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Showing 1 to 12 of 12 for “"symmetry reduction"”.
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Symbolic software for symmetry reduction and computation of invariant solutions of differential equations
… of a Maple-based, symbolic software package for symmetry reduction of differential equations and computation of symmetry-invariant solutions. The package developed in the current thesis is compatible with and can be viewed as an extension of the package GeM for symbolic symmetry analysis, …
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Reduction methods in semidefinite and conic optimization
… that detect and exploit useful structure-such as symmetry, sparsity, or degeneracy-is one research topic. Such methods include facial and symmetry reduction, which have been successful in several applications, often reducing solve time by orders of magnitude. Nevertheless, theoretical and …
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Automatic techniques for detecting and exploiting symmetry in model checking
… Current techniques can handle limited kinds of symmetry, e.g. full symmetry between identical components in a concurrent system. They avoid the problem of automatic symmetry detection by requiring the user to specify the presence of symmetry in a model (explicitly, or by annotating the …
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Optical and Plasmonic Properties of Metallic Tip /Surface Junctions
Reducing symmetry of plasmonic nanostructures allows more in-depth engineering for plasmonic systems to support a range of optical phenomena prohibited by traditional symmetric systems. Symmetry reduction allows for nanoscale control of the near-field and far-field electric and magnetic resonances …
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Optimal control problems on lie groups with symmetry breaking cost functions
… lower than the original system. We apply these symmetry reduction techniques to optimal control problems on Lie groups for which the associated Hamiltonian function is left-invariant under the action of a subgroup of the Lie group. Necessary conditions for optimality are derived by applying …
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Beyond qubits: Quantum optimization and lattice gauge theories in a qudit framework
… and how counterdiabatic driving, enhanced by symmetry reduction, improves variational performance for qudit-based algorithms. We additionally study the noise robustness of variational algorithms on real hardware, and investigate how nonstabilizerness builds up and relates to optimization …
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Size-binary Zincblende: A Colloidal Approach to Omnidirectional Photonic Bandgaps
… (30.7%, ε = 16) and inverse opal (8.0%, ε = 16). Symmetry reduction at the lattice points of the diamond structure (via a basis of spheres of different size) opens a bandgap between the fifth and sixth bands in the direct structure. This gap has only previously been reported in a handful of …
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Analytical approach to unidirectional flow of non-Newtonian fluids of differential type
… for the third-grade fluid are derived using symmetry reduction and new modified homotopy perturbation method (HPM). For a horizontal channel, a new analytical algorithm to solve transient flow of third-grade fluid generated by an oscillating upper wall has been proposed. A new approach of the …
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Modal Analysis of General Cyclically Symmetric Systems with Applications to Multi-Stage Structures
… proved to have properties related to the cyclic symmetry. These symmetry-related properties are used to prove the modal properties of general cyclically symmetric systems. Only three types of modes can exist: substructure modes, translational-tilting modes, and rotational-axial modes. Each mode …
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Fast and optimal pathfinding
… or symmetries, of the same path exist. Symmetry slows down search by forcing otherwise performant algorithms to waste time considering many equivalent states. We speed things up by developing new online and offline symmetry-breaking techniques that eliminate a large number of symmetric …
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Fast and optimal pathfinding
… or symmetries, of the same path exist. Symmetry slows down search by forcing otherwise performant algorithms to waste time considering many equivalent states. We speed things up by developing new online and offline symmetry-breaking techniques that eliminate a large number of symmetric …
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Vortices, Painlevé integrability and projective geometry
… recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a …