[{"has_accepted_license":"1","publication_status":"epub_ahead","OA_type":"hybrid","scopus_import":"1","author":[{"id":"5eb8629e-15b2-11ec-abd3-e6f3e5e01f32","last_name":"Hübl","full_name":"Hübl, Maximilian","first_name":"Maximilian"},{"last_name":"Videbæk","first_name":"Thomas E.","full_name":"Videbæk, Thomas E."},{"full_name":"Hayakawa, Daichi","first_name":"Daichi","last_name":"Hayakawa"},{"last_name":"Rogers","full_name":"Rogers, W. Benjamin","first_name":"W. Benjamin"},{"first_name":"Carl Peter","full_name":"Goodrich, Carl Peter","last_name":"Goodrich","orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","OA_place":"publisher","oa":1,"publication_identifier":{"eissn":["1745-2481"],"issn":["1745-2473"]},"language":[{"iso":"eng"}],"day":"08","year":"2026","acknowledgement":"We thank B. Isaac and A. Tiano for their technical support with the electron microscopy and S. Waitukaitis for helpful comments on the manuscript. The TEM images were prepared and imaged at the Brandeis Electron Microscopy facility. This work was supported by the Gesellschaft für Forschungsförderung Niederösterreich under project FTI23-G-011 (M.C.H. and C.P.G.), the Brandeis University Materials Research Science and Engineering Center (MRSEC) under grant number NSF DMR-2011846 (T.E.V., D.H. and W.B.R.) and the Smith Family Foundation (W.B.R.). Open access funding provided by Institute of Science and Technology (IST Austria).","date_published":"2026-01-08T00:00:00Z","publication":"Nature Physics","article_processing_charge":"Yes (via OA deal)","doi":"10.1038/s41567-025-03120-3","abstract":[{"text":"Modern experimental methods in programmable self-assembly make it possible to precisely design particle concentrations, shapes and interactions. However, more physical insight is needed before we can take full advantage of this vast design space to assemble nanostructures with complex form and function. Here we show how a substantial part of this design space can be quickly and comprehensively understood by identifying a class of thermodynamic constraints that act on it. These thermodynamic constraints form a high-dimensional convex polyhedron that determines which nanostructures can be assembled at high equilibrium yield and reveals limitations that govern the coexistence of structures. We validate our predictions through detailed, quantitative assembly experiments of nanoscale particles synthesized using DNA origami. Our results uncover physical relationships underpinning many-component programmable self-assembly in equilibrium and form the basis for robust inverse design, applicable to various systems from biological protein complexes to synthetic nanomachines.","lang":"eng"}],"main_file_link":[{"url":"https://doi.org/10.1038/s41567-025-03120-3","open_access":"1"}],"corr_author":"1","PlanS_conform":"1","date_created":"2026-01-20T10:02:19Z","oa_version":"Published Version","project":[{"name":"Dynamically reconfigurable self-assembly with triangular DNA-origami bricks","_id":"8dd93da8-16d5-11f0-9cad-d2c70200d9a5","grant_number":"FTI23-G-011"}],"ddc":["570","540"],"citation":{"mla":"Hübl, Maximilian, et al. “A Polyhedral Structure Controls Programmable Self-Assembly.” <i>Nature Physics</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1038/s41567-025-03120-3\">10.1038/s41567-025-03120-3</a>.","ama":"Hübl M, Videbæk TE, Hayakawa D, Rogers WB, Goodrich CP. A polyhedral structure controls programmable self-assembly. <i>Nature Physics</i>. 2026. doi:<a href=\"https://doi.org/10.1038/s41567-025-03120-3\">10.1038/s41567-025-03120-3</a>","chicago":"Hübl, Maximilian, Thomas E. Videbæk, Daichi Hayakawa, W. Benjamin Rogers, and Carl Peter Goodrich. “A Polyhedral Structure Controls Programmable Self-Assembly.” <i>Nature Physics</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1038/s41567-025-03120-3\">https://doi.org/10.1038/s41567-025-03120-3</a>.","ista":"Hübl M, Videbæk TE, Hayakawa D, Rogers WB, Goodrich CP. 2026. A polyhedral structure controls programmable self-assembly. Nature Physics.","short":"M. Hübl, T.E. Videbæk, D. Hayakawa, W.B. Rogers, C.P. Goodrich, Nature Physics (2026).","ieee":"M. Hübl, T. E. Videbæk, D. Hayakawa, W. B. Rogers, and C. P. Goodrich, “A polyhedral structure controls programmable self-assembly,” <i>Nature Physics</i>. Springer Nature, 2026.","apa":"Hübl, M., Videbæk, T. E., Hayakawa, D., Rogers, W. B., &#38; Goodrich, C. P. (2026). A polyhedral structure controls programmable self-assembly. <i>Nature Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1038/s41567-025-03120-3\">https://doi.org/10.1038/s41567-025-03120-3</a>"},"date_updated":"2026-04-28T11:56:45Z","article_type":"original","quality_controlled":"1","related_material":{"link":[{"description":"News on ISTA website","url":"https://ista.ac.at/en/news/behind-natures-blueprints/","relation":"press_release"}]},"department":[{"_id":"CaGo"},{"_id":"GradSch"}],"publisher":"Springer Nature","status":"public","title":"A polyhedral structure controls programmable self-assembly","type":"journal_article","month":"01","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"21006"},{"_id":"21408","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","month":"02","title":"Simultaneous optimization of assembly time and yield in programmable self-assembly","status":"public","publisher":"AIP Publishing","department":[{"_id":"CaGo"},{"_id":"GradSch"}],"quality_controlled":"1","issue":"8","article_type":"original","date_updated":"2026-03-09T10:40:41Z","citation":{"mla":"Hübl, Maximilian, and Carl Peter Goodrich. “Simultaneous Optimization of Assembly Time and Yield in Programmable Self-Assembly.” <i>Journal of Chemical Physics</i>, vol. 164, no. 8, 084904, AIP Publishing, 2026, doi:<a href=\"https://doi.org/10.1063/5.0304731\">10.1063/5.0304731</a>.","ama":"Hübl M, Goodrich CP. Simultaneous optimization of assembly time and yield in programmable self-assembly. <i>Journal of Chemical Physics</i>. 2026;164(8). doi:<a href=\"https://doi.org/10.1063/5.0304731\">10.1063/5.0304731</a>","chicago":"Hübl, Maximilian, and Carl Peter Goodrich. “Simultaneous Optimization of Assembly Time and Yield in Programmable Self-Assembly.” <i>Journal of Chemical Physics</i>. AIP Publishing, 2026. <a href=\"https://doi.org/10.1063/5.0304731\">https://doi.org/10.1063/5.0304731</a>.","ista":"Hübl M, Goodrich CP. 2026. Simultaneous optimization of assembly time and yield in programmable self-assembly. Journal of Chemical Physics. 164(8), 084904.","short":"M. Hübl, C.P. Goodrich, Journal of Chemical Physics 164 (2026).","ieee":"M. Hübl and C. P. Goodrich, “Simultaneous optimization of assembly time and yield in programmable self-assembly,” <i>Journal of Chemical Physics</i>, vol. 164, no. 8. AIP Publishing, 2026.","apa":"Hübl, M., &#38; Goodrich, C. P. (2026). Simultaneous optimization of assembly time and yield in programmable self-assembly. <i>Journal of Chemical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0304731\">https://doi.org/10.1063/5.0304731</a>"},"file_date_updated":"2026-03-09T10:38:55Z","project":[{"name":"Dynamically reconfigurable self-assembly with triangular DNA-origami bricks","_id":"8dd93da8-16d5-11f0-9cad-d2c70200d9a5","grant_number":"FTI23-G-011"}],"ddc":["540"],"article_number":"084904","oa_version":"Published Version","volume":164,"date_created":"2026-03-08T23:01:45Z","corr_author":"1","abstract":[{"lang":"eng","text":"Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge, especially in programmable systems and the so-called semi-addressable regime, where binding is often nondeterministic and the formation of off-target structures negatively influences the assembly. Here, we show that it is possible to simultaneously sculpt the assembly outcome and the assembly kinetics through the underexplored design space of binding energies and particle concentrations. By formulating the assembly process as a complex reaction network, we calculate and optimize the tradeoff between assembly speed and quality and show that parameter optimization can speed up assembly by many orders of magnitude without lowering the yield of the target structure. Although the exact speedup varies from design to design, we find the largest speedups for nondeterministic systems where unoptimized assembly is the slowest, sometimes even making them assemble faster than optimized, fully addressable designs. Therefore, these results not only solve a key challenge in semi-addressable self-assembly but further emphasize the utility of semi-addressability, where designs have the potential to be faster as well as cheaper (fewer particle species) and better (higher yield). More broadly, our results highlight the importance of parameter optimization in programmable self-assembly and provide practical tools for simultaneous optimization of kinetics and yield in a wide range of systems."}],"doi":"10.1063/5.0304731","publication":"Journal of Chemical Physics","date_published":"2026-02-28T00:00:00Z","article_processing_charge":"Yes (via OA deal)","acknowledgement":"The research was supported by the Gesellschaft für Forschungsförderung Niederösterreich under Project No. FTI23-G-011.","intvolume":"       164","arxiv":1,"year":"2026","day":"28","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1089-7690"],"issn":["0021-9606"]},"oa":1,"OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","file_size":6903766,"date_created":"2026-03-09T10:38:55Z","file_id":"21415","success":1,"creator":"dernst","access_level":"open_access","content_type":"application/pdf","file_name":"2026_JourChemPhysics_Huebl.pdf","date_updated":"2026-03-09T10:38:55Z","checksum":"9bdb8870930e83edb973408da3038559"}],"author":[{"id":"5eb8629e-15b2-11ec-abd3-e6f3e5e01f32","last_name":"Hübl","first_name":"Maximilian","full_name":"Hübl, Maximilian"},{"orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425","first_name":"Carl Peter","full_name":"Goodrich, Carl Peter","last_name":"Goodrich"}],"external_id":{"arxiv":["2510.07876"]},"scopus_import":"1","publication_status":"published","OA_type":"hybrid","has_accepted_license":"1"},{"language":[{"iso":"eng"}],"day":"05","oa":1,"publication_identifier":{"eissn":["2643-1564"]},"OA_place":"publisher","file":[{"relation":"main_file","file_size":2680924,"date_created":"2026-03-23T15:53:29Z","file_id":"21493","success":1,"creator":"dernst","access_level":"open_access","file_name":"2026_PhysicalReviewResearch_Huebl.pdf","content_type":"application/pdf","date_updated":"2026-03-23T15:53:29Z","checksum":"6d8a68e4a19f8dad5abdf75f72316f3d"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","OA_type":"gold","has_accepted_license":"1","author":[{"id":"5eb8629e-15b2-11ec-abd3-e6f3e5e01f32","first_name":"Maximilian","full_name":"Hübl, Maximilian","last_name":"Hübl"},{"orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425","full_name":"Goodrich, Carl Peter","first_name":"Carl Peter","last_name":"Goodrich"}],"article_number":"L012054","oa_version":"Published Version","volume":8,"DOAJ_listed":"1","ddc":["530"],"project":[{"grant_number":"FTI23-G-011","name":"Dynamically reconfigurable self-assembly with triangular DNA-origami bricks","_id":"8dd93da8-16d5-11f0-9cad-d2c70200d9a5"}],"corr_author":"1","date_created":"2026-03-23T14:58:31Z","doi":"10.1103/68rs-3qgn","article_processing_charge":"Yes","date_published":"2026-03-05T00:00:00Z","publication":"Physical Review Research","abstract":[{"lang":"eng","text":"Controlling the size and shape of assembled structures is a fundamental challenge in self-assembly and is highly relevant in material design and biology. Here, we show that specific but promiscuous short-range binding interactions make it possible to economically assemble linear filaments of user-defined length. Our approach leads to independent control over the mean and width of the filament size distribution and allows us to smoothly explore design trade-offs between assembly quality (spread in size) and cost (number of particle species). We employ a simple hierarchical assembly protocol to minimize assembly times and show that multiple stages of hierarchy make it possible to extend our approach to the assembly of higher-dimensional structures. Our work provides a conceptually simple solution to size control that is applicable to a broad range of systems, from DNA nanoparticles to supramolecular polymers and beyond."}],"intvolume":"         8","year":"2026","acknowledgement":"We thank Maitane Muñoz-Basagoiti for helpful discussions. The research was supported by the Gesellschaft für Forschungsförderung Niederösterreich under Project No. FTI23-G-011.","article_type":"original","citation":{"ista":"Hübl M, Goodrich CP. 2026. Entropic size control of self-assembled filaments. Physical Review Research. 8, L012054.","short":"M. Hübl, C.P. Goodrich, Physical Review Research 8 (2026).","ieee":"M. Hübl and C. P. Goodrich, “Entropic size control of self-assembled filaments,” <i>Physical Review Research</i>, vol. 8. American Physical Society, 2026.","apa":"Hübl, M., &#38; Goodrich, C. P. (2026). Entropic size control of self-assembled filaments. <i>Physical Review Research</i>. American Physical Society. <a href=\"https://doi.org/10.1103/68rs-3qgn\">https://doi.org/10.1103/68rs-3qgn</a>","ama":"Hübl M, Goodrich CP. Entropic size control of self-assembled filaments. <i>Physical Review Research</i>. 2026;8. doi:<a href=\"https://doi.org/10.1103/68rs-3qgn\">10.1103/68rs-3qgn</a>","mla":"Hübl, Maximilian, and Carl Peter Goodrich. “Entropic Size Control of Self-Assembled Filaments.” <i>Physical Review Research</i>, vol. 8, L012054, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/68rs-3qgn\">10.1103/68rs-3qgn</a>.","chicago":"Hübl, Maximilian, and Carl Peter Goodrich. “Entropic Size Control of Self-Assembled Filaments.” <i>Physical Review Research</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/68rs-3qgn\">https://doi.org/10.1103/68rs-3qgn</a>."},"file_date_updated":"2026-03-23T15:53:29Z","date_updated":"2026-03-23T15:59:11Z","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"21482","publisher":"American Physical Society","month":"03","type":"journal_article","status":"public","title":"Entropic size control of self-assembled filaments","department":[{"_id":"CaGo"},{"_id":"GradSch"}],"quality_controlled":"1"},{"month":"02","type":"journal_article","title":"Accessing semiaddressable self-assembly with efficient structure enumeration","status":"public","publisher":"American Physical Society","_id":"19067","isi":1,"related_material":{"link":[{"url":"https://github.com/mxhbl/Roly.jl","relation":"software"}]},"department":[{"_id":"CaGo"},{"_id":"GradSch"}],"quality_controlled":"1","issue":"5","article_type":"original","date_updated":"2025-09-30T10:35:47Z","citation":{"mla":"Hübl, Maximilian, and Carl Peter Goodrich. “Accessing Semiaddressable Self-Assembly with Efficient Structure Enumeration.” <i>Physical Review Letters</i>, vol. 134, no. 5, 058204, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.134.058204\">10.1103/PhysRevLett.134.058204</a>.","ama":"Hübl M, Goodrich CP. Accessing semiaddressable self-assembly with efficient structure enumeration. <i>Physical Review Letters</i>. 2025;134(5). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.134.058204\">10.1103/PhysRevLett.134.058204</a>","chicago":"Hübl, Maximilian, and Carl Peter Goodrich. “Accessing Semiaddressable Self-Assembly with Efficient Structure Enumeration.” <i>Physical Review Letters</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/PhysRevLett.134.058204\">https://doi.org/10.1103/PhysRevLett.134.058204</a>.","short":"M. Hübl, C.P. Goodrich, Physical Review Letters 134 (2025).","ista":"Hübl M, Goodrich CP. 2025. Accessing semiaddressable self-assembly with efficient structure enumeration. Physical Review Letters. 134(5), 058204.","apa":"Hübl, M., &#38; Goodrich, C. P. (2025). Accessing semiaddressable self-assembly with efficient structure enumeration. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.134.058204\">https://doi.org/10.1103/PhysRevLett.134.058204</a>","ieee":"M. Hübl and C. P. Goodrich, “Accessing semiaddressable self-assembly with efficient structure enumeration,” <i>Physical Review Letters</i>, vol. 134, no. 5. American Physical Society, 2025."},"date_created":"2025-02-23T23:01:55Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.13567"}],"corr_author":"1","project":[{"name":"Dynamically reconfigurable self-assembly with triangular DNA-origami bricks","_id":"8dd93da8-16d5-11f0-9cad-d2c70200d9a5","grant_number":"FTI23-G-011"}],"article_number":"058204","oa_version":"Preprint","volume":134,"acknowledgement":"We thank Daichi Hayakawa, Thomas E. Videbæk, and W. Benjamin Rogers for important discussions and Jérémie Palacci, Anđela Šarić, and Scott Waitukaitis for helpful comments on the manuscript. The research was supported by the Gesellschaft für Forschungsförderung Niederösterreich under Project No. FTI23-G-011.","arxiv":1,"year":"2025","intvolume":"       134","abstract":[{"text":"Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of this inverse problem start with the so-called fully addressable limit, where every particle in a target structure is different. This leads to clear design principles that often result in high assembly yield, but it is not a scalable approach—at some point, one must grapple with “reusing” building blocks, which lowers the degree of addressability and may cause a multitude of off-target structures to form, complicating the design process. Here, we solve a key obstacle preventing robust inverse design in the “semiaddressable regime” by developing a highly efficient algorithm that enumerates all structures that can be formed from a given set of building blocks. By combining this with established partition-function-based yield calculations, we show that it is almost always possible to find economical semiaddressable designs where the entropic gain from reusing building blocks outweighs the presence of off-target structures and even increases the yield of the target. Thus, not only does our enumeration algorithm enable robust and scalable inverse design in the semiaddressable regime, our results demonstrate that it is possible to operate in this regime while maintaining the level of control often associated with full addressability.","lang":"eng"}],"doi":"10.1103/PhysRevLett.134.058204","article_processing_charge":"No","date_published":"2025-02-07T00:00:00Z","publication":"Physical Review Letters","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"day":"07","OA_place":"repository","oa":1,"publication_identifier":{"issn":["0031-9007"],"eissn":["1079-7114"]},"pmid":1,"author":[{"full_name":"Hübl, Maximilian","first_name":"Maximilian","last_name":"Hübl","id":"5eb8629e-15b2-11ec-abd3-e6f3e5e01f32"},{"full_name":"Goodrich, Carl Peter","first_name":"Carl Peter","last_name":"Goodrich","orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425"}],"external_id":{"arxiv":["2405.13567"],"pmid":["39983190"],"isi":["001454696800003"]},"scopus_import":"1","publication_status":"published","OA_type":"green"},{"publication_identifier":{"eissn":["1091-6490"]},"OA_place":"publisher","oa":1,"day":"16","language":[{"iso":"eng"}],"file":[{"file_id":"20744","success":1,"date_created":"2025-12-09T12:45:53Z","relation":"main_file","file_size":10621381,"checksum":"c40dc4c909724b9d1146636612e8821a","access_level":"open_access","file_name":"2025_PNAS_Shi.pdf","content_type":"application/pdf","date_updated":"2025-12-09T12:45:53Z","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","publication_status":"published","OA_type":"hybrid","scopus_import":"1","external_id":{"arxiv":["2507.01739"]},"author":[{"last_name":"Shi","first_name":"Sue","full_name":"Shi, Sue","id":"5c5b9247-15b2-11ec-abd3-fd958715639c"},{"id":"5eb8629e-15b2-11ec-abd3-e6f3e5e01f32","first_name":"Maximilian","full_name":"Hübl, Maximilian","last_name":"Hübl"},{"id":"0C5FDA4A-9CF6-11E9-8939-FF05E6697425","orcid":"0000-0001-5154-417X","last_name":"Grosjean","first_name":"Galien M","full_name":"Grosjean, Galien M"},{"orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425","first_name":"Carl Peter","full_name":"Goodrich, Carl Peter","last_name":"Goodrich"},{"orcid":"0000-0002-2299-3176","id":"3A1FFC16-F248-11E8-B48F-1D18A9856A87","first_name":"Scott R","full_name":"Waitukaitis, Scott R","last_name":"Waitukaitis"}],"volume":122,"oa_version":"Published Version","project":[{"grant_number":"FTI23-G-011","name":"Dynamically reconfigurable self-assembly with triangular DNA-origami bricks","_id":"8dd93da8-16d5-11f0-9cad-d2c70200d9a5"}],"ddc":["530"],"corr_author":"1","date_created":"2025-12-07T23:02:00Z","date_published":"2025-12-16T00:00:00Z","article_processing_charge":"Yes (in subscription journal)","publication":"Proceedings of the National Academy of Sciences","doi":"10.1073/pnas.2516865122","acknowledged_ssus":[{"_id":"M-Shop"}],"abstract":[{"text":"Acoustic levitation provides a unique method for manipulating small particles as it completely evades effects from gravity, container walls, or physical handling. These advantages make it a tantalizing platform for studying complex phenomena in many-particle systems. In most standing-wave traps, however, particles interact via acoustic scattering forces that cause them to merge into a single dense object. Here, we introduce a complementary approach that combines acoustic levitation with electrostatic charging to assemble, adapt, and activate complex, separated many-particle systems. The key idea is to superimpose electrostatic repulsion on the intrinsic acoustic attraction, rendering a so-called “mermaid” potential where interactions are attractive at short range and repulsive at long range. By controlling the attraction–repulsion balance, we can levitate expanded structures where all particles are separated, collapsed structures where they are in contact, and hybrid ones consisting of both expanded and collapsed components. We find that collapsed and expanded structures are inherently stable, whereas hybrid ones exhibit transient stability governed by acoustically unstable dimers. Furthermore, we show how electrostatics allow us to adapt between configurations on the fly, either by quasistatic discharge or discrete up/down charge steps. Finally, we demonstrate how large structures experience selective energy pumping from the acoustic field—thrusting some particles into motion while others remain stationary—leading to complex dynamics including coupled rotations and oscillations. Our approach establishes a design space beyond acoustic collapse, offering possibilities to study many-particle systems with complex interactions, while suggesting pathways toward scalable integration into materials processing and other applications.","lang":"eng"}],"year":"2025","arxiv":1,"intvolume":"       122","acknowledgement":"We thank Dustin Kleckner, Jack-William Barotta, and Daniel M. Harris for insightful discussions. We acknowledge the Miba machine shop at the Institute of Science and Technology Austria for instrumentation support. M.C.H. and C.P.G. acknowledge funding by the Gesellschaft für Forschungsförderung Niederösterreich under project FTI23-G-011.","article_type":"original","issue":"50","APC_amount":"5599.52 EUR","page":"e2516865122","file_date_updated":"2025-12-09T12:45:53Z","citation":{"short":"S. Shi, M. Hübl, G.M. Grosjean, C.P. Goodrich, S.R. Waitukaitis, Proceedings of the National Academy of Sciences 122 (2025) e2516865122.","ista":"Shi S, Hübl M, Grosjean GM, Goodrich CP, Waitukaitis SR. 2025. Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter. Proceedings of the National Academy of Sciences. 122(50), e2516865122.","apa":"Shi, S., Hübl, M., Grosjean, G. M., Goodrich, C. P., &#38; Waitukaitis, S. R. (2025). Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter. <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences. <a href=\"https://doi.org/10.1073/pnas.2516865122\">https://doi.org/10.1073/pnas.2516865122</a>","ieee":"S. Shi, M. Hübl, G. M. Grosjean, C. P. Goodrich, and S. R. Waitukaitis, “Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter,” <i>Proceedings of the National Academy of Sciences</i>, vol. 122, no. 50. National Academy of Sciences, p. e2516865122, 2025.","mla":"Shi, Sue, et al. “Electrostatics Overcome Acoustic Collapse to Assemble, Adapt, and Activate Levitated Matter.” <i>Proceedings of the National Academy of Sciences</i>, vol. 122, no. 50, National Academy of Sciences, 2025, p. e2516865122, doi:<a href=\"https://doi.org/10.1073/pnas.2516865122\">10.1073/pnas.2516865122</a>.","ama":"Shi S, Hübl M, Grosjean GM, Goodrich CP, Waitukaitis SR. Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter. <i>Proceedings of the National Academy of Sciences</i>. 2025;122(50):e2516865122. doi:<a href=\"https://doi.org/10.1073/pnas.2516865122\">10.1073/pnas.2516865122</a>","chicago":"Shi, Sue, Maximilian Hübl, Galien M Grosjean, Carl Peter Goodrich, and Scott R Waitukaitis. “Electrostatics Overcome Acoustic Collapse to Assemble, Adapt, and Activate Levitated Matter.” <i>Proceedings of the National Academy of Sciences</i>. National Academy of Sciences, 2025. <a href=\"https://doi.org/10.1073/pnas.2516865122\">https://doi.org/10.1073/pnas.2516865122</a>."},"date_updated":"2026-05-20T08:41:15Z","tmp":{"image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)"},"_id":"20727","publisher":"National Academy of Sciences","title":"Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter","status":"public","type":"journal_article","month":"12","quality_controlled":"1","related_material":{"link":[{"relation":"press_release","url":"https://ista.ac.at/en/news/science-is-like-magic-just-real/","description":"News on ISTA website"}],"record":[{"relation":"research_data","id":"20749","status":"public"}]},"department":[{"_id":"ScWa"},{"_id":"CaGo"}]}]