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Full-Text Articles in Physics
Machine-Assisted Discovery Of Integrable Symplectic Mappings, T. Zolkin, Y. Kharkov, S. Nagaitsev
Machine-Assisted Discovery Of Integrable Symplectic Mappings, T. Zolkin, Y. Kharkov, S. Nagaitsev
Physics Faculty Publications
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e., integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and ultradiscrete Painlevé equations. In total, …
Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova
Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova
Physics Faculty Publications
This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.
Local Effective Potential Theory: Nonuniqueness Of Potential And Wave Function, Viraht Sahni, Marlina Slamet, Xiao-Yin Pan
Local Effective Potential Theory: Nonuniqueness Of Potential And Wave Function, Viraht Sahni, Marlina Slamet, Xiao-Yin Pan
Physics Faculty Publications
In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT) electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and in the mapping to a model …
Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny
Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny
Physics Faculty Publications
Unusual microstructures of YBa2Cu3Ox (123) crystals have been observed. These structures have been shown to pass very high transport currents. A model of the solidification of 123 from a melt with Y2BaCuO5 (211) inclusions indicates that the stability of the 123 interface can depend on the sizes of the 211 inclusions. The observed formations are interpreted in the light of this instability.
Stability Of Growing Front Of Yba(2)Cu(3)O(X) Superconductor In The Presence Of Pt And Ceo(2) Additions, Gregory Kozlowski, Tom Svobodny
Stability Of Growing Front Of Yba(2)Cu(3)O(X) Superconductor In The Presence Of Pt And Ceo(2) Additions, Gregory Kozlowski, Tom Svobodny
Physics Faculty Publications
Distinctive microstructures of textured YBa2Cu3Ox (123) superconductors were examined by scanning electron microscopy and metallurgical microscopy. The samples were synthesized under a residual thermal gradient by using a modified melt textured growth on a Y2BaCuO5 (211) substrate. Also, the unidirectional solidification by a zone‐melting method was performed to fabricate 123 superconducting bars up to 12 cm long placed on the 211 substrate in the horizontal arrangement, with a growth rate R=0.5 mm/h and a temperature gradient of G=20 °C/cm (G/R=400 °C h/cm2). A ramping …