Pub Date : 2023-11-21DOI: 10.1007/s10665-023-10301-7
R. B. Kaligatla, S. Singh, B. N. Mandal
This article presents a study on surface gravity wave scattering by a rectangular (box-type) breakwater with thin side plates in the situation of oblique incident waves in deep water. Applying the continuity of fluid pressure and velocity to Havelock’s expansion of velocity potentials, the problem is converted to an integral equation of the Fredholm type, whose solution is the horizontal component of fluid velocity. The integral equation is solved by employing Galerkin’s approximation with polynomials as basis functions multiplied by suitable weight functions. The wave reflection and transmission coefficients are calculated numerically to find the breakwater’s performance on wave scattering. The accuracy of the results is verified through numerical convergence and checking of the energy balance equation. The rectangular breakwater reflects long waves to some extent in water of infinite depth, in contrast to a thin breakwater. The thin plates attached to the rectangular breakwater show a reduction in wave transmission. Furthermore, the attachment of thin plates leads to an increment in horizontal force and a reduction in vertical force.
{"title":"Wave scattering by Pi-type breakwater floating in deep water","authors":"R. B. Kaligatla, S. Singh, B. N. Mandal","doi":"10.1007/s10665-023-10301-7","DOIUrl":"https://doi.org/10.1007/s10665-023-10301-7","url":null,"abstract":"<p>This article presents a study on surface gravity wave scattering by a rectangular (box-type) breakwater with thin side plates in the situation of oblique incident waves in deep water. Applying the continuity of fluid pressure and velocity to Havelock’s expansion of velocity potentials, the problem is converted to an integral equation of the Fredholm type, whose solution is the horizontal component of fluid velocity. The integral equation is solved by employing Galerkin’s approximation with polynomials as basis functions multiplied by suitable weight functions. The wave reflection and transmission coefficients are calculated numerically to find the breakwater’s performance on wave scattering. The accuracy of the results is verified through numerical convergence and checking of the energy balance equation. The rectangular breakwater reflects long waves to some extent in water of infinite depth, in contrast to a thin breakwater. The thin plates attached to the rectangular breakwater show a reduction in wave transmission. Furthermore, the attachment of thin plates leads to an increment in horizontal force and a reduction in vertical force.</p>","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-25DOI: 10.1007/s10665-023-10296-1
Keith Davey, Raul Ochoa-Cabrero
Abstract The theory of scaling called finite similitude does not involve dimensional analysis and is founded on a transport-equation approach that is applicable to all of classical physics. It features a countable infinite number of similitude rules and has recently been extended to other types of governing equations (e.g., differential, variational) by the introduction of a scaling space $$Omega _{beta }$$ Ωβ , within which all physical quantities are deemed dependent on a single dimensional parameter $$beta $$ β . The theory is presently limited to physical applications but the focus of this paper is its extension to other quantitative-based theories such as finance. This is achieved by connecting it to an extended form of dimensional analysis, where changes in any quantity can be associated with curves projected onto a dimensional Lie group. It is shown in the paper how differential similitude identities arising out of the finite similitude theory are universal in the sense they can be formed and applied to any quantitative-based theory. In order to illustrate its applicability outside physics the Black-Scholes equation for option valuation in finance is considered since this equation is recognised to be similar in form to an equation from thermal physics. It is demonstrated that the theory of finite similitude can be applied to the Black-Scholes equation and more widely can be used to assess observed size effects in portfolio performance.
{"title":"Extended finite similitude and dimensional analysis for scaling","authors":"Keith Davey, Raul Ochoa-Cabrero","doi":"10.1007/s10665-023-10296-1","DOIUrl":"https://doi.org/10.1007/s10665-023-10296-1","url":null,"abstract":"Abstract The theory of scaling called finite similitude does not involve dimensional analysis and is founded on a transport-equation approach that is applicable to all of classical physics. It features a countable infinite number of similitude rules and has recently been extended to other types of governing equations (e.g., differential, variational) by the introduction of a scaling space $$Omega _{beta }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>β</mml:mi> </mml:msub> </mml:math> , within which all physical quantities are deemed dependent on a single dimensional parameter $$beta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>β</mml:mi> </mml:math> . The theory is presently limited to physical applications but the focus of this paper is its extension to other quantitative-based theories such as finance. This is achieved by connecting it to an extended form of dimensional analysis, where changes in any quantity can be associated with curves projected onto a dimensional Lie group. It is shown in the paper how differential similitude identities arising out of the finite similitude theory are universal in the sense they can be formed and applied to any quantitative-based theory. In order to illustrate its applicability outside physics the Black-Scholes equation for option valuation in finance is considered since this equation is recognised to be similar in form to an equation from thermal physics. It is demonstrated that the theory of finite similitude can be applied to the Black-Scholes equation and more widely can be used to assess observed size effects in portfolio performance.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-19DOI: 10.1007/s10665-023-10298-z
Selina Hossain, Arijit Das, Soumen De, B. N. Mandal
{"title":"Gravity waves generated by an oscillatory surface pressure in a two-layer fluid with a porous bottom","authors":"Selina Hossain, Arijit Das, Soumen De, B. N. Mandal","doi":"10.1007/s10665-023-10298-z","DOIUrl":"https://doi.org/10.1007/s10665-023-10298-z","url":null,"abstract":"","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135731787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1007/s10665-023-10297-0
Yun Zhu, Zai-lin Yang, Jian Zhao, Yi-cun Chen, Yong-tao Mi
{"title":"Dynamic stress response analysis of inhomogeneous medium containing inhomogeneous inclusions under action of SH waves","authors":"Yun Zhu, Zai-lin Yang, Jian Zhao, Yi-cun Chen, Yong-tao Mi","doi":"10.1007/s10665-023-10297-0","DOIUrl":"https://doi.org/10.1007/s10665-023-10297-0","url":null,"abstract":"","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135992634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-27DOI: 10.1007/s10665-023-10294-3
Pulat A. Tadjibaev, Orifjon M. Tojiboev
{"title":"The second law of thermodynamics for open systems","authors":"Pulat A. Tadjibaev, Orifjon M. Tojiboev","doi":"10.1007/s10665-023-10294-3","DOIUrl":"https://doi.org/10.1007/s10665-023-10294-3","url":null,"abstract":"","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135538562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-27DOI: 10.1007/s10665-023-10293-4
Adam J. Butler, Chunendra K. Sahu, Michael J. Bickle, Jerome A. Neufeld
Abstract Mixing of solute in sub-surface flows, for example in the leakage of contaminants into groundwater, is quantified by a dispersion coefficient that depends on the dispersivity of the medium and the transport velocity. Many previous models of solute transport data have assumed Fickian behaviour with constant dispersivity, but found that the inferred dispersivity increases with the distance from the point of injection. This approach assumes that the dispersion on either side of the advective front is symmetric and that the concentration there is close to half of the injected value. However, field data show consistent asymmetry about the advective front. Here, motivated by experimental data and a fractal interpretation of porous media, we consider a simplified heterogeneous medium described by a dispersivity with a power-law dependence on the downstream distance from the source and explore the nature of the asymmetry obtained in the solute transport. In a heterogeneous medium of this type, we show that asymmetry in solute transport gradually increases with the increase in heterogeneity or fractal dimension, and the concentration at the advective front becomes increasingly different from 50% of that at the inlet. In particular, for a sufficiently heterogeneous medium, the concentration profiles at late-time approach a non-trivial steady solution and, as a result, the concentration at a downstream location will never reach that at the inlet. By fitting the Fickian solution to our results, we are able to connect the parameters from our model to those found from experimental data, providing a more physically grounded approach for interpreting them.
{"title":"The effects of heterogeneity on solute transport in porous media: anomalous dispersion","authors":"Adam J. Butler, Chunendra K. Sahu, Michael J. Bickle, Jerome A. Neufeld","doi":"10.1007/s10665-023-10293-4","DOIUrl":"https://doi.org/10.1007/s10665-023-10293-4","url":null,"abstract":"Abstract Mixing of solute in sub-surface flows, for example in the leakage of contaminants into groundwater, is quantified by a dispersion coefficient that depends on the dispersivity of the medium and the transport velocity. Many previous models of solute transport data have assumed Fickian behaviour with constant dispersivity, but found that the inferred dispersivity increases with the distance from the point of injection. This approach assumes that the dispersion on either side of the advective front is symmetric and that the concentration there is close to half of the injected value. However, field data show consistent asymmetry about the advective front. Here, motivated by experimental data and a fractal interpretation of porous media, we consider a simplified heterogeneous medium described by a dispersivity with a power-law dependence on the downstream distance from the source and explore the nature of the asymmetry obtained in the solute transport. In a heterogeneous medium of this type, we show that asymmetry in solute transport gradually increases with the increase in heterogeneity or fractal dimension, and the concentration at the advective front becomes increasingly different from 50% of that at the inlet. In particular, for a sufficiently heterogeneous medium, the concentration profiles at late-time approach a non-trivial steady solution and, as a result, the concentration at a downstream location will never reach that at the inlet. By fitting the Fickian solution to our results, we are able to connect the parameters from our model to those found from experimental data, providing a more physically grounded approach for interpreting them.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-23DOI: 10.1007/s10665-023-10295-2
Juan Luis González-Santander
Abstract In the framework of Samara–Valencia model for heat transfer in dry surface grinding, analytical expressions for the time-dependent temperature field of the workpiece during the transient regime in which the wheel is engaged (cut-in) and disengaged (cut-out) from the workpiece are calculated. The main assumption we consider is a constant heat flux profile along the contact zone between the wheel and the workpiece. According to the analytical expression obtained for the temperature field, a closed-form expression for the maximum temperature during the cut-in transient regime has been obtained. Further, a very rapid method for the numerical evaluation of maximum temperature during the cut-out is described. This maximum temperature is responsible of the thermal damage of the workpiece. Experimental evidence shows that the thermal damage risk is greater during the cut-out transient regime. The present analytical model reproduces this experimental feature. Finally, the analytical results have been numerically validated using FEM analysis and are intended to be very useful for the monitoring of the online grinding process in order to avoid thermal damage.
{"title":"Analytic solution and numerical validation of the transient regime in dry surface grinding","authors":"Juan Luis González-Santander","doi":"10.1007/s10665-023-10295-2","DOIUrl":"https://doi.org/10.1007/s10665-023-10295-2","url":null,"abstract":"Abstract In the framework of Samara–Valencia model for heat transfer in dry surface grinding, analytical expressions for the time-dependent temperature field of the workpiece during the transient regime in which the wheel is engaged (cut-in) and disengaged (cut-out) from the workpiece are calculated. The main assumption we consider is a constant heat flux profile along the contact zone between the wheel and the workpiece. According to the analytical expression obtained for the temperature field, a closed-form expression for the maximum temperature during the cut-in transient regime has been obtained. Further, a very rapid method for the numerical evaluation of maximum temperature during the cut-out is described. This maximum temperature is responsible of the thermal damage of the workpiece. Experimental evidence shows that the thermal damage risk is greater during the cut-out transient regime. The present analytical model reproduces this experimental feature. Finally, the analytical results have been numerically validated using FEM analysis and are intended to be very useful for the monitoring of the online grinding process in order to avoid thermal damage.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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