The present paper reviews advances in the study of two major intercontinental disjunct biogeographic patterns： （i） between Eurasian and western North American deserts with the Mediterranean climate （the Madrean- T...The present paper reviews advances in the study of two major intercontinental disjunct biogeographic patterns： （i） between Eurasian and western North American deserts with the Mediterranean climate （the Madrean- Tethyan disjunctions）; and （ii） between the temperate regions of North and South America （the amphitropical disjunctions）. Both disjunct patterns have multiple times of origin. The amphitropical disjunctions have largely resulted from long-distance dispersal, primarily from the Miocene to the Holocene, with available data indicating that most lineages dispersed from North to South America. Results of recent studies on the Mediterranean disjuncts between the deserts of Eurasia and western North America support the multiple modes of origin and are mostly consistent with hypotheses of long-distance dispersal and the North Atlantic migration. Axelrod＇s Madrean-Tethyan hypothesis, which implies vicariance between the two regions in the early Tertiary, has been favored by a few studies. The Beringian migration corridor for semiarid taxa is also supported in some cases.展开更多
The formation of pantropical intercontinental disjunction(PID)in plants has generally been attributed to vicariance,boreotropical migration,and long-distance dispersal.However,this pattern has primarily been examined ...The formation of pantropical intercontinental disjunction(PID)in plants has generally been attributed to vicariance,boreotropical migration,and long-distance dispersal.However,this pattern has primarily been examined in herbs,shrubs,and trees,and less commonly studied in interlayer plant taxa.Here we examined evolutionary processes that resulted in the PID of a pantropical woody liana,Uncaria(Rubiaceae).We first constructed a comprehensive phylogeny by employing 73 plastid protein-coding sequences from 29 accessions of Uncaria(including 16 newly sequenced)from different continents.We then inferred divergence time,history and ecological niche evolution of this genus.Our results showed that Uncaria consisted of four well-supported clades that belonged to two geographically distinct lineages:the Asia-Oceania lineage and the Afro-Neotropical lineage.Biogeographic reconstruction showed this genus likely originated in Asia during the early Miocene(ca.19.03 Ma)and the Middle Miocene Climatic Optimum may have triggered the early diversification of Uncaria.Due to its recent origin and small seeds with long wings,wind or water-mediated long-distance dispersal may have contributed to the distribution of Uncaria in tropical Oceania(via stepping-stone dispersal)and tropical Africa and America(by transoceanic dispersal).Our findings also indicate that diversification of Uncaria was primarily driven by ecological niche divergence,particularly climatic factors.Our study emphasizes the dual role of climatic niche divergence and long-distance dispersal in shaping the PID of Uncaria,providing references for many other extant lineages with similar distributions.展开更多
To evaluate the heat performance of the lifting-body entry vehicle during the hypersonic gliding phase,entry flight heat tests involving the determination of the maximum peak-heat-flux entry trajectory with complex co...To evaluate the heat performance of the lifting-body entry vehicle during the hypersonic gliding phase,entry flight heat tests involving the determination of the maximum peak-heat-flux entry trajectory with complex constraints are essential.A significant obstacle is the uncertainty of passage time or energy states of the maximum peak entry heat flux point and waypoints.This paper showcases an endeavour to leverage disjunctive programming and combinatorial theory for the max-max type(maximum peak-heat-flux)Entry Trajectory Optimization(ETO)problems with complex constraints such as dynamic pressure,normal load,waypoints,and no-fly zones.The concept of a"generalized waypoint"is introduced,and the maximum peak-heat-flux point is regarded as a"generalized waypoint".Through the application of propositional calculus rules,the derivation of generalized waypoints incorporating various physical quantities and magnitudes such as heat flux density,longitude,and latitude is actualized in one disjunctive normal form,enabling resolution via a unified method.Consequently,a novel method based on combinatorial prior rules is proposed,utilizing Successive Mixed-Integer Nonlinear Programming(SMINLP)to optimize various heat entry test flight trajectories.Numerical experiments are provided to show the computational accuracy,stability,and adaptability of the proposed method in solving maxmax type entry optimal control problems.展开更多
Toxicodendron is a genus in the Rhus complex of Anacardiaceae with a disjunct distribution between eastern Asia and North America, extending to southeastern Asia and the neotropics. Nuclear （internal transcribed spac...Toxicodendron is a genus in the Rhus complex of Anacardiaceae with a disjunct distribution between eastern Asia and North America, extending to southeastern Asia and the neotropics. Nuclear （internal transcribed spacer, external transcribed spacer, and NIA-i3） and chloroplast （ndhF and trnL-F） sequences were used to construct phylogenetic relationships of Toxicodendron. Phylogenetic analysis of these data strongly support Toxieodendron as a monophyletic group distinct from other genera of the Rhus complex, and the phylogeny does not fully corroborate classification at the sectional level. Two temperate disjunct lineages were detected, one from section Toxicodendron and the other between the eastern North American Toxicodendron vernix and the eastern Asian Toxicodendron vernieifluum. Their divergence times were estimated to be 13.46 （7.95-19.42） and 7.53 （2.76-12.86） mya, respectively. The disjunction between section Griffithii （taxa from warm temperate to tropical Asia） and Toxieodendron striatum （from the neotropics） was supported and their divergence time was estimated to be 20.84 （11.1 6-30.52） mya in the early Miocene. Our biogeographic results and the paleontological data support the Bering land bridge as the most likely route to explain the temperate disjunctions, yet the tropical disjunction in Toxicodendron seems to be best explained by the North Atlantic land bridge hypothesis.展开更多
The disjunct distribution of plants between eastern Asia(EA) and North America(NA) is one of the most well-known biogeographic patterns. However, the formation and historical process of this pattern have been long deb...The disjunct distribution of plants between eastern Asia(EA) and North America(NA) is one of the most well-known biogeographic patterns. However, the formation and historical process of this pattern have been long debated. Chamaecyparis is a good model to test previous hypotheses about the formation of this disjunct pattern as it contains six species disjunctly distributed in EA, western North America(WNA)and eastern North America(ENA). In this study, we applied ecological niche models to test the formation of the disjunct pattern of Chamaecyparis. The model calibrated with the EA species was able to predict the distribution of eastern NA species well, but not the western NA species. Furthermore, the eastern Asian species were shown to have higher niche overlap with the eastern North American species. The EA species were also shown to share more similar habitats with ENA species than with WNA species in the genus. Chamaecyparis species in WNA experienced a significant niche shift compared with congeneric species. Chamaecyparis had a low number of suitable regions in Europe and the middle and western NA during the Last Glacial Maximum(LGM) period, and became extinct in the former region whereas it retains residual distribution in the latter. The extirpations in western NA and Europe in response to the late Neogene and Quaternary climatic cooling and the more similar habitats between ENA and EA ultimately shaped the current intercontinental disjunct distribution of Chamaecyparis. Both current hypotheses may be also jointly applied to explain more eastern Asian and eastern North American disjunctions observed today.展开更多
More than 200 research papers on the molecular phylogeny and phylogenetic biogeography ofbryophytes have been published since the beginning of this millenium. These papers corroborated assumptions of a complex genetic...More than 200 research papers on the molecular phylogeny and phylogenetic biogeography ofbryophytes have been published since the beginning of this millenium. These papers corroborated assumptions of a complex genetic structure of morphologically circumscribed bryophytes, and raised reservations against many morphologically justified species concepts, especially within the mosses. However, many molecular studies allowed for corrections and modifications of morphological classification schemes. Several studies reported that the phylogenetic structure of disjunctly distributed bryophyte species reflects their geographical ranges rather than morphological disparities. Molecular data led to new appraisals of distribution ranges and allowed for the reconstruction of refugia and migration routes. Intercontinental ranges of bryophytes are often caused by dispersal rather than geographical vicariance. Many distribution patterns of disjunct bryophytes are likely formed by processes such as short distance dispersal, rare long distance dispersal events, extinction, recolonization and diversification.展开更多
The underlying causes of biodiversity disparities among geographic regions have long been a fundamental theme in ecology and evolution.However,the patterns of phylogenetic diversity(PD) and phylogenetic beta diversity...The underlying causes of biodiversity disparities among geographic regions have long been a fundamental theme in ecology and evolution.However,the patterns of phylogenetic diversity(PD) and phylogenetic beta diversity(PBD) of congeners that are disjunctly distributed between eastern Asia-eastern North America(EA-ENA disjuncts) and their associated factors remain unknown.Here we investigated the standardized effect size of PD(SES-PD),PBD,and potentially associated factors in 11natural mixed forest sites(five in EA and six in ENA) where abundant EA-ENA disjuncts occur.We found that the disjuncts in ENA possessed higher SES-PD than those in EA at the continental scale(1.96vs-1.12),even though the number of disjunct species in ENA is much lower than in EA(128 vs 263).SESPD of the EA-ENA disjuncts tended to decrease with increasing latitude in 11 sites.The latitudinal diversity gradient of SES-PD was stronger in EA sites than in ENA sites.Based on the unweighted unique fraction metric(UniFrac) distance and the phylogenetic community dissimilarity,PBD showed that the two northern sites in EA were more similar to the six-site ENA group than to the remaining southern EA sites.Based on the standardized effect size of mean pairwise distances(SES-MPD),nine of eleven studied sites showed a neutral community structure(-1.96 ≤SES-MPD ≤1.96).Both Pearson’s r and structural equation modeling suggested that SES-PD of the EA-ENA disjuncts was mostly associated with mean divergence time.Moreover,SES-PD of the EA-ENA disjuncts was positively correlated with temperaturerelated climatic factors,although negatively correlated with mean diversification rate and community structure.By applying approaches from phylogenetics and community ecology,our work sheds light on historical patterns of the EA-ENA disjunction and paves the way for further research.展开更多
The genus Thuja is ideal for investigating the genetic basis of the East Asia-North America disjunction.The biogeographical background of the genus is debatable and an adaptive strategy is lacking.Through the analysis...The genus Thuja is ideal for investigating the genetic basis of the East Asia-North America disjunction.The biogeographical background of the genus is debatable and an adaptive strategy is lacking.Through the analysis and mining of comparative transcriptomes,species differentiation and positively selected genes(PSGs)were identified to provide information for understanding the environmental adaptation strategies of the genus Thuja.De novo assembly yielded 44,397-74,252 unigenes of the five Thuja species with contig N50length ranging from 1,559 to 1,724 bp.Annotations revealed a similar distribution of functional categories among them.Based on the phylogenetic trees constructed using the transcriptome data,T.sutchuenensis was divided first,followed by T.plicata and T.occidentalis.The final differentiation of T.koraiensis and T.standishii formed a clade.Enrichment analysis indicated that the PSGs of the North American Thuja species were involved in plant hormone signal transduction and carbon fixation of photosynthetic organisms pathways.The PSGs of East Asian Thuja were related to phenolic,alkaloid,and terpenoid synthesis,important stress-resistant genes and could increase plant resistance to external environmental stresses.This study discovered numerous aroma synthetic-related PSGs including terpene synthase(TPS)genes and lipid phosphate phosphatase 2(LPP2),associated with the synthetic aroma of T.sutchuenensis.Physiological indicators,such as the contents of soluble sugars,total chlorophyll,total phenolics,and total flavonoids were determined,which are consistent with the PSGs enrichment pathways associated with adaptive strategies in the five Thuja species.The results of this study provide an important basis for future studies on conservation genetics.展开更多
Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is develope...Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is developed for the optimal design of refrigeration cycle and heat exchanger network(HEN) simultaneously. Taking the heat integration between the external heat sources/sinks and the refrigeration cycle into consideration, a superstructure with sub-coolers is developed. Through defining logical variables that indicate the relative temperature positions of refrigerant streams after sub-coolers, the synthesis is formulated as a Generalized Disjunctive Programming(GDP) problem based on LP transshipment model, with the target of minimizing the total compressor shaft work in the refrigeration system. The GDP model is then reformulated as a Mixed Integer Nonlinear Programming(MINLP) problem with the aid of binary variables and Big-M Constraint Method. The efficacy of the process synthesis model is demonstrated by a case study of ethylene refrigeration system. The result shows that the optimization can significantly reduce the exergy loss as well as the total compression shaft work.展开更多
基金supported,in part,by grants from the National Science Foundation (DEB 045573 to Michael DILLON and Jun WENand DEB 0743474 to Steve MANCHESTER and Jun WEN)support for S. ICKERT-BOND from the National Museum of Natural History,the Smithsonian Institution
文摘The present paper reviews advances in the study of two major intercontinental disjunct biogeographic patterns： （i） between Eurasian and western North American deserts with the Mediterranean climate （the Madrean- Tethyan disjunctions）; and （ii） between the temperate regions of North and South America （the amphitropical disjunctions）. Both disjunct patterns have multiple times of origin. The amphitropical disjunctions have largely resulted from long-distance dispersal, primarily from the Miocene to the Holocene, with available data indicating that most lineages dispersed from North to South America. Results of recent studies on the Mediterranean disjuncts between the deserts of Eurasia and western North America support the multiple modes of origin and are mostly consistent with hypotheses of long-distance dispersal and the North Atlantic migration. Axelrod＇s Madrean-Tethyan hypothesis, which implies vicariance between the two regions in the early Tertiary, has been favored by a few studies. The Beringian migration corridor for semiarid taxa is also supported in some cases.
基金funded equally by grants from the National Natural Science Foundation of China(32322006 and 32100187)the Second Tibetan Plateau Scientific Expedition and Research(STEP)program(2024QZKK0200)+5 种基金by the Key Projects of the Joint Fund of the National Natural Science Foundation of China(U23A20149)the Key R&D Program of Yunnan Province(202103AF140005 and 202101BC070002)the Yunnan Provincial Science and Technology Talent and Platform Plan(202305AM070005)the Key Specialized Research and Development Breakthrough Program in Henan Province(232102110237)the Natural Science Foundation of Henan Province(242300421572)the Strategic Biological Resources Capacity Building Project of Chinese Academy of Sciences(KFJ-BRP-017-08).
文摘The formation of pantropical intercontinental disjunction(PID)in plants has generally been attributed to vicariance,boreotropical migration,and long-distance dispersal.However,this pattern has primarily been examined in herbs,shrubs,and trees,and less commonly studied in interlayer plant taxa.Here we examined evolutionary processes that resulted in the PID of a pantropical woody liana,Uncaria(Rubiaceae).We first constructed a comprehensive phylogeny by employing 73 plastid protein-coding sequences from 29 accessions of Uncaria(including 16 newly sequenced)from different continents.We then inferred divergence time,history and ecological niche evolution of this genus.Our results showed that Uncaria consisted of four well-supported clades that belonged to two geographically distinct lineages:the Asia-Oceania lineage and the Afro-Neotropical lineage.Biogeographic reconstruction showed this genus likely originated in Asia during the early Miocene(ca.19.03 Ma)and the Middle Miocene Climatic Optimum may have triggered the early diversification of Uncaria.Due to its recent origin and small seeds with long wings,wind or water-mediated long-distance dispersal may have contributed to the distribution of Uncaria in tropical Oceania(via stepping-stone dispersal)and tropical Africa and America(by transoceanic dispersal).Our findings also indicate that diversification of Uncaria was primarily driven by ecological niche divergence,particularly climatic factors.Our study emphasizes the dual role of climatic niche divergence and long-distance dispersal in shaping the PID of Uncaria,providing references for many other extant lineages with similar distributions.
基金funded by the Key Laboratory of Cross-Domain Flight Interdisciplinary Technology,China(No.2024-KF02201)the National Natural Science Foundation of China(No.61973326)。
文摘To evaluate the heat performance of the lifting-body entry vehicle during the hypersonic gliding phase,entry flight heat tests involving the determination of the maximum peak-heat-flux entry trajectory with complex constraints are essential.A significant obstacle is the uncertainty of passage time or energy states of the maximum peak entry heat flux point and waypoints.This paper showcases an endeavour to leverage disjunctive programming and combinatorial theory for the max-max type(maximum peak-heat-flux)Entry Trajectory Optimization(ETO)problems with complex constraints such as dynamic pressure,normal load,waypoints,and no-fly zones.The concept of a"generalized waypoint"is introduced,and the maximum peak-heat-flux point is regarded as a"generalized waypoint".Through the application of propositional calculus rules,the derivation of generalized waypoints incorporating various physical quantities and magnitudes such as heat flux density,longitude,and latitude is actualized in one disjunctive normal form,enabling resolution via a unified method.Consequently,a novel method based on combinatorial prior rules is proposed,utilizing Successive Mixed-Integer Nonlinear Programming(SMINLP)to optimize various heat entry test flight trajectories.Numerical experiments are provided to show the computational accuracy,stability,and adaptability of the proposed method in solving maxmax type entry optimal control problems.
基金supported bygrants from the National Basic Research Program of China (973 Program,grant no. 2007CB411601)the National Natural Science Foundation of China (grant nos.30625004 and 40771073 to H. Sun)+2 种基金the Yunnan Natural Science Foundation (grant no. 2008CC013)the John D. and Catherine T. MacArthur Foundation (to J.Wen)supported by the Laboratory of Analytical Biology of the National Museum of Natural History,Smithsonian Institution,Washington DC,USA
文摘Toxicodendron is a genus in the Rhus complex of Anacardiaceae with a disjunct distribution between eastern Asia and North America, extending to southeastern Asia and the neotropics. Nuclear （internal transcribed spacer, external transcribed spacer, and NIA-i3） and chloroplast （ndhF and trnL-F） sequences were used to construct phylogenetic relationships of Toxicodendron. Phylogenetic analysis of these data strongly support Toxieodendron as a monophyletic group distinct from other genera of the Rhus complex, and the phylogeny does not fully corroborate classification at the sectional level. Two temperate disjunct lineages were detected, one from section Toxicodendron and the other between the eastern North American Toxicodendron vernix and the eastern Asian Toxicodendron vernieifluum. Their divergence times were estimated to be 13.46 （7.95-19.42） and 7.53 （2.76-12.86） mya, respectively. The disjunction between section Griffithii （taxa from warm temperate to tropical Asia） and Toxieodendron striatum （from the neotropics） was supported and their divergence time was estimated to be 20.84 （11.1 6-30.52） mya in the early Miocene. Our biogeographic results and the paleontological data support the Bering land bridge as the most likely route to explain the temperate disjunctions, yet the tropical disjunction in Toxicodendron seems to be best explained by the North Atlantic land bridge hypothesis.
基金funded by grants from the Ministry of Science and Technology of China, Basic Research Project(No. 2013FY112600)the Talent Project of Yunnan Province(No. 2011CI042)
文摘The disjunct distribution of plants between eastern Asia(EA) and North America(NA) is one of the most well-known biogeographic patterns. However, the formation and historical process of this pattern have been long debated. Chamaecyparis is a good model to test previous hypotheses about the formation of this disjunct pattern as it contains six species disjunctly distributed in EA, western North America(WNA)and eastern North America(ENA). In this study, we applied ecological niche models to test the formation of the disjunct pattern of Chamaecyparis. The model calibrated with the EA species was able to predict the distribution of eastern NA species well, but not the western NA species. Furthermore, the eastern Asian species were shown to have higher niche overlap with the eastern North American species. The EA species were also shown to share more similar habitats with ENA species than with WNA species in the genus. Chamaecyparis species in WNA experienced a significant niche shift compared with congeneric species. Chamaecyparis had a low number of suitable regions in Europe and the middle and western NA during the Last Glacial Maximum(LGM) period, and became extinct in the former region whereas it retains residual distribution in the latter. The extirpations in western NA and Europe in response to the late Neogene and Quaternary climatic cooling and the more similar habitats between ENA and EA ultimately shaped the current intercontinental disjunct distribution of Chamaecyparis. Both current hypotheses may be also jointly applied to explain more eastern Asian and eastern North American disjunctions observed today.
基金support from the German Research Foundation(grants HE 3584/1-4)
文摘More than 200 research papers on the molecular phylogeny and phylogenetic biogeography ofbryophytes have been published since the beginning of this millenium. These papers corroborated assumptions of a complex genetic structure of morphologically circumscribed bryophytes, and raised reservations against many morphologically justified species concepts, especially within the mosses. However, many molecular studies allowed for corrections and modifications of morphological classification schemes. Several studies reported that the phylogenetic structure of disjunctly distributed bryophyte species reflects their geographical ranges rather than morphological disparities. Molecular data led to new appraisals of distribution ranges and allowed for the reconstruction of refugia and migration routes. Intercontinental ranges of bryophytes are often caused by dispersal rather than geographical vicariance. Many distribution patterns of disjunct bryophytes are likely formed by processes such as short distance dispersal, rare long distance dispersal events, extinction, recolonization and diversification.
基金supported by the National Natural Science Foundation of China (Grant No.31461123001 to C.X.F.)the US National Science Foundation Dimensions of Biodiversity US-China Program (DEB-1442280 to P.S.S.and D.E.S.)+1 种基金the HZAU Talent Start-up Fund (Grant no.11042210014 to M.S.)the China Scholarship Council (Grant no.201806320056 to H.Y.L.)。
文摘The underlying causes of biodiversity disparities among geographic regions have long been a fundamental theme in ecology and evolution.However,the patterns of phylogenetic diversity(PD) and phylogenetic beta diversity(PBD) of congeners that are disjunctly distributed between eastern Asia-eastern North America(EA-ENA disjuncts) and their associated factors remain unknown.Here we investigated the standardized effect size of PD(SES-PD),PBD,and potentially associated factors in 11natural mixed forest sites(five in EA and six in ENA) where abundant EA-ENA disjuncts occur.We found that the disjuncts in ENA possessed higher SES-PD than those in EA at the continental scale(1.96vs-1.12),even though the number of disjunct species in ENA is much lower than in EA(128 vs 263).SESPD of the EA-ENA disjuncts tended to decrease with increasing latitude in 11 sites.The latitudinal diversity gradient of SES-PD was stronger in EA sites than in ENA sites.Based on the unweighted unique fraction metric(UniFrac) distance and the phylogenetic community dissimilarity,PBD showed that the two northern sites in EA were more similar to the six-site ENA group than to the remaining southern EA sites.Based on the standardized effect size of mean pairwise distances(SES-MPD),nine of eleven studied sites showed a neutral community structure(-1.96 ≤SES-MPD ≤1.96).Both Pearson’s r and structural equation modeling suggested that SES-PD of the EA-ENA disjuncts was mostly associated with mean divergence time.Moreover,SES-PD of the EA-ENA disjuncts was positively correlated with temperaturerelated climatic factors,although negatively correlated with mean diversification rate and community structure.By applying approaches from phylogenetics and community ecology,our work sheds light on historical patterns of the EA-ENA disjunction and paves the way for further research.
基金supported by the National Natural Science Foundation of China(31870664)the 948 Program of National Forestry and Grassland Administration(2013-4-47)the National Key Research and Development Program of China(2022YFD2200103)。
文摘The genus Thuja is ideal for investigating the genetic basis of the East Asia-North America disjunction.The biogeographical background of the genus is debatable and an adaptive strategy is lacking.Through the analysis and mining of comparative transcriptomes,species differentiation and positively selected genes(PSGs)were identified to provide information for understanding the environmental adaptation strategies of the genus Thuja.De novo assembly yielded 44,397-74,252 unigenes of the five Thuja species with contig N50length ranging from 1,559 to 1,724 bp.Annotations revealed a similar distribution of functional categories among them.Based on the phylogenetic trees constructed using the transcriptome data,T.sutchuenensis was divided first,followed by T.plicata and T.occidentalis.The final differentiation of T.koraiensis and T.standishii formed a clade.Enrichment analysis indicated that the PSGs of the North American Thuja species were involved in plant hormone signal transduction and carbon fixation of photosynthetic organisms pathways.The PSGs of East Asian Thuja were related to phenolic,alkaloid,and terpenoid synthesis,important stress-resistant genes and could increase plant resistance to external environmental stresses.This study discovered numerous aroma synthetic-related PSGs including terpene synthase(TPS)genes and lipid phosphate phosphatase 2(LPP2),associated with the synthetic aroma of T.sutchuenensis.Physiological indicators,such as the contents of soluble sugars,total chlorophyll,total phenolics,and total flavonoids were determined,which are consistent with the PSGs enrichment pathways associated with adaptive strategies in the five Thuja species.The results of this study provide an important basis for future studies on conservation genetics.
基金Supported by the National Natural Science Foundation of China(21676183)
文摘Refrigeration system holds an important role in process industries. The optimal synthesis cannot only reduce the energy consumption, but also save the production costs. In this study, a general methodology is developed for the optimal design of refrigeration cycle and heat exchanger network(HEN) simultaneously. Taking the heat integration between the external heat sources/sinks and the refrigeration cycle into consideration, a superstructure with sub-coolers is developed. Through defining logical variables that indicate the relative temperature positions of refrigerant streams after sub-coolers, the synthesis is formulated as a Generalized Disjunctive Programming(GDP) problem based on LP transshipment model, with the target of minimizing the total compressor shaft work in the refrigeration system. The GDP model is then reformulated as a Mixed Integer Nonlinear Programming(MINLP) problem with the aid of binary variables and Big-M Constraint Method. The efficacy of the process synthesis model is demonstrated by a case study of ethylene refrigeration system. The result shows that the optimization can significantly reduce the exergy loss as well as the total compression shaft work.
