The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with dist...The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.展开更多
The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform de...The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.展开更多
The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the ...The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.展开更多
基金the Dirección General de Investigación of the Spanish Ministry for ScienceTechnology through the project BFM2003-05640/MATE and from the Departament d'Universitats,Recerca i Societat de la Informac
文摘The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.
文摘The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.
文摘The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.
