Flux control in networks of diffusion paths

Zhmoginov, Andrey; Fisch, Nathaniel J.

doi:10.1016/j.physleta.2008.06.068

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…1. More general configurations of diffusion paths, including intersecting networks of paths, were considered [22], however, the highest α-channeling efficiency was demonstrated for the system of paths depicted on Fig. 1.…”

Section: Alpha-channeling In Mirror Machinesmentioning

confidence: 99%

Feasibility Studies of Alpha-Channeling in Mirror Machines

Fisch¹

2010

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The linear magnetic trap is an attractive concept both for fusion reactors and for other plasma applications due to its relative engineering simplicity and high-beta operation. Applying the α-channeling technique to linear traps, such as mirror machines, can benefit this concept by efficiently redirecting α particle energy to fuel ion heating or by otherwise sustaining plasma confinement, thus increasing the effective fusion reactivity. To identify waves suitable for α-channeling a rough optimization of the energy extraction rate with respect to the wave parameters is performed. After the optimal regime is identified, a systematic search for modes with similar parameters in mirror plasmas is performed, assuming quasi-longitudinal or quasi-transverse wave propagation. Several modes suitable for α particle energy extraction are identified for both reactor designs and for proofof-principle experiments.

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Section: Alpha-channeling In Mirror Machinesmentioning

confidence: 99%

Feasibility Studies of Alpha-Channeling in Mirror Machines

Fisch¹

2010

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“…Other network problems can be defined which capture the spatial element. 21 A different problem on P 5 arises in the context of maximizing the possible concentration of atoms in a specific state in an ensemble of atoms of helium. Fig.…”

Section: Introductionmentioning

confidence: 99%

On extreme points of the diffusion polytope

Hay

Schiff

Fisch

2017

Physica A: Statistical Mechanics and its Applications

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We consider a class of diffusion problems defined on simple graphs in which the populations at any two vertices may be averaged if they are connected by an edge. The diffusion polytope is the convex hull of the set of population vectors attainable using finite sequences of these operations. A number of physical problems have linear programming solutions taking the diffusion polytope as the feasible region, e.g. the free energy that can be removed from plasma using waves, so there is a need to describe and enumerate its extreme points. We review known results for the case of the complete graph K n , and study a variety of problems for the path graph P n and the cyclic graph C n . We describe the different kinds of extreme points that arise, and identify the diffusion polytope in a number of simple cases. In the case of increasing initial populations on P n the diffusion polytope is topologically an n-dimensional hypercube.

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“…Meanwhile, by the analogy between fluid flow and electrical circuits, Zhmoginov and Fisch [9] obtained an optimal exit flux arrangement in networks of intersecting diffusion domains with a special form of thin paths. Also, inspired by the fractal pattern of mammalian circulatory and respiratory systems [10], Chen and Cheng [11] designed a fractal branching channel conformation to cool down electronic chips, exhibiting a greater heat transfer capability yet requiring a lower pumping power, compared to the traditional parallel network.…”

Section: Introductionmentioning

confidence: 99%

Process intensification

Glaser

2012

Clean Techn Environ Policy

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a b s t r a c tOptimization of a fluid distributing tube network plays a critical role in the operation efficiency and energy conservation of a cooling system. In this paper, we analyze the effect of multi-dimension on the structure of a fluid distributing tube network for cooling heat-generating, and then seek the optimal fluid structure with minimal pressure drop for a given total volume of the tube network. The theoretical results show that the pressure drop of a laminar flow in the tube network reaches the minimum when the cubic value of the parent tube diameter equals to the sum of those of the daughter tube diameter, consistent with Murray's law. Furthermore, it is advantageous to have a higher dimension structure in network arrangement when the number of heat generation units increases, i.e., network performance improves by adopting a two-dimensional and even three-dimensional format as the number of units grows.

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Flux control in networks of diffusion paths

Cited by 5 publications

References 20 publications

Feasibility Studies of Alpha-Channeling in Mirror Machines

Feasibility Studies of Alpha-Channeling in Mirror Machines

On extreme points of the diffusion polytope

Process intensification

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