{"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}
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Abstract
In this paper, we obtain normal dispersive shock waves for dam-break intensity by the nonlinear heat system. Then, we obtain super-fluid normal dispersive shock waves for dam-break microfluidics. Finally, we illustrate thermonormal pressure of wave energy with normal dam-break in shallow water.
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