[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81983-en":3,"doc-seo-81983-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81983,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Topological Signatures of Diffusive Release in Porous Media","Persistent homology is used to quantify multiscale topological and geometric organization of porous media, capturing solid connectivity as well as loop-like and cavity-like structures across spatial scales. Statistical analysis links these features to diffusion-driven release behavior. Even at a fixed target-porosity level, samples with more complex topology show long-tailed release, showing dependence on multiscale solid organization beyond pore amount. A persistent-homology feature set also classifies release-curve regimes via a simple model, while remaining faster than finite element simulations.","arXiv :2607 .0706 1v 1 [ cs .CE] 8 Jul 2026  \nTopological Signatures of Diffusive Release in Porous Media  \nDonghan Kim∗  \nAbstract  \nWe used persistent homology to quantify the multiscale topological and geometric organization of porous media, including solid connectivity and the formation of loop-like and cavity-like structures across spatial scales. Through statistical analysis, we show that these topological and geometric features are closely associated with diffusion-driven release behavior in porous media. In particular, even within each target-porosity level, samples with richer topological features tend to exhibit long-tailed release, indicating that release behavior depends not only on the amount of pore space but also on the multiscale organization of the solid phase. We further show that persistent homology-based features can classify release-curve regimes using a simple classification model. Notably, feature extraction is substantially faster than finite element diffusion simulations. Together, these results suggest that persistent homology provides a lightweight, interpretable, and geometry-based descriptor for screening diffusive release behavior in porous media.  \nKeywords: porous media; diffusion release; persistent homology; topological data analysis.  \n1 Introduction  \nDiffusive release in porous media is strongly influenced by pore-scale geometry. Connectivity, tortuosity, constrictivity, accessible boundary area, and the spatial arrangement of solid obstacles can all affect how solutes escape from an initially loaded porous domain [1–3] . This geometry–transport relationship is important in applications ranging from subsurface contaminant transport and filtration to biomaterials and controlled drug release [4–9] . Mechanistic mathematical and numerical simulations are widely used to study how porous geometry affects transport and release, ranging from pore-scale image-based simulations of flow and transport to continuum models of controlled drug release [5, 10–12] .  \nA practical challenge is that direct numerical simulation of transport in three-dimensional porous geometries can be computationally expensive, especially when many candidate structures must be evaluated [5, 13] . In screening or design settings, early identification of qualitative release profiles can help prioritize candidate structures before more detailed simulation or experimental evaluation [14–16] . This motivates the search for structural descriptors that are interpretable, geometry-based, and informative about release curve behavior.  \nPersistent homology, one of the most widely used tools in topological data analysis, provides a multiscale summary of topological features in data, including connected components, loops, and cavities [17–21] . In porous media, persistent homology has been used to characterize connectivity, pore-size structure, percolation length scales, permeability, elasticity, and fluid trapping [22–26] . These studies suggest that topological summaries can capture geometric information that is not fully represented by simple scalar descriptors such as porosity.  \n∗Department of Mathematical Sciences, KAIST, Daejeon, Republic of Korea. Email: [patrick6231@kaist.ac.kr](patrick6231@kaist.ac.kr)  \npore  solid  Γout  \nFigure 1: A schematic porous medium in a square cross-section of the sample domain Ω . The gray inclusions represent solid grains S, shown as separated for visual clarity. The blue region is the pore space P = Ω \\ S. The red segment on the boundary indicates an absorbing outlet Γout.  \nOur Contribution In this work, we used persistent homology to quantify the multiscale topology and geometry of the solid phase in porous media. A porosity-controlled statistical analysis shows that release regimes have distinct topological signatures even after stratifying samples by target porosity. In particular, more complex solid-phase topology is associated with delayed or long-tail release, indicating that release behavi","cbCainS101tAXimF","https://ap.wps.com/l/cbCainS101tAXimF","pdf",838456,4,1,15,"English","en",105,"# Introduction\n# Diffusion in Porous Media","[{\"question\":\"What method is used to characterize porous media in the document?\",\"answer\":\"Persistent homology is used to quantify multiscale topological and geometric organization of the porous media, including connectivity, loops, and cavities across spatial scales.\"},{\"question\":\"How does topology relate to diffusion-driven release behavior?\",\"answer\":\"Topological and geometric features are shown to be closely associated with diffusion-driven release. At fixed target porosity, samples with richer topological features tend to produce long-tailed release, indicating release depends on multiscale solid organization, not porosity alone.\"},{\"question\":\"How are release regimes determined and how does the approach compare computationally?\",\"answer\":\"Persistent-homology-based features classify release-curve regimes using a simple classification model. Feature extraction is substantially faster than finite element diffusion simulations.\"}]",1784177414,38,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"topological-signatures-of-diffusive-release-in-porous-media","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/topological-signatures-of-diffusive-release-in-porous-media/81983/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-30","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What method is used to characterize porous media in the document?","Question",{"text":75,"@type":76},"Persistent homology is used to quantify multiscale topological and geometric organization of the porous media, including connectivity, loops, and cavities across spatial scales.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does topology relate to diffusion-driven release behavior?",{"text":80,"@type":76},"Topological and geometric features are shown to be closely associated with diffusion-driven release. At fixed target porosity, samples with richer topological features tend to produce long-tailed release, indicating release depends on multiscale solid organization, not porosity alone.",{"name":82,"@type":73,"acceptedAnswer":83},"How are release regimes determined and how does the approach compare computationally?",{"text":84,"@type":76},"Persistent-homology-based features classify release-curve regimes using a simple classification model. Feature extraction is substantially faster than finite element diffusion simulations.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]