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We observe fractal behavior at the critical point and derive the value of the number-of-sites-visited exponent, in excellent agreement with previous work or conjectures, but with a new and imprOVed computational algorithm that extends the calculation to the long time limit. We show the crossover to the classical Euclidean behavior in these lattices and discuss its onset as a function of the fractionp. We compare the observed trends with the two-dimensional case.","publication_date":"1985,,","publication_name":"The Journal of Chemical Physics","grobid_abstract_attachment_id":"42302303"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three-dimensional lattices","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [36744155,32994550]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":42302303,"attachmentType":"pdf"}"><img alt="First page of “Fractal to Euclidean crossover and scaling for random walks on percolation clusters. 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Three-dimensional lattices</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="36744155" href="https://independent.academia.edu/PanosArgyrakis"><img alt="Profile image of Panos Argyrakis" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Panos Argyrakis</a><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="32994550" href="https://independent.academia.edu/RaoulKopelman"><img alt="Profile image of Raoul Kopelman" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Raoul Kopelman</a></div><p class="ds-work-card--detail ds2-5-body-sm">1985, The Journal of Chemical Physics</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" 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href="https://www.academia.edu/47865617/The_geometry_of_percolation_fronts_in_two_dimensional_lattices_with_spatially_varying_densities">The geometry of percolation fronts in two-dimensional lattices with spatially varying densities</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="51216508" href="https://independent.academia.edu/MGastner">Michael Gastner</a></div><p class="ds-related-work--metadata ds2-5-body-xs">New Journal of Physics, 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The geometry of percolation fronts in two-dimensional lattices with spatially varying 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href="https://www.academia.edu/54413746/Diffusion_in_three_dimensional_random_systems_at_their_percolation_thresholds">Diffusion in three-dimensional random systems at their percolation thresholds</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="101630805" href="https://independent.academia.edu/EduardoRoman28">Eduardo Roman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Physics, 1990</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Diffusion in three-dimensional random systems at their percolation thresholds","attachmentId":70788570,"attachmentType":"pdf","work_url":"https://www.academia.edu/54413746/Diffusion_in_three_dimensional_random_systems_at_their_percolation_thresholds","alternativeTracking":true}"><span 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lattices</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="188279725" href="https://independent.academia.edu/VladimirMiljkovic4">Vladimir Miljkovic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chaos, Solitons &amp; Fractals, 2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Statistics of the two self-avoiding random walks on the three-dimensional fractal lattices","attachmentId":115926596,"attachmentType":"pdf","work_url":"https://www.academia.edu/120926039/Statistics_of_the_two_self_avoiding_random_walks_on_the_three_dimensional_fractal_lattices","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a 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Aharony</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 1984</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Physical Properties of a New Fractal Model of Percolation Clusters","attachmentId":93609890,"attachmentType":"pdf","work_url":"https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters"><span class="ds2-5-text-link__content">View PDF</span><span 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