Six-dimensional space

A six-dimensional space refers to a set of parameters that are explored in order to understand and control tasks in a given environment. These parameters include the task itself, the type of communication used, the number of robots involved, the number and mass of attractors, and the percentage of obstacle coverage. By exploring these parameters, researchers can gain a better understanding of how to optimize performance in a given task and environment.From: Coordination Theory and Collaboration Technology [2019]

Small-Strain Plasticity

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Published in Michael R. Gosz, Finite Element Method, 2017

Michael R. Gosz

For a given state of material deformation described by the yield stress and set of history variables, the yield condition can be thought of as a level surface in six-dimensional stress space. The level surface in stress space would correspond to the locus of points, σij, that satisfy equation (9.10). Unfortunately we are incapable of illustrating such a six-dimensional space.

Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems

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Published in Nuclear Science and Engineering, 2019

Luke R. Cornejo, Dmitriy Y. Anistratov, Kord Smith

The phase-space of neutron transport problems has high dimensionality. It includes the spatial position of the particle, its energy, and the direction of particle motion. In general, it is a six-dimensional space. To reduce the dimensionality of the problem and complexity of neutron transport simulations, various approximate methods have been developed. One group of neutron transport models is based on the P1 equations that belong to the family of the method of spherical harmonics also known as the PN method.2 In neutron transport theory it is common to formulate the Boltzmann equation for the neutron angular flux, which is the product of the distribution function and the particle speed. The P1 equations are defined for the first two moments of the neutron angular flux and hence of the distribution function. The moment equations are closed assuming that the angular flux linearly depends on the direction of particle motion. The P1 equations can be reduced to the neutron diffusion equation for the zeroth angular moment of the angular flux.

Six-dimensional space

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Small-Strain Plasticity

Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems