This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the beh...This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.展开更多
We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th...We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.展开更多
The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female populat...The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female population to replace the traditional standard that utilizes simplified breast models,for the accurate estimation of the mean glandular dose of a patient undergoing digital breast tomosynthesis(DBT).The first set of detailed Chinese female breast models and representative breast parameters was constructed.Considering backscatter radiation and computational efficiency,we improved the combination of these models and the Chinese reference adult female whole-body voxel phantom.Image acquisition for four commercial DBT systems that are widely employed in China was simulated using the Monte Carlo method to obtain the normalized glandular dose coefficients of DBT(D_(gN)^(DBT))and the glandular depth dose(D_(g)^(dep)(z))for different breast characteristics and X-ray spectra.We calculated a series of D_(gN)^(DBT) values for breasts with different percentage mass glandularities(5%,25%,50%,75%,and 100%)and compressed breast thicknesses(2,3,4,5,6,and 7 cm)at various tube potentials(25,28,30,32,35,and 49 kV)and target/filter combinations(W/Rh,W/Al,Mo/Mo,Rh/Rh,and Rh/Ag).The parameter dependence of the breast characteristics and beam conditions on D_(gN)^(DBT) in detailed breast models was investigated.The D_(gN)^(DBT) results were 14.6-51.0%lower than those of the traditional dosimetry standard in China.The difference in D_(gN)^(DBT) was mainly due to a decrease in the depth of the main energy deposition area caused by the glandular distribution along the depth direction.The results obtained in this study may be used to improve breast dosimetry in China and provide more detailed information on risk assessment during DBT.展开更多
Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modula...Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.展开更多
[Introduction] Accurate calculation of the hydrodynamic coefficients for floating structures and the investigation of the flow field distribution around floating bodies on the marine free surface are essential for imp...[Introduction] Accurate calculation of the hydrodynamic coefficients for floating structures and the investigation of the flow field distribution around floating bodies on the marine free surface are essential for improving the engineering design and application of marine structures.[Method] This study utilized the computational fluid dynamics(CFD) approach and the Reynolds Averaged NavierStokes(RANS) method and considered the effects of viscosity and free surface interactions on the hydrodynamic behavior of floating structures.By employing the dynamic mesh technique,this study simulated the periodic movements of simplified three-dimensional(3D)shapes:spheres,cylinders,and cubes,which were representative of complex marine structures.The volume of fluid(VOF) method was leveraged to accurately track the nonlinear behavior of the free surface.In this analysis,the added mass and damping coefficients for the fundamental modes of motion(surge,heave,and roll) were calculated across a spectrum of frequencies,facilitating the fast determination of hydrodynamic forces and moments exerted on floating structures.[Result] The results of this study are not only consistent with the results of the 3D potential flow theory but also further reflect the role of viscosity.This method can be used for precise calculation of the hydrodynamic coefficients of floating structures and for describing the flow field of such structures in motion on a free surface.[Conclusion] The methodology presented goes beyond the traditional potential flow approach.展开更多
Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient esti...Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient estimates for the polynomials with positive real part in the unit disk are established in this paper.展开更多
Applications of computational fluid dynamic(CFD) to the maritime industry continue to grow with the increasing development of computers.Numerical approaches have evolved to a level of accuracy which allows them to be ...Applications of computational fluid dynamic(CFD) to the maritime industry continue to grow with the increasing development of computers.Numerical approaches have evolved to a level of accuracy which allows them to be applied for hydrodynamic computations in industry areas.Hydrodynamic tests,especially planar-motion-mechanism(PMM) tests are simulated by CFD software-FLUENT,and all of the corresponding hydrodynamic coefficients are obtained,which satisfy the need of establishing the simulation system to evaluate maneuverability of vehicles during the autonomous underwater vehicle scheme design stage.The established simulation system performed well in tests.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generaliz...Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.展开更多
By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of ...By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.展开更多
The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variabl...MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variable-length codes (VLCs) are adopted. However, HE-AAC has originally been designed for storage and error-free transmission conditions. For the transmission over bit error-prone channels, error propagation is a serious problem for the VLCs. Therefore, a robust HE-AAC decoder is desired, especially for mobile communications. In contrast to traditional hard-decision decoding, utilizing bit-wise channel reliability information, softdecision (SD) decoding has been known to offer better audio quality. In HE-AAC, the global gain parameter is coded with fixedlength codes (FLCs), while the scale factors and quantized spectral coefficients are coded with VLCs. In this work, we apply FL/SD decoding to the global gain parameter, VL/SD decoding to the parameters scale factors and quantized spectral coefficients. Especially, in order to apply VL/SD decoding to the quantized spectral coefficients, a new modified trellis representation in VL/SD decoding is proposed. An improved HE-AAC performance is clearly observed, with the support of both instrumental measurements and a subjective listening test.展开更多
This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational funct...This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.展开更多
The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay result...A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.展开更多
The diffusion coefficients of several alloying elements（Al,Mo,Co,Ta,Ru,W,Cr,Re） in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors...The diffusion coefficients of several alloying elements（Al,Mo,Co,Ta,Ru,W,Cr,Re） in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor（D 0） and the activation energy（Q） of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order：DAl〉DCr〉DCo〉DTa〉DMo〉DRu〉DW〉D Re.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair（E 1）.The value of E 2-E 1（E 2 is the solute diffusion energy） and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.展开更多
The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is mod...The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.展开更多
A computerized method for determining rock joint coefficients is presented.Two relative similarity indicators are introduced to classify surface morphology of rock joints.The classification enables to compare investig...A computerized method for determining rock joint coefficients is presented.Two relative similarity indicators are introduced to classify surface morphology of rock joints.The classification enables to compare investigated and database rock joints.Such a comparison aims at finding the couple of surfaces that are distinguished by the highest dynamical conformity.The first absolute indicator results from the Fourier matrix and evaluates wavy shapes of surfaces.The second absolute indicator quantifies the heights of surface reliefs and is defined as the root mean square height of the surface outline.Numerical reliability of these indicators is tested within the surface analysis of a series of limestone specimens.Besides the computerized assessment,25 people have performed visual assessment of these limestone specimens.The results of visual assessments have been statistically processed and compared to the results received from the computerized procedure.The newly introduced absolute indicators have proved to be prospective numerical tools for evaluating joint rock coefficients.展开更多
Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solut...Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.展开更多
In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with vary...In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.展开更多
基金Supported by Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021MA003 and ZR2020MA020).
文摘This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.
基金supported by National Natural Science Foundation of China(12061080,12161087 and 12261093)the Science and Technology Project of the Education Department of Jiangxi Province(GJJ211601)supported by National Natural Science Foundation of China(11871305).
文摘We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
基金supported by the National Natural Science Foundation of China(Nos.U2167209 and 12175114)the National Key R&D Program of China(No.2021YFF0603600).
文摘The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female population to replace the traditional standard that utilizes simplified breast models,for the accurate estimation of the mean glandular dose of a patient undergoing digital breast tomosynthesis(DBT).The first set of detailed Chinese female breast models and representative breast parameters was constructed.Considering backscatter radiation and computational efficiency,we improved the combination of these models and the Chinese reference adult female whole-body voxel phantom.Image acquisition for four commercial DBT systems that are widely employed in China was simulated using the Monte Carlo method to obtain the normalized glandular dose coefficients of DBT(D_(gN)^(DBT))and the glandular depth dose(D_(g)^(dep)(z))for different breast characteristics and X-ray spectra.We calculated a series of D_(gN)^(DBT) values for breasts with different percentage mass glandularities(5%,25%,50%,75%,and 100%)and compressed breast thicknesses(2,3,4,5,6,and 7 cm)at various tube potentials(25,28,30,32,35,and 49 kV)and target/filter combinations(W/Rh,W/Al,Mo/Mo,Rh/Rh,and Rh/Ag).The parameter dependence of the breast characteristics and beam conditions on D_(gN)^(DBT) in detailed breast models was investigated.The D_(gN)^(DBT) results were 14.6-51.0%lower than those of the traditional dosimetry standard in China.The difference in D_(gN)^(DBT) was mainly due to a decrease in the depth of the main energy deposition area caused by the glandular distribution along the depth direction.The results obtained in this study may be used to improve breast dosimetry in China and provide more detailed information on risk assessment during DBT.
基金supported by the National Magnetic Confinement Fusion Program of China(No.2019YFE03090200)by National Natural Science Foundation of China(Nos.11975231,12175277 and 12305249).
文摘Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.
文摘[Introduction] Accurate calculation of the hydrodynamic coefficients for floating structures and the investigation of the flow field distribution around floating bodies on the marine free surface are essential for improving the engineering design and application of marine structures.[Method] This study utilized the computational fluid dynamics(CFD) approach and the Reynolds Averaged NavierStokes(RANS) method and considered the effects of viscosity and free surface interactions on the hydrodynamic behavior of floating structures.By employing the dynamic mesh technique,this study simulated the periodic movements of simplified three-dimensional(3D)shapes:spheres,cylinders,and cubes,which were representative of complex marine structures.The volume of fluid(VOF) method was leveraged to accurately track the nonlinear behavior of the free surface.In this analysis,the added mass and damping coefficients for the fundamental modes of motion(surge,heave,and roll) were calculated across a spectrum of frequencies,facilitating the fast determination of hydrodynamic forces and moments exerted on floating structures.[Result] The results of this study are not only consistent with the results of the 3D potential flow theory but also further reflect the role of viscosity.This method can be used for precise calculation of the hydrodynamic coefficients of floating structures and for describing the flow field of such structures in motion on a free surface.[Conclusion] The methodology presented goes beyond the traditional potential flow approach.
文摘Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
文摘Let Q be the class of real coefficient polynomials of degree 2 with positive real part in the unit disk and constant term equal to 1. aam coefficient region of polynomials in Q is found and some sharp coefficient estimates for the polynomials with positive real part in the unit disk are established in this paper.
基金Supported by the Open Research Foundation of SKLabAUV,HEU under Grant No.2008003
文摘Applications of computational fluid dynamic(CFD) to the maritime industry continue to grow with the increasing development of computers.Numerical approaches have evolved to a level of accuracy which allows them to be applied for hydrodynamic computations in industry areas.Hydrodynamic tests,especially planar-motion-mechanism(PMM) tests are simulated by CFD software-FLUENT,and all of the corresponding hydrodynamic coefficients are obtained,which satisfy the need of establishing the simulation system to evaluate maneuverability of vehicles during the autonomous underwater vehicle scheme design stage.The established simulation system performed well in tests.
基金Project Supported by the Natural Science Foundation of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.
基金Project supported by the National Natural Science Foundation of China（Grant No 10461006）, the High Education Science Research Program（Grant No NJ02035） of Inner Mongolia Autonomous Region, Natural Science Foundation of Inner Mongolia Autonomous Region（Grant No 2004080201103） and the Youth Research Program of Inner Mongolia Normal University（Grant No QN005023）.
文摘By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
文摘MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variable-length codes (VLCs) are adopted. However, HE-AAC has originally been designed for storage and error-free transmission conditions. For the transmission over bit error-prone channels, error propagation is a serious problem for the VLCs. Therefore, a robust HE-AAC decoder is desired, especially for mobile communications. In contrast to traditional hard-decision decoding, utilizing bit-wise channel reliability information, softdecision (SD) decoding has been known to offer better audio quality. In HE-AAC, the global gain parameter is coded with fixedlength codes (FLCs), while the scale factors and quantized spectral coefficients are coded with VLCs. In this work, we apply FL/SD decoding to the global gain parameter, VL/SD decoding to the parameters scale factors and quantized spectral coefficients. Especially, in order to apply VL/SD decoding to the quantized spectral coefficients, a new modified trellis representation in VL/SD decoding is proposed. An improved HE-AAC performance is clearly observed, with the support of both instrumental measurements and a subjective listening test.
基金Project supported by the Fundamental Research Funds for the Central Universities （Grant No. 2010B17914） and the National Natural Science Foundation of China （Grant No. 10926162）.
文摘This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.
基金Supported by the National Natural Science Foundation of China（10771093） Supported by the Youth Foundation of Luoyang Normal College（2013-QNJJ-001） Supported by the Youth Foundation of the Luoyang Institute of Science and Technology（2012QZ05）
文摘The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
文摘A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50971005)
文摘The diffusion coefficients of several alloying elements（Al,Mo,Co,Ta,Ru,W,Cr,Re） in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor（D 0） and the activation energy（Q） of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order：DAl〉DCr〉DCo〉DTa〉DMo〉DRu〉DW〉D Re.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair（E 1）.The value of E 2-E 1（E 2 is the solute diffusion energy） and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.
文摘The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.
基金the Grant Agency of the Czech Republic under contract No.13-03403S.
文摘A computerized method for determining rock joint coefficients is presented.Two relative similarity indicators are introduced to classify surface morphology of rock joints.The classification enables to compare investigated and database rock joints.Such a comparison aims at finding the couple of surfaces that are distinguished by the highest dynamical conformity.The first absolute indicator results from the Fourier matrix and evaluates wavy shapes of surfaces.The second absolute indicator quantifies the heights of surface reliefs and is defined as the root mean square height of the surface outline.Numerical reliability of these indicators is tested within the surface analysis of a series of limestone specimens.Besides the computerized assessment,25 people have performed visual assessment of these limestone specimens.The results of visual assessments have been statistically processed and compared to the results received from the computerized procedure.The newly introduced absolute indicators have proved to be prospective numerical tools for evaluating joint rock coefficients.
文摘Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.
基金supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge,University of Rzeszów
文摘In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.
