{"id":32578325,"url":"https://github.com/hugomvale/pbepack","last_synced_at":"2026-02-23T20:08:03.011Z","repository":{"id":64168762,"uuid":"538134668","full_name":"HugoMVale/pbepack","owner":"HugoMVale","description":"Package to solve population balance equations for particulate processes.","archived":false,"fork":false,"pushed_at":"2024-08-24T22:05:06.000Z","size":493,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"main","last_synced_at":"2024-08-24T23:21:55.741Z","etag":null,"topics":["aggregation","breakage","coagulation","fortran","pbe","population-balance-equation"],"latest_commit_sha":null,"homepage":"https://hugomvale.github.io/pbepack/","language":"Fortran","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/HugoMVale.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE.md","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2022-09-18T14:26:30.000Z","updated_at":"2024-08-24T22:05:09.000Z","dependencies_parsed_at":"2023-01-15T01:45:36.651Z","dependency_job_id":"86b3fca6-367d-419f-b73c-ea54b3cfc0a5","html_url":"https://github.com/HugoMVale/pbepack","commit_stats":{"total_commits":180,"total_committers":1,"mean_commits":180.0,"dds":0.0,"last_synced_commit":"1d71541269849b2a05847c19c71dab91468d22bd"},"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/HugoMVale/pbepack","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/HugoMVale%2Fpbepack","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/HugoMVale%2Fpbepack/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/HugoMVale%2Fpbepack/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/HugoMVale%2Fpbepack/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/HugoMVale","download_url":"https://codeload.github.com/HugoMVale/pbepack/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/HugoMVale%2Fpbepack/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":281642036,"owners_count":26536358,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","status":"online","status_checked_at":"2025-10-29T02:00:06.901Z","response_time":59,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["aggregation","breakage","coagulation","fortran","pbe","population-balance-equation"],"created_at":"2025-10-29T14:56:13.136Z","updated_at":"2025-10-29T14:56:15.664Z","avatar_url":"https://github.com/HugoMVale.png","language":"Fortran","funding_links":[],"categories":[],"sub_categories":[],"readme":"# pbepack\n\n[![CI](https://github.com/HugoMVale/pbetools/actions/workflows/CI.yml/badge.svg)](https://github.com/HugoMVale/pbetools/actions)\n[![codecov](https://codecov.io/gh/HugoMVale/pbepack/graph/badge.svg?token=HPSERAGMA4)](https://codecov.io/gh/HugoMVale/pbepack)\n[![Language](https://img.shields.io/badge/-Fortran-734f96?logo=fortran\u0026logoColor=white)](https://github.com/topics/fortran)\n\n## Status\n\n`pbepack` is currently being developed and not yet ready for use.\n\n## Description\n\n`pbepack` is a modern-Fortran package to solve population balance equations (PBE) for one- and two-component aggregation processes using the (extended) fixed pivot method. For single component systems, the code implements the method of [Kumar \u0026 Ramkrishna (1996)](https://doi.org/10.1016/0009-2509(96)88489-2), and for bivariate aggregation the method of [Vale \u0026 McKenna (2005)](https://doi.org/10.1021/ie050179s).\n\n## Underlying PBE\n\nIf the system is spatially homogeneous, a two-component aggregation process is described by the following PBE:\n\n\u003cimg src=\"https://latex.codecogs.com/svg.latex?\\large\u0026space;\\begin{align*}\u0026space;\u0026\u0026space;\\frac{{\\partial\u0026space;n(x,y,t)}}{{\\partial\u0026space;t}}\u0026space;=\u0026space;\\\\\u0026space;\u0026\u0026space;\\frac{1}{2}\\int_0^x\u0026space;{\\int_0^y\u0026space;{\\beta\u0026space;(x\u0026space;-\u0026space;x',y\u0026space;-\u0026space;y';x',y';t)n(x\u0026space;-\u0026space;x',y\u0026space;-\u0026space;y',t)n(x',y',t)\u0026space;d\u0026space;x'\u0026space;d\u0026space;y'}}\u0026space;\\\\\u0026space;\u0026\u0026space;-n(x,y,t)\\int_0^\\infty\u0026space;{\\int_0^\\infty\u0026space;{\\beta\u0026space;(x,y;x',y';t)n(x',y',t)d\u0026space;x'\u0026space;d\u0026space;y'}}\u0026space;\\end{align*}\" title=\"\\large \\begin{align*} \u0026 \\frac{{\\partial n(x,y,t)}}{{\\partial t}} = \\\\ \u0026 \\frac{1}{2}\\int_0^x {\\int_0^y {\\beta (x - x',y - y';x',y';t)n(x - x',y - y',t)n(x',y',t) d x' d y'}} \\\\ \u0026 -n(x,y,t)\\int_0^\\infty {\\int_0^\\infty {\\beta (x,y;x',y';t)n(x',y',t)d x' d y'}} \\end{align*}\" /\u003e\n\nwhere \u003cimg src=\"https://latex.codecogs.com/svg.latex?\\inline\u0026space;n(x,y,t)\u0026space;dx\u0026space;dy\" title=\"n(x,y,t) dx dy\" /\u003e is the number of particles of state \u003cimg src=\"https://latex.codecogs.com/svg.latex?\\inline\u0026space;(x,y)\" title=\"(x,y)\" /\u003e per unit volume at time \u003cimg src=\"https://latex.codecogs.com/svg.latex?t\" title=\"t\" /\u003e and \u003cimg src=\"https://latex.codecogs.com/svg.latex?\\beta\u0026space;(x,y;x',y';t)\" title=\"\\beta (x,y;x',y';t)\" /\u003e is the aggregation rate coefficient. The internal coordinates \u003cimg src=\"https://latex.codecogs.com/svg.latex?x\" title=\"x\" /\u003e and \u003cimg src=\"https://latex.codecogs.com/svg.latex?y\" title=\"y\" /\u003e denote the amount (mass, moles, etc.) of each component in the particle.\n\n## Getting started\n\n### Build\n\nThe easiest way to build/test the code and run the examples is by means of [`fpm`](https://fpm.fortran-lang.org/en/index.html). To run a given example, just do:\n\n```\nfpm run --example \"example-filename\"\n```\n\nand the numerical results will be stored in the [`output`](/output) subfolder. You can then use the provided Python script to read the data and plot the results.\n\n### Usage\n\ncomming soon...\n\n## Examples\n\ncomming soon...\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhugomvale%2Fpbepack","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fhugomvale%2Fpbepack","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhugomvale%2Fpbepack/lists"}