The Experts below are selected from a list of 6 Experts worldwide ranked by ideXlab platform
Robert Feger - One of the best experts on this subject based on the ideXlab platform.
-
lieart a mathematica application for lie algebras and representation theory
Computer Physics Communications, 2015Co-Authors: Robert Feger, Thomas W KephartAbstract:Abstract We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART ( Lie A lgebras and R epresentation T heory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15. Program summary Program Title: LieART 2.0 CPC Library link to program files: http://dx.doi.org/10.17632/8vm7j67bwt.1 Licensing provisions: GNU Lesser General Public License Programming language: Mathematica External routines/libraries: Wolfram Mathematica 8–12 Nature of problem: The use of Lie algebras and their representations is widespread in physics, especially in particle physics. The description of nature in terms of gauge theories requires the assignment of fields to representations of compact Lie groups and their Lie algebras. Mass and interaction terms in the Lagrangian give rise to the need for computing tensor products of representations of Lie algebras. The mechanism of spontaneous symmetry breaking leads to the application of subalgebra decomposition. This computer code was designed for the purpose of Grand Unified Theory (GUT) model building, (where compact Lie groups beyond the U ( 1 ) , SU ( 2 ) and SU ( 3 ) of the Standard Model of particle physics are needed), but it has found use in a variety of other applications. Tensor product decomposition and subalgebra decomposition have been implemented for all classical Lie groups SU ( N ) , SO ( N ) and Sp ( 2 N ) and all the exceptional groups E 6 , E 7 , E 8 , F 4 and G 2 . This includes both regular and irregular (special) subgroup decomposition of all Lie groups up through rank 15, and many more. Solution method: LieART generates the weight system of an irreducible representation (irrep) of a Lie algebra by exploiting the Weyl reflection groups, which is inherent in all simple Lie algebras. Tensor products are computed by the application of Klimyk’s formula, except for SU ( N ) ’s, where the Young-tableaux algorithm is used. Subalgebra decomposition of SU ( N ) ’s are performed by projection matrices, which are generated from an algorithm to determine maximal subalgebras as originally developed by Dynkin [1] , [2] . We generate projection matrices by the Dynkin procedure, i.e., removing dots from the Dynkin or extended Dynkin diagram, for regular subalgebras, and we implement explicit projection matrices for special subalgebras. Restrictions: Internally irreps are represented by their unique Dynkin label. LieART’s default behavior in Traditionalform is to print the dimensional name, which is the labeling preferred by physicist. Most Lie algebras can have more than one irrep of the same dimension and different irreps with the same dimension are usually distinguished by one or more primes (e.g. 175 and 175 ′ of A 4 ). To determine the need for one or more primes of an irrep a brute-force loop over other irreps must be performed to search for irreps with the same dimensionality. Since Lie algebras have an infinite number of irreps, this loop must be cut off, which is done by limiting the maximum Dynkin digit in the loop. In rare cases for irreps of high dimensionality in high-rank algebras the used cutoff is too low and the assignment of primes is incorrect. However, this only affects the display of the irrep. All computations involving this irrep are correct, since the internal unique representation of Dynkin labels is used.
Thomas W Kephart - One of the best experts on this subject based on the ideXlab platform.
-
lieart a mathematica application for lie algebras and representation theory
Computer Physics Communications, 2015Co-Authors: Robert Feger, Thomas W KephartAbstract:Abstract We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART ( Lie A lgebras and R epresentation T heory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15. Program summary Program Title: LieART 2.0 CPC Library link to program files: http://dx.doi.org/10.17632/8vm7j67bwt.1 Licensing provisions: GNU Lesser General Public License Programming language: Mathematica External routines/libraries: Wolfram Mathematica 8–12 Nature of problem: The use of Lie algebras and their representations is widespread in physics, especially in particle physics. The description of nature in terms of gauge theories requires the assignment of fields to representations of compact Lie groups and their Lie algebras. Mass and interaction terms in the Lagrangian give rise to the need for computing tensor products of representations of Lie algebras. The mechanism of spontaneous symmetry breaking leads to the application of subalgebra decomposition. This computer code was designed for the purpose of Grand Unified Theory (GUT) model building, (where compact Lie groups beyond the U ( 1 ) , SU ( 2 ) and SU ( 3 ) of the Standard Model of particle physics are needed), but it has found use in a variety of other applications. Tensor product decomposition and subalgebra decomposition have been implemented for all classical Lie groups SU ( N ) , SO ( N ) and Sp ( 2 N ) and all the exceptional groups E 6 , E 7 , E 8 , F 4 and G 2 . This includes both regular and irregular (special) subgroup decomposition of all Lie groups up through rank 15, and many more. Solution method: LieART generates the weight system of an irreducible representation (irrep) of a Lie algebra by exploiting the Weyl reflection groups, which is inherent in all simple Lie algebras. Tensor products are computed by the application of Klimyk’s formula, except for SU ( N ) ’s, where the Young-tableaux algorithm is used. Subalgebra decomposition of SU ( N ) ’s are performed by projection matrices, which are generated from an algorithm to determine maximal subalgebras as originally developed by Dynkin [1] , [2] . We generate projection matrices by the Dynkin procedure, i.e., removing dots from the Dynkin or extended Dynkin diagram, for regular subalgebras, and we implement explicit projection matrices for special subalgebras. Restrictions: Internally irreps are represented by their unique Dynkin label. LieART’s default behavior in Traditionalform is to print the dimensional name, which is the labeling preferred by physicist. Most Lie algebras can have more than one irrep of the same dimension and different irreps with the same dimension are usually distinguished by one or more primes (e.g. 175 and 175 ′ of A 4 ). To determine the need for one or more primes of an irrep a brute-force loop over other irreps must be performed to search for irreps with the same dimensionality. Since Lie algebras have an infinite number of irreps, this loop must be cut off, which is done by limiting the maximum Dynkin digit in the loop. In rare cases for irreps of high dimensionality in high-rank algebras the used cutoff is too low and the assignment of primes is incorrect. However, this only affects the display of the irrep. All computations involving this irrep are correct, since the internal unique representation of Dynkin labels is used.
Iris D Tommelein - One of the best experts on this subject based on the ideXlab platform.
-
just in time concrete delivery mapping alternatives for vertical supply chain integration
7th Annual Conference of the International Group for Lean Construction, 1999Co-Authors: Iris D TommeleinAbstract:This paper explains concepts underlying a just-in-time production system. Just-in-time production systems as implemented by Toyota are pull systems in which ‘kanban’ convey the need to replenish the right inventory at the right time and in the right amount. In this paper, symbols from manufacturing are introduced to map resource flows in order to help distinguish traditionalfrom lean production processes. These symbols are then applied to construction. Ready-mix concrete provides a prototypical example of a just-in-time construction process. Ready-mix concrete is a perishable commodity, batched to specifications upon customer demand. This makes just-in-time delivery necessary. Based on data from industry case studies, alternative forms of vertical supply chain integration were investigated. The most common one is where the batch plant also delivers the mix to the contractor’s project site. An alternative is for the contractor to haul the mix from the batch plant to the project site with their own revolving-drum trucks. One alternative is favored over the other depending on the amount of control the contractor wants in terms of on-time site delivery of concrete and the variability in the contractor’s demand for concrete project after project. Insights can be gained from these two examples on how the construction industry has adopted a just-in-time production system for at least one part of the concrete supply chain. The examples provided will help the reader think through issues pertaining to the need for having information, materials, and time buffers at strategic locations in construction processes.
