Understanding Non-Equilibrium Thermodynamics - Springer 2008 Episode 6 potx

... chemical reactions in the Brusselator is the following A k 1 −→X, (6. 65a) 2X + Y k 2 −→3X, (6. 65b) B + X k 3 −→Y + D, (6. 65c) X k 4 −→E, (6. 65d) the four steps are assumed to be irreversible which is ... solutions (6. 1.11) and (6. 1.12) in (6. 1.8) and (6. 1.9) leads to the following amplitude differential equations (D 2 − k 2 )(D 2 − k 2 − σ)W = Ra k 2 Θ, (6. 1.13) (D 2 − k 2 − σPr)Θ = −...

Ngày tải lên: 12/08/2014, 08:22

... ¯µ k ∂m l     ≥ 0. (1 .66 ) The criteria (1 .65 ) or (1 .66 ) are referred to as the conditions of stability with respect to diffusion. The first inequality (1 .66 ) indicates that the stabil- ity of equilibrium ... and tools from equilibrium thermodynamics but transposed at a local scale because non-equilibrium states are usually in- homogeneous. The objective is to cope with non-equi...

Ngày tải lên: 12/08/2014, 08:22

... of variational principles in non-equilibrium thermodynamics. 2.5.1 Minimum Entropy Production Principle Consider a non-equilibrium process, for instance heat conduction or thermod- iffusion taking place ... here for the sake of clarity: ρ dρ −1 dt = ∇·v, (2 .63 ) ρ dv dt = −∇ ·P + ρF , (2 .64 ) ρ du dt = −∇ ·q −P : V. (2 .65 ) 66 2 Classical Irreversible Thermodynamics rod. (b) Determ...

Ngày tải lên: 12/08/2014, 08:22

... − L VD L VV = −  J D J V  ∆π=0 , (3 .62 ) or, in terms of the velocities introduced in relation (3. 56) ,  2v 2 v 1 + v 2  ∆π=0 =1− r. (3 .63 ) For an ideal semi-permeable membrane (r = 1), one has ... Machines −1.0 −0.8 −0 .6 −0.4 −0.2 0.0 0.0 0.2 0.4 0 .6 0.8 1.0 1.00 0.99 0.95 0.90 0.80 0.70 η Zx 0 .60 Fig. 4.2 Efficiency η vs. the parameter Zx for several values of the coupling coe...

Ngày tải lên: 12/08/2014, 08:22

... curves (Ma) c (Bi)andk c (Bi). 6. 6 Miscellaneous Examples of Pattern Formation 171 Fig. 6. 16 Salt fingers (from Vidal et al. 1994) Fig. 6. 17 Temperature distributions in the ballast resistor 6. 6.2 Patterns in Electricity 6. 6.2.1 ... same above the second threshold 6. 6.3 Dendritic Pattern Formation Formation of dendrites, i.e. tree-like or snowflake-like structures as shown in Fig....

Ngày tải lên: 12/08/2014, 08:22

... connection be- tween dynamics and thermodynamics should be underlined. EIT enlarges the range of applicability of non-equilibrium thermodynamics to a vast do- main of phenomena where memory, non-local, ... 7.00 (c 0 /v p ) (Fourier–Newton–Stokes) 0.40 0. 26 0.19 0.13 0.10 0.07 (c 0 /v p ) (Maxwell–Cattaneo) 0.52 0.43 0.44 0.47 0.48 0.49 (c 0 /v p ) (experimental) 0.51 0. 46 0.50 0. 46...

Ngày tải lên: 12/08/2014, 08:22

... the entropy flux (9 .65 ) is given by the usual expression J s = q/θ. (9 .68 ) Moreover, in virtue of (9 .66 a) and (9 .66 b), one has dθ −1 ≡ dϕ = ∂ϕ ∂u du + ∂ϕ ∂q 2 dq 2 = γda, (9 .69 ) a result that will ... results (9 .62 ) and (9 .63 ), the entropy inequality (9 .61 ) reduces to the residual inequality bΛ 1 · q ≥ 0. (9 .64 ) 240 9 Rational Thermodynamics the entropy flux, see extended ir...

Ngày tải lên: 12/08/2014, 08:22

... 24, 27, 36, 267 , 270, 2 76, 281 hexagonal patterns, 1 56 history, 237, 238, 240, 241 Hopf bifurcation, 138 hydrodynamics, 38, 60 , 62 , 63 , 1 36, 162 , 167 , 173, 208, 210, 247, 248, 251, 266 – 268 , 270, ... and 303 Index 323 Fourier’s law, 38, 56, 65 , 66 , 68 , 76, 181–183, 185, 187, 190, 193, 195, 211, 254, 257 Fourier’s law with, 194 frame-indifference, 201, 2 26, 242, 247,...

Ngày tải lên: 12/08/2014, 08:22

Ngày tải lên: 12/08/2014, 08:22

... D i sc. a 0C oop . − 900 1 5 6. 48* 0.9704 # 0.1 5 02 0.92 26 4 ( 320. 6 4) (0.014) (0.102) 0 Non- C oop. − 900 − 26 5 .17* 0. 962 8 # 0.14 16 0.94 63 0 ( 2 06. 5 3) (0.009) (0.071) 1 Coo p. − 9 00 − 62 3.31* 0. 99 01 ... Coo p . 36 19 12 $6. 31 $0 $23.0 9 ( $18.93 )( $0 )( $69 . 26 ) 0 Non-coop. 24 2 7 $ 12.92 $ 0 $ 42.99 ($ 38.77) ( $ 1 .60 ) ( $ 87 .61 ) 1 Coop. 36 9 12 $ 11...

Ngày tải lên: 06/08/2014, 20:21