[{"publication":"Physical Review Letters","article_type":"original","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"APS","article_number":"036802","title":"Conductance-matrix symmetries of a three-terminal hybrid device","arxiv":1,"author":[{"full_name":"Ménard, G. C.","last_name":"Ménard","first_name":"G. C."},{"last_name":"Anselmetti","first_name":"G. L. R.","full_name":"Anselmetti, G. L. R."},{"last_name":"Martinez","first_name":"E. A.","full_name":"Martinez, E. A."},{"full_name":"Puglia, D.","last_name":"Puglia","first_name":"D."},{"full_name":"Malinowski, F. K.","last_name":"Malinowski","first_name":"F. K."},{"first_name":"J. S.","last_name":"Lee","full_name":"Lee, J. S."},{"first_name":"S.","last_name":"Choi","full_name":"Choi, S."},{"full_name":"Pendharkar, M.","last_name":"Pendharkar","first_name":"M."},{"full_name":"Palmstrøm, C. J.","first_name":"C. J.","last_name":"Palmstrøm"},{"full_name":"Flensberg, K.","first_name":"K.","last_name":"Flensberg"},{"full_name":"Marcus, C. M.","first_name":"C. M.","last_name":"Marcus"},{"full_name":"Casparis, L.","first_name":"L.","last_name":"Casparis"},{"first_name":"Andrew P","last_name":"Higginbotham","full_name":"Higginbotham, Andrew P","orcid":"0000-0003-2607-2363","id":"4AD6785A-F248-11E8-B48F-1D18A9856A87"}],"day":"24","issue":"3","language":[{"iso":"eng"}],"doi":"10.1103/physrevlett.124.036802","quality_controlled":"1","publication_identifier":{"issn":["0031-9007","1079-7114"]},"_id":"7477","year":"2020","volume":124,"date_created":"2020-02-11T08:50:02Z","month":"01","type":"journal_article","oa_version":"Preprint","abstract":[{"text":"We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that antisymmetric components of pairs of local and nonlocal conductances qualitatively match at energies below the superconducting gap, and we compare this finding with symmetry relations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional single-probe measurements in the search for Majorana zero modes.","lang":"eng"}],"date_updated":"2021-01-12T08:13:48Z","extern":"1","intvolume":"       124","citation":{"short":"G.C. Ménard, G.L.R. Anselmetti, E.A. Martinez, D. Puglia, F.K. Malinowski, J.S. Lee, S. Choi, M. Pendharkar, C.J. Palmstrøm, K. Flensberg, C.M. Marcus, L. Casparis, A.P. Higginbotham, Physical Review Letters 124 (2020).","chicago":"Ménard, G. C., G. L. R. Anselmetti, E. A. Martinez, D. Puglia, F. K. Malinowski, J. S. Lee, S. Choi, et al. “Conductance-Matrix Symmetries of a Three-Terminal Hybrid Device.” <i>Physical Review Letters</i>. APS, 2020. <a href=\"https://doi.org/10.1103/physrevlett.124.036802\">https://doi.org/10.1103/physrevlett.124.036802</a>.","ieee":"G. C. Ménard <i>et al.</i>, “Conductance-matrix symmetries of a three-terminal hybrid device,” <i>Physical Review Letters</i>, vol. 124, no. 3. APS, 2020.","apa":"Ménard, G. C., Anselmetti, G. L. R., Martinez, E. A., Puglia, D., Malinowski, F. K., Lee, J. S., … Higginbotham, A. P. (2020). Conductance-matrix symmetries of a three-terminal hybrid device. <i>Physical Review Letters</i>. APS. <a href=\"https://doi.org/10.1103/physrevlett.124.036802\">https://doi.org/10.1103/physrevlett.124.036802</a>","ista":"Ménard GC, Anselmetti GLR, Martinez EA, Puglia D, Malinowski FK, Lee JS, Choi S, Pendharkar M, Palmstrøm CJ, Flensberg K, Marcus CM, Casparis L, Higginbotham AP. 2020. Conductance-matrix symmetries of a three-terminal hybrid device. Physical Review Letters. 124(3), 036802.","mla":"Ménard, G. C., et al. “Conductance-Matrix Symmetries of a Three-Terminal Hybrid Device.” <i>Physical Review Letters</i>, vol. 124, no. 3, 036802, APS, 2020, doi:<a href=\"https://doi.org/10.1103/physrevlett.124.036802\">10.1103/physrevlett.124.036802</a>.","ama":"Ménard GC, Anselmetti GLR, Martinez EA, et al. Conductance-matrix symmetries of a three-terminal hybrid device. <i>Physical Review Letters</i>. 2020;124(3). doi:<a href=\"https://doi.org/10.1103/physrevlett.124.036802\">10.1103/physrevlett.124.036802</a>"},"status":"public","external_id":{"arxiv":["1905.05505"]},"date_published":"2020-01-24T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1905.05505","open_access":"1"}],"oa":1,"publication_status":"published"},{"year":"2020","_id":"7478","type":"journal_article","month":"01","oa_version":"Preprint","date_updated":"2021-01-12T08:13:48Z","abstract":[{"text":"Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments.","lang":"eng"}],"volume":124,"date_created":"2020-02-11T08:55:40Z","status":"public","external_id":{"arxiv":["1905.05438"]},"extern":"1","intvolume":"       124","citation":{"apa":"Danon, J., Hellenes, A. B., Hansen, E. B., Casparis, L., Higginbotham, A. P., &#38; Flensberg, K. (2020). Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges. <i>Physical Review Letters</i>. APS. <a href=\"https://doi.org/10.1103/physrevlett.124.036801\">https://doi.org/10.1103/physrevlett.124.036801</a>","ista":"Danon J, Hellenes AB, Hansen EB, Casparis L, Higginbotham AP, Flensberg K. 2020. Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges. Physical Review Letters. 124(3), 036801.","mla":"Danon, Jeroen, et al. “Nonlocal Conductance Spectroscopy of Andreev Bound States: Symmetry Relations and BCS Charges.” <i>Physical Review Letters</i>, vol. 124, no. 3, 036801, APS, 2020, doi:<a href=\"https://doi.org/10.1103/physrevlett.124.036801\">10.1103/physrevlett.124.036801</a>.","ama":"Danon J, Hellenes AB, Hansen EB, Casparis L, Higginbotham AP, Flensberg K. Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges. <i>Physical Review Letters</i>. 2020;124(3). doi:<a href=\"https://doi.org/10.1103/physrevlett.124.036801\">10.1103/physrevlett.124.036801</a>","short":"J. Danon, A.B. Hellenes, E.B. Hansen, L. Casparis, A.P. Higginbotham, K. Flensberg, Physical Review Letters 124 (2020).","chicago":"Danon, Jeroen, Anna Birk Hellenes, Esben Bork Hansen, Lucas Casparis, Andrew P Higginbotham, and Karsten Flensberg. “Nonlocal Conductance Spectroscopy of Andreev Bound States: Symmetry Relations and BCS Charges.” <i>Physical Review Letters</i>. APS, 2020. <a href=\"https://doi.org/10.1103/physrevlett.124.036801\">https://doi.org/10.1103/physrevlett.124.036801</a>.","ieee":"J. Danon, A. B. Hellenes, E. B. Hansen, L. Casparis, A. P. Higginbotham, and K. Flensberg, “Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges,” <i>Physical Review Letters</i>, vol. 124, no. 3. APS, 2020."},"oa":1,"publication_status":"published","date_published":"2020-01-24T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1905.05438","open_access":"1"}],"publisher":"APS","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Physical Review Letters","article_type":"original","article_processing_charge":"No","author":[{"first_name":"Jeroen","last_name":"Danon","full_name":"Danon, Jeroen"},{"last_name":"Hellenes","first_name":"Anna Birk","full_name":"Hellenes, Anna Birk"},{"last_name":"Hansen","first_name":"Esben Bork","full_name":"Hansen, Esben Bork"},{"full_name":"Casparis, Lucas","first_name":"Lucas","last_name":"Casparis"},{"id":"4AD6785A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2607-2363","full_name":"Higginbotham, Andrew P","last_name":"Higginbotham","first_name":"Andrew P"},{"first_name":"Karsten","last_name":"Flensberg","full_name":"Flensberg, Karsten"}],"day":"24","article_number":"036801","arxiv":1,"title":"Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges","issue":"3","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0031-9007","1079-7114"]},"doi":"10.1103/physrevlett.124.036801","quality_controlled":"1"},{"author":[{"first_name":"Amy L.","last_name":"Graves","full_name":"Graves, Amy L."},{"last_name":"Nashed","first_name":"Samer","full_name":"Nashed, Samer"},{"first_name":"Elliot","last_name":"Padgett","full_name":"Padgett, Elliot"},{"id":"EB352CD2-F68A-11E9-89C5-A432E6697425","orcid":"0000-0002-1307-5074","full_name":"Goodrich, Carl Peter","first_name":"Carl Peter","last_name":"Goodrich"},{"full_name":"Liu, Andrea J.","first_name":"Andrea J.","last_name":"Liu"},{"last_name":"Sethna","first_name":"James P.","full_name":"Sethna, James P."}],"oa_version":"None","month":"06","type":"journal_article","date_updated":"2021-01-12T08:15:21Z","abstract":[{"lang":"eng","text":"We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, χp. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χp∝|ϕ−ϕ∞c|−γp where ϕ∞c is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors γp=1.018±0.026(0.291) in d=2 and γp=1.534±0.120(0.822) in d=3. Logarithmic corrections raise the exponent in d=2 to close to the d=3 value, although the systematic errors are very large."}],"day":"10","article_number":"235501","volume":116,"title":"Pinning susceptibility: The effect of dilute, quenched disorder on jamming","date_created":"2020-04-30T11:40:10Z","publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2016","_id":"7761","publication":"Physical Review Letters","article_type":"original","article_processing_charge":"No","publication_identifier":{"issn":["0031-9007","1079-7114"]},"publication_status":"published","doi":"10.1103/physrevlett.116.235501","date_published":"2016-06-10T00:00:00Z","quality_controlled":"1","status":"public","intvolume":"       116","extern":"1","issue":"23","citation":{"apa":"Graves, A. L., Nashed, S., Padgett, E., Goodrich, C. P., Liu, A. J., &#38; Sethna, J. P. (2016). Pinning susceptibility: The effect of dilute, quenched disorder on jamming. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.116.235501\">https://doi.org/10.1103/physrevlett.116.235501</a>","ista":"Graves AL, Nashed S, Padgett E, Goodrich CP, Liu AJ, Sethna JP. 2016. Pinning susceptibility: The effect of dilute, quenched disorder on jamming. Physical Review Letters. 116(23), 235501.","mla":"Graves, Amy L., et al. “Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming.” <i>Physical Review Letters</i>, vol. 116, no. 23, 235501, American Physical Society, 2016, doi:<a href=\"https://doi.org/10.1103/physrevlett.116.235501\">10.1103/physrevlett.116.235501</a>.","ama":"Graves AL, Nashed S, Padgett E, Goodrich CP, Liu AJ, Sethna JP. Pinning susceptibility: The effect of dilute, quenched disorder on jamming. <i>Physical Review Letters</i>. 2016;116(23). doi:<a href=\"https://doi.org/10.1103/physrevlett.116.235501\">10.1103/physrevlett.116.235501</a>","short":"A.L. Graves, S. Nashed, E. Padgett, C.P. Goodrich, A.J. Liu, J.P. Sethna, Physical Review Letters 116 (2016).","chicago":"Graves, Amy L., Samer Nashed, Elliot Padgett, Carl Peter Goodrich, Andrea J. Liu, and James P. Sethna. “Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming.” <i>Physical Review Letters</i>. American Physical Society, 2016. <a href=\"https://doi.org/10.1103/physrevlett.116.235501\">https://doi.org/10.1103/physrevlett.116.235501</a>.","ieee":"A. L. Graves, S. Nashed, E. Padgett, C. P. Goodrich, A. J. Liu, and J. P. Sethna, “Pinning susceptibility: The effect of dilute, quenched disorder on jamming,” <i>Physical Review Letters</i>, vol. 116, no. 23. American Physical Society, 2016."},"language":[{"iso":"eng"}]},{"doi":"10.1103/physrevlett.116.088001","date_published":"2016-02-23T00:00:00Z","quality_controlled":"1","publication_status":"published","publication_identifier":{"issn":["0031-9007","1079-7114"]},"extern":"1","intvolume":"       116","language":[{"iso":"eng"}],"citation":{"apa":"Rieser, J. M., Goodrich, C. P., Liu, A. J., &#38; Durian, D. J. (2016). Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.116.088001\">https://doi.org/10.1103/physrevlett.116.088001</a>","mla":"Rieser, Jennifer M., et al. “Divergence of Voronoi Cell Anisotropy Vector: A Threshold-Free Characterization of Local Structure in Amorphous Materials.” <i>Physical Review Letters</i>, vol. 116, no. 8, 088001, American Physical Society, 2016, doi:<a href=\"https://doi.org/10.1103/physrevlett.116.088001\">10.1103/physrevlett.116.088001</a>.","ista":"Rieser JM, Goodrich CP, Liu AJ, Durian DJ. 2016. Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials. Physical Review Letters. 116(8), 088001.","ama":"Rieser JM, Goodrich CP, Liu AJ, Durian DJ. Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials. <i>Physical Review Letters</i>. 2016;116(8). doi:<a href=\"https://doi.org/10.1103/physrevlett.116.088001\">10.1103/physrevlett.116.088001</a>","short":"J.M. Rieser, C.P. Goodrich, A.J. Liu, D.J. Durian, Physical Review Letters 116 (2016).","chicago":"Rieser, Jennifer M., Carl Peter Goodrich, Andrea J. Liu, and Douglas J. Durian. “Divergence of Voronoi Cell Anisotropy Vector: A Threshold-Free Characterization of Local Structure in Amorphous Materials.” <i>Physical Review Letters</i>. American Physical Society, 2016. <a href=\"https://doi.org/10.1103/physrevlett.116.088001\">https://doi.org/10.1103/physrevlett.116.088001</a>.","ieee":"J. M. Rieser, C. P. Goodrich, A. J. Liu, and D. J. Durian, “Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials,” <i>Physical Review Letters</i>, vol. 116, no. 8. American Physical Society, 2016."},"issue":"8","status":"public","title":"Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials","volume":116,"article_number":"088001 ","date_created":"2020-04-30T11:40:25Z","author":[{"full_name":"Rieser, Jennifer M.","last_name":"Rieser","first_name":"Jennifer M."},{"id":"EB352CD2-F68A-11E9-89C5-A432E6697425","orcid":"0000-0002-1307-5074","full_name":"Goodrich, Carl Peter","last_name":"Goodrich","first_name":"Carl Peter"},{"full_name":"Liu, Andrea J.","last_name":"Liu","first_name":"Andrea J."},{"first_name":"Douglas J.","last_name":"Durian","full_name":"Durian, Douglas J."}],"day":"23","abstract":[{"text":"Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, where positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with the packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.","lang":"eng"}],"date_updated":"2021-01-12T08:15:22Z","type":"journal_article","oa_version":"None","month":"02","publication":"Physical Review Letters","_id":"7762","article_processing_charge":"No","article_type":"original","publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2016"},{"extern":"1","intvolume":"       114","issue":"22","citation":{"apa":"Goodrich, C. P., Liu, A. J., &#38; Nagel, S. R. (2015). The principle of independent bond-level response: Tuning by pruning to exploit disorder for global behavior. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.114.225501\">https://doi.org/10.1103/physrevlett.114.225501</a>","ista":"Goodrich CP, Liu AJ, Nagel SR. 2015. The principle of independent bond-level response: Tuning by pruning to exploit disorder for global behavior. Physical Review Letters. 114(22), 225501.","mla":"Goodrich, Carl Peter, et al. “The Principle of Independent Bond-Level Response: Tuning by Pruning to Exploit Disorder for Global Behavior.” <i>Physical Review Letters</i>, vol. 114, no. 22, 225501, American Physical Society, 2015, doi:<a href=\"https://doi.org/10.1103/physrevlett.114.225501\">10.1103/physrevlett.114.225501</a>.","ama":"Goodrich CP, Liu AJ, Nagel SR. The principle of independent bond-level response: Tuning by pruning to exploit disorder for global behavior. <i>Physical Review Letters</i>. 2015;114(22). doi:<a href=\"https://doi.org/10.1103/physrevlett.114.225501\">10.1103/physrevlett.114.225501</a>","short":"C.P. Goodrich, A.J. Liu, S.R. Nagel, Physical Review Letters 114 (2015).","chicago":"Goodrich, Carl Peter, Andrea J. Liu, and Sidney R. Nagel. “The Principle of Independent Bond-Level Response: Tuning by Pruning to Exploit Disorder for Global Behavior.” <i>Physical Review Letters</i>. American Physical Society, 2015. <a href=\"https://doi.org/10.1103/physrevlett.114.225501\">https://doi.org/10.1103/physrevlett.114.225501</a>.","ieee":"C. P. Goodrich, A. J. Liu, and S. R. Nagel, “The principle of independent bond-level response: Tuning by pruning to exploit disorder for global behavior,” <i>Physical Review Letters</i>, vol. 114, no. 22. American Physical Society, 2015."},"language":[{"iso":"eng"}],"status":"public","date_published":"2015-06-04T00:00:00Z","doi":"10.1103/physrevlett.114.225501","quality_controlled":"1","publication_identifier":{"issn":["0031-9007","1079-7114"]},"publication_status":"published","_id":"7765","publication":"Physical Review Letters","article_type":"original","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"American Physical Society","year":"2015","article_number":"225501","volume":114,"title":"The principle of independent bond-level response: Tuning by pruning to exploit disorder for global behavior","date_created":"2020-04-30T11:41:08Z","author":[{"orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425","full_name":"Goodrich, Carl Peter","last_name":"Goodrich","first_name":"Carl Peter"},{"full_name":"Liu, Andrea J.","first_name":"Andrea J.","last_name":"Liu"},{"full_name":"Nagel, Sidney R.","first_name":"Sidney R.","last_name":"Nagel"}],"type":"journal_article","oa_version":"None","month":"06","abstract":[{"text":"We introduce a principle unique to disordered solids wherein the contribution of any bond to one global perturbation is uncorrelated with its contribution to another. Coupled with sufficient variability in the contributions of different bonds, this “independent bond-level response” paves the way for the design of real materials with unusual and exquisitely tuned properties. To illustrate this, we choose two global perturbations: compression and shear. By applying a bond removal procedure that is both simple and experimentally relevant to remove a very small fraction of bonds, we can drive disordered spring networks to both the incompressible and completely auxetic limits of mechanical behavior.","lang":"eng"}],"day":"04","date_updated":"2021-01-12T08:15:23Z"},{"publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","article_type":"letter_note","publication":"Physical Review Letters","day":"20","author":[{"full_name":"Goodrich, Carl Peter","id":"EB352CD2-F68A-11E9-89C5-A432E6697425","orcid":"0000-0002-1307-5074","first_name":"Carl Peter","last_name":"Goodrich"},{"full_name":"Liu, Andrea J.","last_name":"Liu","first_name":"Andrea J."},{"first_name":"Sidney R.","last_name":"Nagel","full_name":"Nagel, Sidney R."}],"arxiv":1,"title":"Comment on “Repulsive contact interactions make jammed particulate systems inherently nonharmonic”","article_number":"049801 ","language":[{"iso":"eng"}],"issue":"4","publication_identifier":{"issn":["0031-9007","1079-7114"]},"doi":"10.1103/physrevlett.112.049801","year":"2014","_id":"7771","abstract":[{"lang":"eng","text":"In their Letter, Schreck, Bertrand, O'Hern and Shattuck [Phys. Rev. Lett. 107, 078301 (2011)] study nonlinearities in jammed particulate systems that arise when contacts are altered. They conclude that there is \"no harmonic regime in the large system limit for all compressions\" and \"at jamming onset for any system size.\" Their argument rests on the claim that for finite-range repulsive potentials, of the form used in studies of jamming, the breaking or forming of a single contact is sufficient to destroy the linear regime. We dispute these conclusions and argue that linear response is both justified and essential for understanding the nature of the jammed solid. "}],"date_updated":"2021-01-12T08:15:26Z","type":"journal_article","oa_version":"Preprint","month":"04","date_created":"2020-04-30T11:42:39Z","volume":112,"external_id":{"arxiv":["1306.1285"]},"status":"public","citation":{"short":"C.P. Goodrich, A.J. Liu, S.R. Nagel, Physical Review Letters 112 (2014).","ieee":"C. P. Goodrich, A. J. Liu, and S. R. Nagel, “Comment on ‘Repulsive contact interactions make jammed particulate systems inherently nonharmonic,’” <i>Physical Review Letters</i>, vol. 112, no. 4. American Physical Society, 2014.","chicago":"Goodrich, Carl Peter, Andrea J. Liu, and Sidney R. Nagel. “Comment on ‘Repulsive Contact Interactions Make Jammed Particulate Systems Inherently Nonharmonic.’” <i>Physical Review Letters</i>. American Physical Society, 2014. <a href=\"https://doi.org/10.1103/physrevlett.112.049801\">https://doi.org/10.1103/physrevlett.112.049801</a>.","ista":"Goodrich CP, Liu AJ, Nagel SR. 2014. Comment on “Repulsive contact interactions make jammed particulate systems inherently nonharmonic”. Physical Review Letters. 112(4), 049801.","mla":"Goodrich, Carl Peter, et al. “Comment on ‘Repulsive Contact Interactions Make Jammed Particulate Systems Inherently Nonharmonic.’” <i>Physical Review Letters</i>, vol. 112, no. 4, 049801, American Physical Society, 2014, doi:<a href=\"https://doi.org/10.1103/physrevlett.112.049801\">10.1103/physrevlett.112.049801</a>.","apa":"Goodrich, C. P., Liu, A. J., &#38; Nagel, S. R. (2014). Comment on “Repulsive contact interactions make jammed particulate systems inherently nonharmonic.” <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.112.049801\">https://doi.org/10.1103/physrevlett.112.049801</a>","ama":"Goodrich CP, Liu AJ, Nagel SR. Comment on “Repulsive contact interactions make jammed particulate systems inherently nonharmonic.” <i>Physical Review Letters</i>. 2014;112(4). doi:<a href=\"https://doi.org/10.1103/physrevlett.112.049801\">10.1103/physrevlett.112.049801</a>"},"extern":"1","intvolume":"       112","oa":1,"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1306.1285"}],"date_published":"2014-04-20T00:00:00Z"},{"quality_controlled":"1","doi":"10.1103/physrevlett.109.095704","date_published":"2012-08-27T00:00:00Z","publication_identifier":{"issn":["0031-9007","1079-7114"]},"publication_status":"published","issue":"9","language":[{"iso":"eng"}],"citation":{"ama":"Goodrich CP, Liu AJ, Nagel SR. Finite-size scaling at the jamming transition. <i>Physical Review Letters</i>. 2012;109(9). doi:<a href=\"https://doi.org/10.1103/physrevlett.109.095704\">10.1103/physrevlett.109.095704</a>","apa":"Goodrich, C. P., Liu, A. J., &#38; Nagel, S. R. (2012). Finite-size scaling at the jamming transition. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevlett.109.095704\">https://doi.org/10.1103/physrevlett.109.095704</a>","ista":"Goodrich CP, Liu AJ, Nagel SR. 2012. Finite-size scaling at the jamming transition. Physical Review Letters. 109(9), 095704.","mla":"Goodrich, Carl Peter, et al. “Finite-Size Scaling at the Jamming Transition.” <i>Physical Review Letters</i>, vol. 109, no. 9, 095704, American Physical Society, 2012, doi:<a href=\"https://doi.org/10.1103/physrevlett.109.095704\">10.1103/physrevlett.109.095704</a>.","chicago":"Goodrich, Carl Peter, Andrea J. Liu, and Sidney R. Nagel. “Finite-Size Scaling at the Jamming Transition.” <i>Physical Review Letters</i>. American Physical Society, 2012. <a href=\"https://doi.org/10.1103/physrevlett.109.095704\">https://doi.org/10.1103/physrevlett.109.095704</a>.","ieee":"C. P. Goodrich, A. J. Liu, and S. R. Nagel, “Finite-size scaling at the jamming transition,” <i>Physical Review Letters</i>, vol. 109, no. 9. American Physical Society, 2012.","short":"C.P. Goodrich, A.J. Liu, S.R. Nagel, Physical Review Letters 109 (2012)."},"extern":"1","intvolume":"       109","status":"public","date_created":"2020-04-30T11:44:12Z","article_number":"095704","title":"Finite-size scaling at the jamming transition","volume":109,"month":"08","type":"journal_article","oa_version":"None","date_updated":"2021-01-12T08:15:27Z","day":"27","abstract":[{"text":"We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a nontrivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both two and three dimensions, indicating an upper critical dimension of 2.","lang":"eng"}],"author":[{"first_name":"Carl Peter","last_name":"Goodrich","full_name":"Goodrich, Carl Peter","orcid":"0000-0002-1307-5074","id":"EB352CD2-F68A-11E9-89C5-A432E6697425"},{"first_name":"Andrea J.","last_name":"Liu","full_name":"Liu, Andrea J."},{"full_name":"Nagel, Sidney R.","first_name":"Sidney R.","last_name":"Nagel"}],"article_type":"original","article_processing_charge":"No","_id":"7776","publication":"Physical Review Letters","year":"2012","publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]