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{"title":"浅层模型中微流体的机械法向色散𝒩ℒℋ𝒮冲击波","authors":"Fatih Şevgin, Talat Körpinar","doi":"10.1142/s0217984924503810","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we obtain normal dispersive <span><math altimg=\"eq-00003.gif\" display=\"inline\"><mi mathvariant=\"cal\">𝒩</mi><mi mathvariant=\"cal\">ℒ</mi><mi mathvariant=\"cal\">ℋ</mi><mi mathvariant=\"cal\">𝒮</mi></math></span><span></span> shock waves for <span><math altimg=\"eq-00004.gif\" display=\"inline\"><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> dam-break intensity by the nonlinear heat system. Then, we obtain super-fluid normal dispersive <span><math altimg=\"eq-00005.gif\" display=\"inline\"><mi mathvariant=\"cal\">𝒩</mi><mi mathvariant=\"cal\">ℒ</mi><mi mathvariant=\"cal\">ℋ</mi><mi mathvariant=\"cal\">𝒮</mi></math></span><span></span> shock waves for <span><math altimg=\"eq-00006.gif\" display=\"inline\"><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> dam-break microfluidics. Finally, we illustrate thermonormal <span><math altimg=\"eq-00007.gif\" display=\"inline\"><mi mathvariant=\"cal\">𝒩</mi><mi mathvariant=\"cal\">ℒ</mi><mi mathvariant=\"cal\">ℋ</mi><mi mathvariant=\"cal\">𝒮</mi></math></span><span></span> pressure of <span><math altimg=\"eq-00008.gif\" display=\"inline\"><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\"false\">(</mo><msub><mrow><mi mathvariant=\"cal\">𝒥</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy=\"false\">)</mo></math></span><span></span> wave energy with normal dam-break in shallow water.</p>","PeriodicalId":18570,"journal":{"name":"Modern Physics Letters B","volume":"66 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mechanical normal dispersive 𝒩ℒℋ𝒮 shock waves of microfluidics in shallow model\",\"authors\":\"Fatih Şevgin, Talat Körpinar\",\"doi\":\"10.1142/s0217984924503810\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we obtain normal dispersive <span><math altimg=\\\"eq-00003.gif\\\" display=\\\"inline\\\"><mi mathvariant=\\\"cal\\\">𝒩</mi><mi mathvariant=\\\"cal\\\">ℒ</mi><mi mathvariant=\\\"cal\\\">ℋ</mi><mi mathvariant=\\\"cal\\\">𝒮</mi></math></span><span></span> shock waves for <span><math altimg=\\\"eq-00004.gif\\\" display=\\\"inline\\\"><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> dam-break intensity by the nonlinear heat system. Then, we obtain super-fluid normal dispersive <span><math altimg=\\\"eq-00005.gif\\\" display=\\\"inline\\\"><mi mathvariant=\\\"cal\\\">𝒩</mi><mi mathvariant=\\\"cal\\\">ℒ</mi><mi mathvariant=\\\"cal\\\">ℋ</mi><mi mathvariant=\\\"cal\\\">𝒮</mi></math></span><span></span> shock waves for <span><math altimg=\\\"eq-00006.gif\\\" display=\\\"inline\\\"><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> dam-break microfluidics. Finally, we illustrate thermonormal <span><math altimg=\\\"eq-00007.gif\\\" display=\\\"inline\\\"><mi mathvariant=\\\"cal\\\">𝒩</mi><mi mathvariant=\\\"cal\\\">ℒ</mi><mi mathvariant=\\\"cal\\\">ℋ</mi><mi mathvariant=\\\"cal\\\">𝒮</mi></math></span><span></span> pressure of <span><math altimg=\\\"eq-00008.gif\\\" display=\\\"inline\\\"><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo><mo>,</mo><mi>ϕ</mi><mo stretchy=\\\"false\\\">(</mo><msub><mrow><mi mathvariant=\\\"cal\\\">𝒥</mi></mrow><mrow><mn>3</mn></mrow></msub><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> wave energy with normal dam-break in shallow water.</p>\",\"PeriodicalId\":18570,\"journal\":{\"name\":\"Modern Physics Letters B\",\"volume\":\"66 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Modern Physics Letters B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/s0217984924503810\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Modern Physics Letters B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s0217984924503810","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
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