{"id":"https://openalex.org/W7204458586","doi":"https://doi.org/10.3390/fractalfract10090599","title":"Revealing Morphological Complexity in Silver Aggregates Through Multifractal Analysis","display_name":"Revealing Morphological Complexity in Silver Aggregates Through Multifractal Analysis","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204458586","doi":"https://doi.org/10.3390/fractalfract10090599"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract10090599","doi":"https://doi.org/10.3390/fractalfract10090599","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10090599","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/fractalfract10090599","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055272007","display_name":"Layla Badr","orcid":"https://orcid.org/0000-0002-5010-7688","observed_orcids":["https://orcid.org/0000-0002-5010-7688"]},"institutions":[{"id":"https://openalex.org/I60770847","display_name":"Notre Dame University \u2013 Louaize","ror":"https://ror.org/030br0314","country_code":"LB","type":"education","lineage":["https://openalex.org/I60770847"]}],"countries":["LB"],"is_corresponding":true,"raw_author_name":"Layla Badr","raw_affiliation_strings":["Department of Sciences, Faculty of Natural and Applied Sciences, Notre Dame University\u2014Louaize, Zouk Mosbeh P.O. Box 72, Lebanon"],"raw_orcid":"https://orcid.org/0000-0002-5010-7688","affiliations":[{"raw_affiliation_string":"Department of Sciences, Faculty of Natural and Applied Sciences, Notre Dame University\u2014Louaize, Zouk Mosbeh P.O. Box 72, Lebanon","institution_ids":["https://openalex.org/I60770847"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055272007"],"corresponding_institution_ids":["https://openalex.org/I60770847"],"apc_list":{"value":2700,"currency":"CHF","value_usd":3258},"apc_paid":{"value":2700,"currency":"CHF","value_usd":3258},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.614455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"9","first_page":"599","last_page":"599"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.18209999799728394,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.18209999799728394,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.1315000057220459,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.10459999740123749,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/silver-aggregates","display_name":"silver aggregates","score":0.9229999780654907},{"id":"https://openalex.org/keywords/multifractal-analysis","display_name":"multifractal analysis","score":0.8759999871253967},{"id":"https://openalex.org/keywords/silver-ion-reduction","display_name":"silver ion reduction","score":0.7710000276565552},{"id":"https://openalex.org/keywords/self-organization","display_name":"self-organization","score":0.7210000157356262},{"id":"https://openalex.org/keywords/generalized-fractal-dimension","display_name":"generalized fractal dimension","score":0.7900000214576721},{"id":"https://openalex.org/keywords/renyi-entropy","display_name":"R\u00e9nyi entropy","score":0.9649999737739563},{"id":"https://openalex.org/keywords/multifractal-spectrum","display_name":"multifractal spectrum","score":0.8610000014305115},{"id":"https://openalex.org/keywords/capacity-dimension","display_name":"capacity dimension","score":0.8690000176429749},{"id":"https://openalex.org/keywords/diffusion-limited-aggregation","display_name":"diffusion-limited aggregation","score":0.9599999785423279},{"id":"https://openalex.org/keywords/lacunarity","display_name":"lacunarity","score":0.8360000252723694},{"id":"https://openalex.org/keywords/correlation-dimension","display_name":"correlation dimension","score":0.9200000166893005},{"id":"https://openalex.org/keywords/ionic-repulsion","display_name":"ionic repulsion","score":0.7120000123977661},{"id":"https://openalex.org/keywords/concentration-gradient","display_name":"concentration gradient","score":0.49799999594688416},{"id":"https://openalex.org/keywords/scaling-behavior","display_name":"scaling behavior","score":0.46000000834465027}],"concepts":[{"id":"https://openalex.org/C133905733","wikidata":"https://www.wikidata.org/wiki/Q2629238","display_name":"Multifractal system","level":3,"score":0.843500018119812},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.6381000280380249},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5891000032424927},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.579800009727478},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5178999900817871},{"id":"https://openalex.org/C110729304","wikidata":"https://www.wikidata.org/wiki/Q1224521","display_name":"Diffusion-limited aggregation","level":4,"score":0.5156999826431274},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C136534824","wikidata":"https://www.wikidata.org/wiki/Q2771020","display_name":"Lacunarity","level":4,"score":0.48010000586509705},{"id":"https://openalex.org/C110601934","wikidata":"https://www.wikidata.org/wiki/Q5172849","display_name":"Correlation dimension","level":4,"score":0.47049999237060547},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C2182769","wikidata":"https://www.wikidata.org/wiki/Q62500","display_name":"Ionic bonding","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C169345407","wikidata":"https://www.wikidata.org/wiki/Q8216221","display_name":"Uncorrelated","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/fractalfract10090599","doi":"https://doi.org/10.3390/fractalfract10090599","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10090599","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6d7d4d093eac4b15a64a34a286163bf4","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/6d7d4d093eac4b15a64a34a286163bf4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fractal and Fractional, Vol 10, Iss 9, p 599 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/fractalfract10090599","doi":"https://doi.org/10.3390/fractalfract10090599","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10090599","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1548439805","https://openalex.org/W1965262908","https://openalex.org/W1968391990","https://openalex.org/W1981223952","https://openalex.org/W1981868363","https://openalex.org/W1991038884","https://openalex.org/W1995875735","https://openalex.org/W2007298029","https://openalex.org/W2017719233","https://openalex.org/W2023623787","https://openalex.org/W2029425888","https://openalex.org/W2029849672","https://openalex.org/W2046969942","https://openalex.org/W2060865587","https://openalex.org/W2086754351","https://openalex.org/W2099540110","https://openalex.org/W2104962944","https://openalex.org/W2112995297","https://openalex.org/W2167942735","https://openalex.org/W2516167713","https://openalex.org/W2782078109","https://openalex.org/W2884466769","https://openalex.org/W2900754571","https://openalex.org/W2907907107","https://openalex.org/W3002683472","https://openalex.org/W3119505370","https://openalex.org/W3132283506","https://openalex.org/W3148918439","https://openalex.org/W3149217474","https://openalex.org/W3176144106","https://openalex.org/W4321372714","https://openalex.org/W4361007348","https://openalex.org/W4380268543","https://openalex.org/W4386917869","https://openalex.org/W4396227921","https://openalex.org/W4396544796","https://openalex.org/W4399055624","https://openalex.org/W4404664413","https://openalex.org/W4410493919","https://openalex.org/W4414609831","https://openalex.org/W7167912624"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,12,27,41,47,52,57,67,72,83,89,93,99,110,115,128,136],"morphological":[4],"complexity":[5],"of":[6,14,40,85,88,95],"self-organized":[7],"silver":[8,15,90],"aggregates":[9,28,91],"formed":[10],"via":[11],"reduction":[13],"ions":[16,97],"in":[17,59],"a":[18],"gelatin":[19],"medium.":[20],"A":[21],"comprehensive":[22],"multifractal":[23,54,80],"analysis":[24],"showed":[25],"that":[26],"exhibit":[29],"complex":[30],"scaling":[31],"behavior":[32],"beyond":[33],"simple":[34],"mono-fractality.":[35],"The":[36,77,102,123],"reverse":[37],"sigmoidal":[38],"dependence":[39],"generalized":[42],"fractal":[43],"dimension":[44,105,130],"Dq":[45],"on":[46],"moment":[48],"order":[49],"q":[50,65],"confirms":[51],"aggregates\u2019":[53],"nature,":[55],"and":[56,66,120,127],"variation":[58],"Renyi":[60],"entropy":[61],"Hq":[62],"with":[63,109],"both":[64],"size":[68],"scale":[69],"\u03b5":[70],"underscores":[71],"system\u2019s":[73],"inherent":[74],"chaotic":[75],"dynamics.":[76],"left-sided":[78],"f(\u03b1)":[79],"spectra":[81],"indicate":[82],"dominance":[84],"peripheral":[86],"growth":[87],"by":[92],"diffusion":[94],"Ag+":[96],"towards":[98],"growing":[100],"electrode.":[101],"observed":[103],"capacity":[104],"Db":[106],"range":[107],"aligns":[108],"diffusion-limited":[111],"aggregation":[112],"process,":[113],"reflecting":[114],"interplay":[116],"between":[117,125],"concentration":[118],"gradient":[119],"ionic":[121],"repulsion.":[122],"correlation":[124,129],"lacunarity":[126],"D2":[131],"is":[132],"approached":[133],"only":[134],"at":[135],"smallest":[137],"scales.":[138]},"counts_by_year":[],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2026-08-28T00:00:00"}