China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design princi...China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design principles, methods and construction requirements are different from those of common shallow water breakwaters. However, the specifications do not make any mention of how to choose wave force calculation methods of deep-water breakwaters. To study the feasibility of different formulae for wave force estimation of deep water combined breakwaters, the wave force calculated by the Sainflou's, Goda's, modified Goda's and specifications' methods are compared for various water depths and wave heights in this paper. The calculated results are also compared with experimental data. The total horizontal forcing and the pattern of pressure distributions are presented. Comparisons show that the wave pressure distributions by the four methods are similar, but the total horizontal forces are different. The results obtained by the Goda's method and the specified formulae are much closer to the experimental data. As for the wave force estimation for the deepwater mixed embankment foundation bed parapet, the Goda's formula is applied in the case with a water depth of less than 42 m. The Specifications method is suitable for standing waves. In the wave force estimates of breastworks, Sainflou's and the modified Gaoda's formulae are no longer applicable for the foundation bed of mixed embankment.展开更多
We derive the basic canonical brackets amongst the creation and annihilation operators for a two(1 + 1)-dimensional(2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field(Aμ) is coupl...We derive the basic canonical brackets amongst the creation and annihilation operators for a two(1 + 1)-dimensional(2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field(Aμ) is coupled with the fermionic Dirac fields(ψ andˉψ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries(and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta(corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries(and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.展开更多
基金supported by the Shandong Sci-tech Development Plan(Item No.2008GGB01099)
文摘China's newly enacted Breakwater Design Specifications(JTS154-2011) explicitly state that breakwaters with water depths greater than 20 m are categorized as deep-water breakwaters, and emphasize that design principles, methods and construction requirements are different from those of common shallow water breakwaters. However, the specifications do not make any mention of how to choose wave force calculation methods of deep-water breakwaters. To study the feasibility of different formulae for wave force estimation of deep water combined breakwaters, the wave force calculated by the Sainflou's, Goda's, modified Goda's and specifications' methods are compared for various water depths and wave heights in this paper. The calculated results are also compared with experimental data. The total horizontal forcing and the pattern of pressure distributions are presented. Comparisons show that the wave pressure distributions by the four methods are similar, but the total horizontal forces are different. The results obtained by the Goda's method and the specified formulae are much closer to the experimental data. As for the wave force estimation for the deepwater mixed embankment foundation bed parapet, the Goda's formula is applied in the case with a water depth of less than 42 m. The Specifications method is suitable for standing waves. In the wave force estimates of breastworks, Sainflou's and the modified Gaoda's formulae are no longer applicable for the foundation bed of mixed embankment.
基金the financial support from CSIR and UGC, New Delhi, Government of India, respectively
文摘We derive the basic canonical brackets amongst the creation and annihilation operators for a two(1 + 1)-dimensional(2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field(Aμ) is coupled with the fermionic Dirac fields(ψ andˉψ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries(and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta(corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries(and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.
