{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-8510084","patent":{"patent_number":"US-8510084","title":"Method, apparatus and computer program for multiple time stepping simulation of a thermodynamic system using shadow hamiltonians","assignee":null,"inventors":[],"filing_date":"2010-07-08T00:00:00.000Z","publication_date":"2013-08-13T00:00:00.000Z","cpc_codes":["G06F","G06F"],"num_claims":14,"abstract":"A computer-implemented method including a momentum refreshment process and a conservative dynamics process, wherein the refreshment process including carrying out an operation of mixing the collective momentum vector with a noise vector and carrying out an acceptance/rejection (acceptance and rejection) operation; the dynamics process including applying a multiple time stepping conservative dynamics operation to a current state, in which calculations corresponding to more slowly varying energy parts undergo an averaging procedure and are carried out at a larger time step than calculations corresponding to more quickly varying energy parts; and carrying out an acceptance/rejection operation based on an approximation of the system energy expressed using shadow Hamiltonians and include accepting a current state or returning a replacement state."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Method, apparatus and computer program for multiple time stepping simulation of a thermodynamic system using shadow hamiltonians","description":"A computer-implemented method including a momentum refreshment process and a conservative dynamics process, wherein the refreshment process including carrying out an operation of mixing the collective","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-8510084","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-8510084","citation_suggestion":"Patentable. \"Method, apparatus and computer program for multiple time stepping simulation of a thermodynamic system using shadow hamiltonians\" (US-8510084). https://patentable.app/patents/US-8510084","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-8510084","json":"https://patentable.app/api/llm-context/US-8510084","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-05-30T18:47:42.779Z"}