Flux closure

B., Zhang, M. and Yu, S.H. (2008) High yield synthesis of bracelet-like hydrophilic Ni-Co magnetic alloy flux-closure nanorings. Journal of the American Chemical Society, 130 (35), 11606-11607. 

Fig. 9.8 Idealized magnetic domain configurations (a) antiparallel domains (b) flux closure domains.

For shape anisotropy, Kx = ju0(1-3D)Ms2/4, where D is the demagnetizing factor (D = 0 for long cylinders, D= 1/3 for spheres, and D = 1 for plates) [56]. It is important to note that shape anisotropy is limited to very small particles ( 2.2). In large particles, shape anisotropy is destroyed by internal flux closure, indicated at the bottom of Fig. 5(a). 

Note than typical domain-wall widths are much smaller than the domains themselves. When the size of a magnetic particle is smaller than the domain-wall width Sa, as encountered for example in small soft-magnetic nanodots, then the distinction between domains and domain walls blurrs, and the determination of the micromagnetic spin structure requires additional considerations [102], One example is curling-type flux-closure or vortex states. 

Comparison of Eqs. (10) and (11) yields the radius Rcoh for the transition from coherent rotation to curling. For R < i coh, the exchange energy dominates, and the nucleation is realized by coherent rotation, whereas for R > i coh the nucleation behavior is dominated by flux closure and realized by curling. For spheres and wires (cylinders), one obtains Rcoh = 5.099 /ex and... 

An important application of soft materials is inductive and magnetoresistive recording heads [9]. The function of inductive head materials is to realize flux closure for reading and writing on recording media. Typical... 

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that if an inconsistent diffusive flux closure like the Wilke equation is adopted (i.e., the sum of the diffusive mass fluxes is not necessarily equal to zero) instead, the sum of the species mass balances does not exactly coincide with the mixture continuity equation. 

By use of the Fickian mole diffusion flux closure the Pick s second law is obtained ... 

Tripp SL, Dunin-Borkowski RE, Wei A (2003) Flux closure in self-assembled cobalt nanoptir-ticle rings. Angew Chem Int Ed 42(45) 5591-5593... 

Fig. 34.17 Self-assembled Co NP ring imaged by brightfield TEM (center) and by off-axis electron holography (top) bar = 50 nm. The latter reveals bistable flux-closure (FC) states, polarized either CW (/e ) or CCW (right). FC polarization can be switched by applying an out-of-plane magnetic pulse with a peak strength of 2-4 kOe. Line-bond representations for the Co NP ring and FC states are shown below for clarity [40] (Reprinted with permission from the Royal Society of Chemistry)...

More recently, Solsvik and Jakobsen [140] performed a numerical study comparing several closures for mass diffusion fluxes of multicomponent gas mixtures the Wilke, Maxwell-Stefan, dusty gas, and Wilke-Bosanquet models, on the level of the single catalyst pellet and the impacts of the mass diffusion flux closures employed for the pellet, on the reactor performance. For this investigation, the methanol synthesis operated in a fixed packed bed reactor was the chemical process adopted. In the mathematical modeling study of a novel combined catalyst/sorbent pellet. Rout et al. [121] investigated the performance of the sorption-enhanced steam methane reforming (SE-SMR) process at the level of a single pellet. Different closures... 

Table 23 Diffusion flux closures based on the mass average velocity definition ...

Solsvik J, Jakobsen HA (2012) A survey of multicomponent mass diffusion flux closures for... 

Granular Transport Coefficient, Source and Flux Closures... 

The success in deriving the Maxwellian type macroscopic transport equations and in obtaining appropriate source and flux closures based on the kinetic theory of granular flow relies heavily on the knowledge about the distribution function involved. In principle, for reactive systems the single particle distribution function should satisfy... 

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