The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. U...The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.展开更多
The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are in...The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.展开更多
The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of...The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.展开更多
The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within...The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.展开更多
The development of optical methods in modern medicine in the areas of diagnostics,therapy,and surgery has stimulated the investigation of optical properties of various biological tissues,since the efficacy of laser tr...The development of optical methods in modern medicine in the areas of diagnostics,therapy,and surgery has stimulated the investigation of optical properties of various biological tissues,since the efficacy of laser treatment depends on the photon propagation and fluence rate distribution within irradiated tissues.In this work,an overview of published absorption and scattering properties of skin and subcutaneous tissues measured in wide wavelength range is presented.Basic principles of measurements of the tissue optical properties and techniques used for processing of the measured data are outlined.展开更多
In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular...In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.展开更多
Near-infrared spectroscopy(NIRS)technology and Mie theory are utilized for fundamental research on radiofrequency ablation of biological tissue.Firstly,NIRS is utilized to monitor rats undergoing radiofrequency ablati...Near-infrared spectroscopy(NIRS)technology and Mie theory are utilized for fundamental research on radiofrequency ablation of biological tissue.Firstly,NIRS is utilized to monitor rats undergoing radiofrequency ablation surgery in real time so as to explore the relationship between reduced scattering coefficient(μ_(s)')and the degree of thermally induced tissue coagulation.Then,Mie theory is utilized to analyze the morphological structure change of biological tissue so as to explore the basic mechanism of the change of optical parameters caused by thermally induced tissue coagulation.Results show that there is a close relationship between μ_(s)' and the degree of thermally induced tissue coagulation;the degree of thermal coagulation can be obtained by the value of μ_(s)';when biological tissue thermally coagulates,the average equivalent scattering particle decreases,the particle density increases,and the anisotropy factor decreases.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
采用一套专门设计的由微创光纤探头组成的光纤光谱仪生物组织光学参数测试系统,对颅脑创伤的大鼠创伤侧和对照侧进行近红外光谱检测及脑水含量(brain water content:BWC)测定。通过采用Feeney's自由落体撞击法建立大鼠急性局灶性脑...采用一套专门设计的由微创光纤探头组成的光纤光谱仪生物组织光学参数测试系统,对颅脑创伤的大鼠创伤侧和对照侧进行近红外光谱检测及脑水含量(brain water content:BWC)测定。通过采用Feeney's自由落体撞击法建立大鼠急性局灶性脑挫裂伤模型,以近红外光谱技术和干湿比重法监测伤后脑水肿的变化。实验发现:伤后1h,伤侧脑组织已发生水肿,伤后24～72h,伤侧脑水肿达高峰,随后逐渐下降;用脱水剂后,脑水肿情况逐渐好转,随着药物失效,水肿又一次发生。生物组织优化散射系数(Reduced Scat-tering Coefficient:μ′s)与BWC的变化规律一致,有很好的线性相关性,能够较好的反映脑组织水肿程度以及药物脱水效果。证实近红外光谱技术用于颅脑创伤实时监测的可行性,为颅脑创伤的研究提出了一种新技术。展开更多
基金partially supported by a research grant from Department of Science and Technology(DST),India(No.SB/FTP/MS-003/2013)
文摘The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.
基金Supported by SERB-DST Grant(No.SB/FTP/MS-034/2013)
文摘The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.
基金supported by the Department of Science and Technology of New Delhi (No.SR/SY/MS:521/08)
文摘The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.
基金Partially supported by a research grant from Department of Science and Technology(DST),India(No.SB/FTP/MS-003/2013)
文摘The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.
文摘The development of optical methods in modern medicine in the areas of diagnostics,therapy,and surgery has stimulated the investigation of optical properties of various biological tissues,since the efficacy of laser treatment depends on the photon propagation and fluence rate distribution within irradiated tissues.In this work,an overview of published absorption and scattering properties of skin and subcutaneous tissues measured in wide wavelength range is presented.Basic principles of measurements of the tissue optical properties and techniques used for processing of the measured data are outlined.
基金Partially Supported by the Department of Science and Technology Through a Research Grant to RG(No.SR/FTP/MS-020/2010)
文摘In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.
基金supported by the National Natural Science Foundation(Grant No.30671997)the National High Technology Research and Development Program of China(No.2008AA02Z438).
文摘Near-infrared spectroscopy(NIRS)technology and Mie theory are utilized for fundamental research on radiofrequency ablation of biological tissue.Firstly,NIRS is utilized to monitor rats undergoing radiofrequency ablation surgery in real time so as to explore the relationship between reduced scattering coefficient(μ_(s)')and the degree of thermally induced tissue coagulation.Then,Mie theory is utilized to analyze the morphological structure change of biological tissue so as to explore the basic mechanism of the change of optical parameters caused by thermally induced tissue coagulation.Results show that there is a close relationship between μ_(s)' and the degree of thermally induced tissue coagulation;the degree of thermal coagulation can be obtained by the value of μ_(s)';when biological tissue thermally coagulates,the average equivalent scattering particle decreases,the particle density increases,and the anisotropy factor decreases.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
文摘采用一套专门设计的由微创光纤探头组成的光纤光谱仪生物组织光学参数测试系统,对颅脑创伤的大鼠创伤侧和对照侧进行近红外光谱检测及脑水含量(brain water content:BWC)测定。通过采用Feeney's自由落体撞击法建立大鼠急性局灶性脑挫裂伤模型,以近红外光谱技术和干湿比重法监测伤后脑水肿的变化。实验发现:伤后1h,伤侧脑组织已发生水肿,伤后24～72h,伤侧脑水肿达高峰,随后逐渐下降;用脱水剂后,脑水肿情况逐渐好转,随着药物失效,水肿又一次发生。生物组织优化散射系数(Reduced Scat-tering Coefficient:μ′s)与BWC的变化规律一致,有很好的线性相关性,能够较好的反映脑组织水肿程度以及药物脱水效果。证实近红外光谱技术用于颅脑创伤实时监测的可行性,为颅脑创伤的研究提出了一种新技术。
