Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions

Structures composed of classical dipoles in higher-dimensional space present a unique opportunity to venture beyond the conventional paradigm of few-body or cluster physics. In this work, we consider the six convex regular polychora that exist in an Euclidean four-dimensional space as a theoretical...

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Main Authors: Orion Ciftja, Josep Batle, Mohamed Ahmed Hafez
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Nanomaterials
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Online Access:https://www.mdpi.com/2079-4991/15/10/771
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author Orion Ciftja
Josep Batle
Mohamed Ahmed Hafez
author_facet Orion Ciftja
Josep Batle
Mohamed Ahmed Hafez
author_sort Orion Ciftja
collection DOAJ
description Structures composed of classical dipoles in higher-dimensional space present a unique opportunity to venture beyond the conventional paradigm of few-body or cluster physics. In this work, we consider the six convex regular polychora that exist in an Euclidean four-dimensional space as a theoretical benchmark for hte investigation of dipolar systems in higher dimensions. The structures under consideration represent the four-dimensional counterparts of the well-known Platonic solids in three-dimensions. A dipole is placed in each vertex of the structure and is allowed to interact with the rest of the system via the usual dipole–dipole interaction generalized to the higher dimension. We use numerical tools to minimize the total interaction energy of the systems and observe that all six structures represent dipole clusters with a zero net dipole moment. The minimum energy is achieved for dipoles arranging themselves with orientations whose angles are commensurate or irrational fractions of the number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>.
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institution Kabale University
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spelling doaj-art-60889a9ba9e14deeaf6a975d6d1973012025-08-20T03:47:58ZengMDPI AGNanomaterials2079-49912025-05-01151077110.3390/nano15100771Convex Regular Polychora Nanocrystals with Dipole–Dipole InteractionsOrion Ciftja0Josep Batle1Mohamed Ahmed Hafez2Department of Physics, Prairie View A&M University, Prairie View, TX 77446, USADepartament de Física and Institut d’Aplicacions Computacionals de Codi Comunitari (IAC3), University of the Balearic Islands, E-07122 Palma de Mallorca, SpainDepartment of Civil Engineering, Faculty of Engineering, INTI International University, Nilai 71800, MalaysiaStructures composed of classical dipoles in higher-dimensional space present a unique opportunity to venture beyond the conventional paradigm of few-body or cluster physics. In this work, we consider the six convex regular polychora that exist in an Euclidean four-dimensional space as a theoretical benchmark for hte investigation of dipolar systems in higher dimensions. The structures under consideration represent the four-dimensional counterparts of the well-known Platonic solids in three-dimensions. A dipole is placed in each vertex of the structure and is allowed to interact with the rest of the system via the usual dipole–dipole interaction generalized to the higher dimension. We use numerical tools to minimize the total interaction energy of the systems and observe that all six structures represent dipole clusters with a zero net dipole moment. The minimum energy is achieved for dipoles arranging themselves with orientations whose angles are commensurate or irrational fractions of the number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>.https://www.mdpi.com/2079-4991/15/10/771dipole–dipole interactionequilibrium configurationPlatonic solidsregular polychora
spellingShingle Orion Ciftja
Josep Batle
Mohamed Ahmed Hafez
Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions
Nanomaterials
dipole–dipole interaction
equilibrium configuration
Platonic solids
regular polychora
title Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions
title_full Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions
title_fullStr Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions
title_full_unstemmed Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions
title_short Convex Regular Polychora Nanocrystals with Dipole–Dipole Interactions
title_sort convex regular polychora nanocrystals with dipole dipole interactions
topic dipole–dipole interaction
equilibrium configuration
Platonic solids
regular polychora
url https://www.mdpi.com/2079-4991/15/10/771
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AT josepbatle convexregularpolychorananocrystalswithdipoledipoleinteractions
AT mohamedahmedhafez convexregularpolychorananocrystalswithdipoledipoleinteractions