar 2023: 4𝜉3. 𝜕𝜙𝜕𝜉. 𝜂3𝜕𝜙𝜕𝜂. = 1𝛤𝜉. 𝜕(𝜉𝜙𝑣𝑟)𝜕𝜉. 𝜕(𝜙𝑣𝑧)𝜕𝜂. (24). Integrating from 𝑤 to 𝑤 with respect to 𝜂, leaving details to Appendix A for brevity, we obtain.

1 Jun 2006: I. / / ,. /. /. 4 8. 36. (TI1 24. I 32. / / / ’. I. -. -_ -._ - _ -.-__ ---_ -.__. 4.5 0 2 4 6 8 10. %. ... 1 4 8 Unstable. It. / / ,. /. /. 36. (TI1 24. 0 0.2 0.4 0.6 6. FIGURE 5. The critical Rayleigh numbers as they vary with the dimensionless

6 May 2010: Sd 75 0.24. V 1 20 200 V a 44 0.20 V 2 60 100 V b 75 0.25V 3 40 150 V 4 40 62.

14 Feb 2013: 24] An upscaled model for convective dissolution canthen be incorporated into models such as equation (1) byintroducing a constant loss or sink term [Gasda et al.,2011 ; MacMinn et al., 2011],.

10 Mar 2009: Conservation of volume. v = 0. (2.24)2. Momentum balance. ρDv. Dt= p (ρ ρb)g ẑ μ2v, (2.25). ... After some algebra and use of(2.24), we obtain. ρD. Dt. [1.

25 Jan 2007: 0.01 (for Ra, = lo@), convection continues in the melt until t = 0.24, by which time the system is about 40% solidified.

9 Feb 2004: 5H1 2(H0U1)′=0, (24)3U1 H ′1 H ′0ϕ1. 1. 2H0ϕ. ′1=0, (25)ϕ1=2720. ... 4y2)], (38). and then subsequent substitution into (24) yields a second-order differential equation forH1(y), namely(1.

29 Jul 2010: JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B9, PAGES 15,891-15,901, SEPTEMBER 10, 1993. The Crystallization of Lava Lakes. M. GRAE WORSTER AND HERBERT E. HUPPERT. Institute of Theoretical Geophysics, Department of Applied Mathematics and

9 Mar 2004: e-mail: grae@esc.cam.ac.uk; heh1@esc.cam.ac.uk. (Received 24 July and in revised form 27 March 1997). ... 24/3λRa1/3 (3.1). between the Nusselt number Nu for thermal convection in the liquid region and theRayleigh number.

9 Mar 2004: Received 24 April 2000 and in revised form 7 December 2000).

21 Dec 2012: Carbon budgets have been introduced to capemissions [24] (Figure 1). The power sector is the single largest emitter. ... and are designed to capemissions [24] (green line).

16 Jan 2007: J. Fluid M e c h. (1990). vol. 212, p p. 209-240. Printed in Great Britain 209. The fluid mechanics of solidification. By H E R B E R T E. H U P P E R T Institute of Theoretical Geophysics and Department of Applied Mathematics and Theoretical.

30 Jul 2013: 24). The perturbation equations are given, at O(βN), by. 1. η.

16 Jul 2010: nly. 24 HUPPERT & SPARKS. compositional film is to substitute the film thickness into the compositional Rayleigh number, which can be re-expressed as. ... 24. I. A. -.:---n;o • • Pl AA GIOCl A S E.

18 Jul 2014: Email address for correspondence: ssp23@cam.ac.uk. first published online 24 March 2014). ... upper fluid to speeds above those induced by the background-pressure-driven flow (3.24) alone.

23 Dec 2021: 2πϕ r0. 0. h00. s0[h0(r), z]dzr dr =V, (2.24). where s0[h0(r), z] is the initial saturation distribution. ... By applying scaling analysis to (2.14) and (2.24) and rearranging, we find thefollowing relations between the dimensions of radius, height,

14 Sep 2009: casting [17,24]) to natural (e.g. for-. All rights reserved. Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, United Kingdom.

5 May 2006: We areinterested in cases with small C2H because otherwise the distance of propagation issmall, see (3.24), and no real gravity current appears. ... Using the approximations (3.19)–(3.24), we find: (i) for S < 1.

26 Apr 2006: Ẇφ̇′. )=(. R 1+ S/C SVC1 V. )(Wφ′. ), (24). whereφ′ = φφe. ... The characteristics of the eigenso-lutions of Equation 24 are shown in Figure 6, the topology of which is preservedby the full system of Equations 9–12 (Anderson & Worster 1996

19 Jul 2010: JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B9, PAGES 15,891-15,901, SEPTEMBER 10, 1993. The Crystallization of Lava Lakes. M. GRAE WORSTER AND HERBERT E. HUPPERT. Institute of Theoretical Geophysics, Department of Applied Mathematics and

9 Mar 2004: 6 1.9 1.7ID 20 26.5 1.4 1.3IE 23 20 3.9 10.5IF 12 18 4.0 11.25IG 24 20 4.1 11.5. ... IIA 23 26 5.22 2.62 29 48IIB 17.5 24 5.36 2.68 30 48IIC 15 21 5.94 2.01 25 24IID 28 15 7.02

24 Sep 2009: J. Fluid Mech. (2009), vol. 631, pp. 419–440. c 2009 Cambridge University Pressdoi:10.1017/S0022112009007174 Printed in the United Kingdom. 419. Particulate gravity currents alongV-shaped valleys. JOE J. MONAGHAN1†, CATHERINE MÉRIEUX1,HERBERT E

30 May 2006: University of Cambridge, Silver Street, Cambridge CB3 9EW, UK. (Received 17 October 1994 and in revised form 24 May 1995). ... Each freezing experiment took on the order of 24 hours, after which the solid crystalline block was cut up into pieces and the

9 Mar 2004: Consequently, the relationships between the variables on the characteristics with. 24 M. ... v = r[1. (rinitr. )2]. (2.24). In particular, at the nose.

26 Mar 2023: 1. IntroductionGeophysical granular flows driven by gravity occur frequently on the Earth's surface, as a result of climatic, tectonic, or volcanic events (Delannay et  al., 2017). Granular flows contribute significantly to the global sediment

18 May 2017: Note that (2.24) implies thatui is independent of z in the interior of each isopycnal layer, hi1 < z < hi. ... that theflow is independent of the vertical coordinate z in the interior of each layer, ui/z=0,as implied by (2.24).

27 Apr 2006: Volcanol. Geothermal Res. 24, 1-24, 1985. 7 R.H. Nilson, A.R. McBirney and B.H. ... Volcanol. Geothermal Res. 24, 25-54, 1985. 8 I.H. Campbell and J.S.

5 May 2006: T = T(c) 5.176 c 13.27 c2 24.16 c3 75.52 c4 (2.1)for 0 < c < 0.7, where T (. C) is the temperature of the freezing ... 1:47, 2:14, 2:22, 2:49, 2:58, 3:24, 3:33, 3:59, 5:16, 5:43, 6:52, 7:46,.

27 Apr 2006: Once the local Rayleigh number based on 8 exceeds a critical value, as determined by Smith [24] for example, the boundary layer breaks down and the magma begins to convect.

27 Apr 2006: f_0q(z,) d z ' = A 2. (3.24) The functional form for the source strength q(z') is d e t e r m i n e d by matching

30 Jun 2010: J. Fluid Mech. (1979), vol. 95, part 3, p p. 431-464. Printed i n Great Britain 43 1. On heating a stable salinity gradient from below. By H E R B E R T E. H U P P E R T A N D P. F. L I N D E N Department of Applied Mathematics and Theoretical

15 Jul 2010: This length has been calculated as several hundred kilometres for flows travelling with velocities of order 1 m / s in dykes a few metres wide [19,24]. ... 0 a n d K / Z r = 24.

9 Mar 2004: J. Fluid Mech. (2003), vol. 497, pp. 167–199. c 2003 Cambridge University PressDOI: 10.1017/S002211200300661X Printed in the United Kingdom. 167. Solidification and compositional convectionof a ternary alloy. By ANDREW F. THOMPSON†, HERBERT E.

19 Jul 2010: Komatiites I: Eruption and Flow. by HERBERT E. HUPPERT1 AND R. STEPHEN J. SPARKS2. 1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Silver Street, Cambridge CB3 9EW. 2Department of Earth Sciences, University of