{"id":"https://openalex.org/W4385707868","doi":"https://doi.org/10.3390/axioms12080770","title":"The Laplace Transform Shortcut Solution to a One-Dimensional Heat Conduction Model with Dirichlet Boundary Conditions","display_name":"The Laplace Transform Shortcut Solution to a One-Dimensional Heat Conduction Model with Dirichlet Boundary Conditions","publication_year":2023,"publication_date":"2023-08-09","ids":{"openalex":"https://openalex.org/W4385707868","doi":"https://doi.org/10.3390/axioms12080770"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12080770","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080770","pdf_url":"https://www.mdpi.com/2075-1680/12/8/770/pdf?version=1691567103","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/8/770/pdf?version=1691567103","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101472723","display_name":"Dan Wu","orcid":"https://orcid.org/0009-0008-5592-3079"},"institutions":[{"id":"https://openalex.org/I39774598","display_name":"Hefei University","ror":"https://ror.org/01f5rdf64","country_code":"CN","type":"education","lineage":["https://openalex.org/I39774598"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Wu","raw_affiliation_strings":["School of Urban Construction and Transportation, Hefei University, Hefei 230601, China"],"raw_orcid":"https://orcid.org/0009-0008-5592-3079","affiliations":[{"raw_affiliation_string":"School of Urban Construction and Transportation, Hefei University, Hefei 230601, China","institution_ids":["https://openalex.org/I39774598"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024123657","display_name":"Yuezan Tao","orcid":"https://orcid.org/0000-0003-2102-2930"},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuezan Tao","raw_affiliation_strings":["School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080766858","display_name":"Honglei Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I16365422","display_name":"Hefei University of Technology","ror":"https://ror.org/02czkny70","country_code":"CN","type":"education","lineage":["https://openalex.org/I16365422"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Honglei Ren","raw_affiliation_strings":["School of Civil Engineering, Hefei University of Technology, Hefei 230009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil Engineering, Hefei University of Technology, Hefei 230009, China","institution_ids":["https://openalex.org/I16365422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024123657"],"corresponding_institution_ids":["https://openalex.org/I16365422"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1782},"fwci":0.2493,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.39907945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"12","issue":"8","first_page":"770","last_page":"770"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11205","display_name":"Numerical methods in inverse problems","score":0.9934999942779541,"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/laplace-transform","display_name":"Laplace transform","score":0.7583659887313843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6790128350257874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.587040364742279},{"id":"https://openalex.org/keywords/inverse-laplace-transform","display_name":"Inverse Laplace transform","score":0.5327107310295105},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.474425733089447},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4725118577480316},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46329984068870544},{"id":"https://openalex.org/keywords/convolution-theorem","display_name":"Convolution theorem","score":0.4276392459869385},{"id":"https://openalex.org/keywords/inflection-point","display_name":"Inflection point","score":0.42367738485336304},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4130701720714569},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.385440856218338},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1658317744731903},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.14102521538734436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07546725869178772}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7583659887313843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6790128350257874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.587040364742279},{"id":"https://openalex.org/C60455284","wikidata":"https://www.wikidata.org/wiki/Q2162701","display_name":"Inverse Laplace transform","level":3,"score":0.5327107310295105},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.474425733089447},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4725118577480316},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46329984068870544},{"id":"https://openalex.org/C79587385","wikidata":"https://www.wikidata.org/wiki/Q2638931","display_name":"Convolution theorem","level":5,"score":0.4276392459869385},{"id":"https://openalex.org/C74545648","wikidata":"https://www.wikidata.org/wiki/Q212794","display_name":"Inflection point","level":2,"score":0.42367738485336304},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4130701720714569},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.385440856218338},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1658317744731903},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.14102521538734436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07546725869178772},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12080770","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080770","pdf_url":"https://www.mdpi.com/2075-1680/12/8/770/pdf?version=1691567103","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:18fde992b39245bdb8d171d25c3e9f08","is_oa":true,"landing_page_url":"https://doaj.org/article/18fde992b39245bdb8d171d25c3e9f08","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 8, p 770 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/8/770/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12080770","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 8; Pages: 770","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12080770","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080770","pdf_url":"https://www.mdpi.com/2075-1680/12/8/770/pdf?version=1691567103","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385707868.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1561487091","https://openalex.org/W1666055319","https://openalex.org/W1977212683","https://openalex.org/W2128222314","https://openalex.org/W2334324548","https://openalex.org/W2348826992","https://openalex.org/W2349153748","https://openalex.org/W2350918796","https://openalex.org/W2353927698","https://openalex.org/W2354036501","https://openalex.org/W2369828760","https://openalex.org/W2384119256","https://openalex.org/W2408519364","https://openalex.org/W2575870713","https://openalex.org/W2755345807","https://openalex.org/W2789274122","https://openalex.org/W2794433085","https://openalex.org/W2900511345","https://openalex.org/W2904469108","https://openalex.org/W2912913403","https://openalex.org/W2939233443","https://openalex.org/W3102845167","https://openalex.org/W3197810406","https://openalex.org/W3210506648","https://openalex.org/W4313509096","https://openalex.org/W4323310381","https://openalex.org/W4361267875","https://openalex.org/W4366286457"],"related_works":["https://openalex.org/W1996624184","https://openalex.org/W3153902684","https://openalex.org/W1822970805","https://openalex.org/W2511927568","https://openalex.org/W4297824036","https://openalex.org/W2623382060","https://openalex.org/W3153959854","https://openalex.org/W2268749972","https://openalex.org/W4234603349","https://openalex.org/W838373261"],"abstract_inverted_index":{"When":[0],"using":[1],"the":[2,16,27,31,48,51,55,59,63,71,75,88,93,96,100,104,110,123,132,137,146,150,158,182,194,197,211,221],"Laplace":[3,56,97],"transform":[4,57,98],"to":[5,26,62,70,84],"solve":[6],"a":[7,39,112,169],"one-dimensional":[8],"heat":[9],"conduction":[10],"model":[11,64,224],"with":[12,175],"Dirichlet":[13],"boundary":[14,32,195],"conditions,":[15],"integration":[17],"and":[18,23,58,99,127,136,196,205,214],"transformation":[19,89],"processes":[20],"become":[21],"complex":[22,40],"cumbersome":[24],"due":[25,69],"varying":[28],"properties":[29,94],"of":[30,50,54,95,107,122,125,134,139,185,199,223],"function":[33,53],"f(t).":[34,140],"Meanwhile,":[35],"if":[36],"f(t)":[37,86,108,117,144,167],"has":[38],"functional":[41],"form,":[42],"e.g.,":[43],"an":[44,176],"exponential":[45],"decay":[46],"function,":[47],"product":[49,124],"image":[52],"general":[60,113,147,159],"solution":[61,115,153],"cannot":[65],"be":[66],"obtained":[67],"directly":[68],"difficulty":[72],"in":[73,87,109],"solving":[74],"inverse.":[76],"To":[77],"address":[78],"this":[79],"issue,":[80],"operators":[81],"are":[82,164,218],"introduced":[83],"replace":[85],"process.":[90],"Based":[91,156],"on":[92,157,181],"convolution":[101,133],"theorem,":[102],"without":[103],"direct":[105],"involvement":[106],"transformation,":[111],"theoretical":[114,148,160],"incorporating":[116],"is":[118,154],"derived,":[119],"which":[120],"consists":[121],"erfc(t)":[126,135],"f(0),":[128],"as":[129,131,168],"well":[130],"derivative":[138],"Then,":[141],"by":[142],"substituting":[143],"into":[145],"solution,":[149,161],"corresponding":[151],"analytical":[152,162],"formulated.":[155],"solutions":[163],"given":[165],"for":[166,220],"commonly":[170],"used":[171],"function.":[172],"Finally,":[173],"combined":[174],"exemplifying":[177],"application":[178],"demonstration":[179],"based":[180],"test":[183],"data":[184],"temperature":[186],"T(x,":[187,201],"t)":[188,202],"at":[189],"point":[190,213],"x":[191],"away":[192],"from":[193],"characteristics":[198],"curve":[200,206,215],"\u2212":[203,209],"t":[204],"\ud835\udf15T(x,":[207],"t)/\ud835\udf15t":[208],"t,":[210],"inflection":[212],"fitting":[216],"methods":[217],"established":[219],"inversion":[222],"parameters.":[225]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2023-08-10T00:00:00"}