Analytical solution for the convectively-mixed atmospheric boundary layer
Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.
2013-01-01
Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation
Analytical Solutions for Beams Passing Apertures with Sharp Boundaries
Luz, Eitam; Malomed, Boris A
2016-01-01
An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the condition that the thickness of its edges is much smaller than any other length scale in the beam's initial profile. The approximation can be easily generalized for any beam whose initial profile has several sharp features. Therefore, this method can be used as a tool to investigate the diffraction of beams on complex obstacles. The analytical results are compared to numerical solutions and experimental findings, which demonstrates high accuracy of the approximation. For an initially uniform field confined by sharp boundaries, this solution becomes exact for any propagation distance and any sharpness of the edges. Thus, it can be used as an efficient tool to represent the beams, produced by series of slits with a complex structure, by a simple but exact analytical solution.
Institute of Scientific and Technical Information of China (English)
熊岳山; 韦永康
2001-01-01
The sediment reaction and diffusion equation with generalized initial and boundary condition is studied. By using Laplace transform and Jordan lemma , an analytical solution is got, which is an extension of analytical solution provided by Cheng Kwokming James ( only diffusion was considered in analytical solution of Cheng ). Some problems arisen in the computation of analytical solution formula are also analysed.
Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan
2016-01-01
Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.
Analytical solutions to a compressible boundary layer problem with heat transfer
Institute of Scientific and Technical Information of China (English)
Liancun Zheng; Xinxin Zhang; Jicheng He
2004-01-01
The problem of momentum and heat transfer in a compressible boundary layer behind a thin expansion wave was solved by the application of the similarity transformation and the shooting technique. Utilizing the analytical expression of a two-point boundary value problem for momentum transfer, the energy boundary layer solution was represented as a function of the dimensionless velocity, and as the parameters of the Prandtl number, the velocity ratio, and the temperature ratio.
Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan
2017-02-01
We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.
Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations
Institute of Scientific and Technical Information of China (English)
Seripah Awang Kechil; Ishak Hashim; Sim Siaw Jiet
2007-01-01
A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a general analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.
Belay, T.; Kim, C. I.; Schiavone, P.
2016-03-01
We develop a complete analytical solution predicting the deformation of rectangular lipid membranes resulting from boundary forces acting on the perimeter of the membrane. The shape equation describing the equilibrium state of a lipid membrane is taken from the classical Helfrich model. A linearized version of the shape equation describing membrane morphology (within the Monge representation) is obtained via a limit of superposed incremental deformations. We obtain a complete analytical solution by reducing the corresponding problem to a single partial differential equation and by using Fourier series representations for various types of boundary forces. The solution obtained predicts smooth morphological transition over the domain of interest. Finally, we note that the methods used in our analysis are not restricted to the particular type of boundary conditions considered here and can accommodate a wide class of practical and important edge conditions.
Institute of Scientific and Technical Information of China (English)
WANG Rouhuai
2006-01-01
The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.
Latyshev, A V
2012-01-01
Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the gaseous molecules is constructed. The velocity of gas in half-space is found, also its value direct at a wall is found. The force resistance operating from gas on border is found. Besides, the capacity of dissipation of the energy falling to unit of area of the fluctuating plate limiting gas is obtained.
Analytical solution of conjugate turbulent forced convection boundary layer flow over plates
Directory of Open Access Journals (Sweden)
Joneydi Shariatzadeh Omid
2016-01-01
Full Text Available A conjugate (coupled forced convection heat transfer from a heated conducting plate under turbulent boundary layer flow is considered. A heated plate of finite thickness is cooled under turbulent forced convection boundary layer flow. Because the conduction and convection boundary layer flow is coupled (conjugated in the problem, a semi-analytical solution based on Differential Transform Method (DTM is presented for solving the non-linear integro-differential equation occurring in the problem. The main conclusion is that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the non-conjugate case. This feature is more pronounced under turbulent flow when compared with the laminar flow.
Institute of Scientific and Technical Information of China (English)
SU Xiao-hong; ZHENG Lian-cun; JIANG Feng
2008-01-01
This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids.The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained.The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms.Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature.Moreover,the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.
Analytical solutions for thermal forcing vortices in boundary layer and its applications
Institute of Scientific and Technical Information of China (English)
LIU Xiao-ran; LI Guo-ping
2007-01-01
Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.
Some analytical solutions for flows of Casson fluid with slip boundary conditions
Directory of Open Access Journals (Sweden)
K. Ramesh
2015-09-01
Full Text Available In the present paper, we have studied three fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible Casson fluid between parallel plates using slip boundary conditions. The equations governing the flow of Casson fluid are non-linear in nature. Analytical solutions of the non-linear governing equations with non-linear boundary conditions are obtained for each case. The effect of the various parameters on the velocity and volume flow rate for each problem is studied and the results are presented through graphs. It is observed that, the presence of Casson number decreases the velocity and volume flow rate of the fluid. Increasing of slip parameter increases the velocity and volume flow rate in both Poiseuille and generalized Couette flows.
UNSTEADY BOUNDARY LAYER FLOW ALONG A STRETCHING CYLINDER AN ANALYTICAL SOLUTION
Directory of Open Access Journals (Sweden)
M. Y. Akl
2014-01-01
Full Text Available The axisymetric laminar boundary layer unsteady flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is studied. The governing partial boundary layer equations in cylindrical form are first transformed into ordinary differential equations these equations are solved analytically using the optimal modified Homotopy Asymptotic method in order to get a closed form solution for the dimensionless functions f and è. The main object of this study is to investigate the effect of an unsteady motion of a stretching cylinder on the flow and heat transfer characteristics such as surface skin friction and surface heat flux. These characteristics have a direct effect on the quality of the final product of the fiber manufacturing and extrusion processes. Considerable effects were found for the dynamic parameter (γ, the curvature parameter (ρ and the prandtl number (pr on the velocity and the heat transfer.
Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary
Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing
2016-04-01
An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.
Directory of Open Access Journals (Sweden)
J.-S. Chen
2011-04-01
Full Text Available This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Several special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.
Analytical solutions of couple stress fluid flows with slip boundary conditions
Directory of Open Access Journals (Sweden)
Devakar M.
2014-09-01
Full Text Available In the present article, the exact solutions for fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible couple stress fluid between parallel plates are obtained using slip boundary conditions. The effect of various parameters on velocity for each problem is discussed. It is found that, for each of the problems, the solution in the limiting case as couple stresses approaches to zero is similar to that of classical viscous Newtonian fluid. The results indicate that, the presence of couple stresses decreases the velocity of the fluid.
Directory of Open Access Journals (Sweden)
L. Buligon
2010-03-01
Full Text Available A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT, which combines series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wind data measured in Wangara experiment.
Directory of Open Access Journals (Sweden)
L. Buligon
2009-09-01
Full Text Available A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT, which joints series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wind data measured in Wangara experiment.
Buligon, L.; Degrazia, G. A.; Acevedo, O. C.; Szinvelski, C. R. P.; Goulart, A. G. O.
2010-03-01
A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT), which combines series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wind data measured in Wangara experiment.
Analytical solution for beam with time-dependent boundary conditions versus response spectrum
Energy Technology Data Exchange (ETDEWEB)
Gou, P.F.; Panahi, K.K. [GE Nuclear Energy, San Jose, CA (United States)
2001-07-01
This paper studies the responses of a uniform simple beam for which the supports are subjected to time-dependent conditions. Analytical solution in terms of series was presented for two cases: (1) Two supports of a simple beam are subjected to a harmonic motion, and (2) One of the two supports is stationary while the other is subjected to a harmonic motion. The results of the analytical solution were investigated and compared with the results of conventional response spectrum method using the beam finite element model. One of the applications of the results presented in this paper can be used to assess the adequacy and accuracy of the engineering approaches such as response spectra methods. It has been found that, when the excitation frequency equals the fundamental frequency of the beam, the results from response spectrum method are in good agreement with the exact calculation. The effects of initial conditions on the responses are also examined. It seems that the non-zero initial velocity has pronounced effects on the displacement time histories but it has no effect on the maximum accelerations. (author)
Costa, C. P.; Vilhena, M. T.; Moreira, D. M.; Tirabassi, T.
We present a three-dimensional solution of the steady-state advection-diffusion equation considering a vertically inhomogeneous planetary boundary layer (PBL). We reach this goal applying the generalized integral transform technique (GITT), a hybrid method that had solved a wide class of direct and inverse problems mainly in the area of heat transfer and fluid mechanics. The transformed problem is solved by the advection-diffusion multilayer model (ADMM) method, a semi-analytical solution based on a discretization of the PBL in sub-layers where the advection-diffusion equation is solved by the Laplace transform technique. Numerical simulations are presented and the performances of the solution are compared against field experiments data.
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya; Tasawar Hayat; Ahmed Alsaedi
2013-01-01
In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.
Marshall, J. S.
2016-12-01
We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.
Institute of Scientific and Technical Information of China (English)
Yingqin Luo; Ming Hong; Yuan Liu
2015-01-01
In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layersN > 8–10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.
Analytical Solution of Forced-Convective Boundary-Layer Flow over a Flat Plate
DEFF Research Database (Denmark)
Mirgolbabaei, H.; Barari, Amin; Ibsen, Lars Bo;
2010-01-01
In this letter, the problem of forced convection heat transfer over a horizontal flat plate is investigated by employing the Adomian Decomposition Method (ADM). The series solution of the nonlinear differential equations governing on the problem is developed. Comparison between results obtained...
Directory of Open Access Journals (Sweden)
G. H. Gudmundsson
2008-07-01
Full Text Available New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.
Energy Technology Data Exchange (ETDEWEB)
Yokoi, T. [Building Research Institute, Tokyo (Japan); Sanchez-Sesma, F. [Universidad National Autonoma de Mexico, (Mexico). Institute de Ingenieria
1997-05-27
Formulation is introduced for discretizing a boundary integral equation into an indirect boundary element method for the solution of 3-dimensional topographic problems. Yokoi and Takenaka propose an analytical solution-capable reference solution (solution for the half space elastic body with flat free surface) to problems of topographic response to seismic motion in a 2-dimensional in-plane field. That is to say, they propose a boundary integral equation capable of effectively suppressing the non-physical waves that emerge in the result of computation in the wake of the truncation of the discretized ground surface making use of the wave field in a semi-infinite elastic body with flat free surface. They apply the proposed boundary integral equation discretized into the indirect boundary element method to solve some examples, and succeed in proving its validity. In this report, the equation is expanded to deal with 3-dimensional topographic problems. A problem of a P-wave vertically landing on a flat and free surface is solved by the conventional boundary integral equation and the proposed boundary integral equation, and the solutions are compared with each other. It is found that the new method, different from the conventional one, can delete non-physical waves from the analytical result. 4 figs.
Directory of Open Access Journals (Sweden)
Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
Institute of Scientific and Technical Information of China (English)
王晓冬; 朱光亚; 王磊
2015-01-01
By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical solutions for both constant-rate and constant-pressure inner boundary constraint problems are obtained by applying the Green’s function. Two transcendental equations for moving boundary problems are obtained and solved using the Newton-Raphson iteration. The exact analytical solutions are then compared with the approximate solutions. The Pascal’s approximate formula in reference is fairly accurate for the moving boundary development under the constant-rate condition. But another Pascal’s approximate formula given in reference is not very robust for constant-pressure condition problems during the early production period, and could lead to false results at the maximum moving boundary distance. Our results also show that, in presence of larger TPG, more pressure drop is required to maintain a constant-rate production. Under the constant-pressure producing condition, the flow rate may decline dramatically due to a large TPG. What’s more, there exists a maximum distance for a given TPG, beyond which the porous media is not disturbed.
Energy Technology Data Exchange (ETDEWEB)
Goncalez, Tifani T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Segatto, Cynthia F.; Vilhena, Marco Tullio, E-mail: csegatto@pq.cnpq.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada
2011-07-01
In this work, we report an analytical solution for the set of S{sub N} equations for the angular flux, in a rectangle, using the double Laplace transform technique. Its main idea comprehends the steps: application of the Laplace transform in one space variable, solution of the resulting equation by the LTS{sub N} method and reconstruction of the double Laplace transformed angular flux using the inversion theorem of the Laplace transform. We must emphasize that we perform the Laplace inversion by the LTS{sub N} method in the x direction, meanwhile we evaluate the inversion in the y direction performing the calculation of the corresponding line integral solution by the Stefest method. We have also to figure out that the application of Laplace transform to this type of boundary value problem introduces additional unknown functions associated to the partial derivatives of the angular flux at boundary. Based on the good results attained by the nodal LTS{sub N} method, we assume that the angular flux at boundary is also approximated by an exponential function. By analytical we mean that no approximation is done along the solution derivation except for the exponential hypothesis for the exiting angular flux at boundary. For sake of completeness, we report numerical comparisons of the obtained results against the ones of the literature. (author)
Sabaeian, Mohammad
2012-10-20
The problem of finding analytical solutions for time-dependent or time-independent heat equations, especially for solid-state laser media, has required a lot of work in the field of thermal effects. However, to calculate the temperature distributions analytically, researchers often have to make some approximations or employ complex methods. In this work, we present full analytical solutions for anisotropic time-dependent heat equations in the Cartesian coordinates with various source terms corresponding to various pumping schemes. Moreover, the most general boundary condition of Robin (or impedance boundary condition), corresponding to the convection cooling mechanism, was applied. This general condition can be easily switched to constant temperature and thermal insulation as special cases. To this end, we first proposed a general approach to solving time-dependent heat equations with an arbitrary heat source. We then applied our approach to explore the temperature distribution for three cases: steady-state pumping or long transient, single-shot pumping or short transient, and repetitively pulsed pumping. Our results show the possibility of an easier and more accurate approach to analytical calculations of the thermal dispersion, thermal stresses (strains), thermal bending, thermal phase shift, and other thermal effects.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2017-03-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, Dumitru; Lorenzini, Giulio
2016-12-01
In this paper, we investigate the theoretical analysis for the unsteady magnetohydrodynamic laminar boundary layer flow due to impulsively stretching sheet. The third-order highly nonlinear partial differential equation modeling the unsteady boundary layer flow brought on by an impulsively stretching flat sheet was solved by applying Adomian decomposition method and Pade approximants. The exact analytical solution so obtained is in terms of rapidly converging power series and each of the variants are easily computable. Variations in parameters such as mass transfer (suction/injection) and Chandrasekhar number on the velocity are observed by plotting the graphs. This particular problem is technically sound and has got applications in expulsion process and related process in fluid dynamics problems.
Directory of Open Access Journals (Sweden)
Muhammad Awais
Full Text Available Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.
Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Alsaedi, Ahmed
2015-01-01
Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM) has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.
Xie, Wei; Wang, Ding-Xiong
2016-01-01
A stellar mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of "no torque" boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses, and reexamine their properties. We find that NDAF with such boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can ...
Directory of Open Access Journals (Sweden)
Hamid Khan
2012-01-01
Full Text Available We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions ur(r,z,t=(1/r(∂ψ/∂z and uz(r,z,t=−(1/r(∂ψ/∂r and a transformation ψ(r,z=r2F(z. The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-03-01
Full Text Available This paper deals with an analytical solution of free convective flow of dilatant nanofluid past a vertical cone/plate. A two-phase mixture model is used for nanofluid in which the Brownian motion and thermophoretic diffusivities are the important slip mechanisms between solid and liquid phases. The governing transport equations along with physically realistic thermal and mass convective boundary conditions are reduced to similarity equations using relevant similarity transformations before being solved by homotopy analysis method. The effects of the governing parameters (Brownian motion, thermophoresis, convection–conduction, convection–diffusion, Lewis number, buoyancy ratio, and power-law on the dimensionless velocity, temperature and nanoparticle volume fraction, friction and heat transfer rates are plotted and discussed. It is found that friction factor decreases with the increase in Le and Nr for both vertical plate and cone. The local Nusselt number decreases with the increase in the thermophoresis and Brownian motion parameters for both the plate and cone. The local Sherwood number increases with the Brownian motion parameter and decreases for thermophoresis parameter. The results have been compared with the published ones and an excellent agreement has been noticed.
Exact analytical solutions for ADAFs
Habibi, Asiyeh; Shadmehri, Mohsen
2016-01-01
We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is $T_{r\\varphi}$. Furthermore we assume that the value of viscosity coefficient $\\alpha$ varies with $\\theta$. We find radially self-similar solutions and compare them with the numerical and the analytical solutions already studied in the literature. The no-wind solution obtained in this paper may be applied to the nuclei of some cool-core clusters.
A simplified analytic form for generation of axisymmetric plasma boundaries
Luce, T. C.
2017-04-01
An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. Examples of generation of boundaries, including tests with an equilibrium solver, are given.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Directory of Open Access Journals (Sweden)
M. M. Rashidi
2012-01-01
Full Text Available In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid. It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a prescribed surface temperature (PST and (b prescribed heat flux (PHF. The effect of involved parameters on velocity and temperature is investigated.
The Analytical Approximate Solution of the 2D Thermal Displacement
Institute of Scientific and Technical Information of China (English)
Chu－QuanGuan; Zeng－YuanGuo; 等
1996-01-01
The 2D plane gas flow under heating (with nonentity boundary condition)has been discussed by the analytical approach in this paper.The approximate analytical solutions have been obtained for the flow passing various kinds of heat sources.Solutions demonstrate the thermal displacement phenomena are strongly depend on the heating intensity.
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-01
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
Analytic anisotropic solution for holography
Ren, Jie
2016-01-01
An exact solution to Einstein's equations for holographic models is presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution's appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined in detail. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimension reduction.
Analytic functions smooth up to the boundary
1988-01-01
This research monograph concerns the Nevanlinna factorization of analytic functions smooth, in a sense, up to the boundary. The peculiar properties of such a factorization are investigated for the most common classes of Lipschitz-like analytic functions. The book sets out to create a satisfactory factorization theory as exists for Hardy classes. The reader will find, among other things, the theorem on smoothness for the outer part of a function, the generalization of the theorem of V.P. Havin and F.A. Shamoyan also known in the mathematical lore as the unpublished Carleson-Jacobs theorem, the complete description of the zero-set of analytic functions continuous up to the boundary, generalizing the classical Carleson-Beurling theorem, and the structure of closed ideals in the new wide range of Banach algebras of analytic functions. The first three chapters assume the reader has taken a standard course on one complex variable; the fourth chapter requires supplementary papers cited there. The monograph addresses...
AN ANALYTICAL SOLUTION FOR AN EXPONENTIAL TYPE DISPERSION PROCESS
Institute of Scientific and Technical Information of China (English)
王子亭
2001-01-01
The dispersion process in heterogeneous porous media is distance-dependent,which results from multi-scaling property of heterogeneous structure. An analytical model describing the dispersion with an exponential dispersion function is built, which is transformed into ODE problem with variable coefficients, and obtained analytical solution for two type boundary conditions using hypergeometric function and inversion technique.According to the analytical solution and computing results the difference between the exponential dispersion and constant dispersion process is analyzed.
Analytic prediction for planar turbulent boundary layers
Chen, Xi
2016-01-01
Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions are the friction velocity $u_\\tau$: ${ U_e/u_\\tau }\\approx 2.22\\ln Re_x+2.86-3.83\\ln(\\ln Re_x)$; the boundary layer thickness $\\delta_e$: $x/\\delta_e \\approx 7.27\\ln Re_x-5.18-12.52\\ln(\\ln Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_\\theta=4.94[{(\\ln {{\\mathop{\\rm Re}\
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load,which can be expanded in terms of sinusoidal series.For plane stress problems,the stress function is assumed to consist of two parts,one being a product of a trigonometric function of the longitudinal coordinate(x) and an undetermined function of the thickness coordinate(y),and the other a linear polynomial of x with unknown coefficients depending on y.The governing equations satisfied by these y-dependent functions are derived.The expressions for stresses,resultant forces and displacements are then deduced,with integral constants determinable from the boundary conditions.While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness,the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness.The present analysis is applicable to beams with various boundary conditions at the two ends.Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.
Institute of Scientific and Technical Information of China (English)
HUANG DeJin; DING Haodiang; CHEN WeiQiu
2009-01-01
Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams sub-ject to an arbitrary load, which can be expanded in terms of sinusoidal series. For plane stress prob-lems, the stress function is assumed to consist of two parts, one being a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (y), and the other a linear polynomial of x with unknown coefficients depending on y. The governing equa-tions satisfied by these y-dependent functions are derived. The expressions for stresses, resultant forces and displacements are then deduced, with integral constants determinable from the boundary conditions. While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness, the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness. The present analysis is applicable to beams with various boundary conditions at the two ends. Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters.
Zero Viscosity Limit for Analytic Solutions of the Primitive Equations
Kukavica, Igor; Lombardo, Maria Carmela; Sammartino, Marco
2016-10-01
The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be {O(√{ν})}. The main assumption is spatial analyticity of the initial datum.
ANALYTIC SOLUTIONS OF MATRIX RICCATI EQUATIONS WITH ANALYTIC COEFFICIENTS
Curtain, Ruth; Rodman, Leiba
2010-01-01
For matrix Riccati equations of platoon-type systems and of systems arising from PDEs, assuming the coefficients are analytic or rational functions in a suitable domain, analyticity of the stabilizing solution is proved under various hypotheses. General results on analytic behavior of stabilizing so
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solution may be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solutions were verified by numerical ones in the literature. The approximate analytical solutions can be successfully applied to give the values of skin friction coefficient.
Analytic solution of an oscillatory migratory alpha^2 stellar dynamo
Brandenburg, Axel
2016-01-01
Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for uniform helical turbulence or constant alpha effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant alpha. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant alpha, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two ends. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory dynamos are possible for dynamos with...
Institute of Scientific and Technical Information of China (English)
Xuehui Chen; Liancun Zheng; Xinxin Zhang
2006-01-01
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
Analytic solution of an oscillatory migratory α2 stellar dynamo
Brandenburg, A.
2017-02-01
Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α. Aims: We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods: We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. Results: The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α. Conclusions: The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α.
A combined analytic-numeric approach for some boundary-value problems
Directory of Open Access Journals (Sweden)
Mustafa Turkyilmazoglu
2016-02-01
Full Text Available A combined analytic-numeric approach is undertaken in the present work for the solution of boundary-value problems in the finite or semi-infinite domains. Equations to be treated arise specifically from the boundary layer analysis of some two and three-dimensional flows in fluid mechanics. The purpose is to find quick but accurate enough solutions. Taylor expansions at either boundary conditions are computed which are next matched to the other asymptotic or exact boundary conditions. The technique is applied to the well-known Blasius as well as Karman flows. Solutions obtained in terms of series compare favorably with the existing ones in the literature.
Analytical Special Solutions of the Bohr Hamiltonian
Bonatsos, D; Petrellis, D; Terziev, P A; Yigitoglu, I
2005-01-01
The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.
An analytical model of capped turbulent oscillatory bottom boundary layers
Shimizu, Kenji
2010-03-01
An analytical model of capped turbulent oscillatory bottom boundary layers (BBLs) is proposed using eddy viscosity of a quadratic form. The common definition of friction velocity based on maximum bottom shear stress is found unsatisfactory for BBLs under rotating flows, and a possible extension based on turbulent kinetic energy balance is proposed. The model solutions show that the flow may slip at the top of the boundary layer due to capping by the water surface or stratification, reducing the bottom shear stress, and that the Earth's rotation induces current and bottom shear stress components perpendicular to the interior flow with a phase lag (or lead). Comparisons with field and numerical experiments indicate that the model predicts the essential characteristics of the velocity profiles, although the agreement is rather qualitative due to assumptions of quadratic eddy viscosity with time-independent friction velocity and a well-mixed boundary layer. On the other hand, the predicted linear friction coefficients, phase lead, and veering angle at the bottom agreed with available data with an error of 3%-10%, 5°-10°, and 5°-10°, respectively. As an application of the model, the friction coefficients are used to calculate e-folding decay distances of progressive internal waves with a semidiurnal frequency.
ANALYTICAL SOLUTION OF NONLINEAR BAROTROPIC VORTICITY EQUATION
Institute of Scientific and Technical Information of China (English)
WANG Yue-peng; SHI Wei-hui
2008-01-01
The stability of nonlinear barotropic vorticity equation was proved. The necessary and sufficient conditions for the initial value problem to be well-posed were presented. Under the conditions of well-posedness, the corresponding analytical solution was also gained.
POSITIVE SOLUTION FOR NONLINEARSINGULAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
吕海深
2004-01-01
Under suitable conditions on f(·, u), it is shown that the two-point boundary value problem(φp(u'))'+ λq(t)f(u)=0 in (0, 1),u(0)=u(1)=0,has two positive solution or at least one positive solution for A in a compatible interval.
The boundary value problem for discrete analytic functions
Skopenkov, Mikhail
2013-06-01
This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.
ANALYTICAL SOLUTION FOR FIXED-FIXED ANISOTROPIC BEAM SUBJECTED TO UNIFORM LOAD
Institute of Scientific and Technical Information of China (English)
DING Hao-jiang; HUANG De-jin; WANG Hui-ming
2006-01-01
The analytical solutions of the stresses and displacements were obtained for fixed-fixed anisotropic beams subjected to uniform load. A stress function involving unknown coefficients was constructed, and the general expressions of stress and displacement were obtained by means of Airy stress function method. Two types of the description for the fixed end boundary condition were considered. The introduced unknown coefficients in stress function were determined by using the boundary conditions. The analytical solutions for stresses and displacements were finally obtained. Numerical tests show that the analytical solutions agree with the FEM results. The analytical solution supplies a classical example for the elasticity theory.
Analytic solutions of nonlinear Cournot duopoly game
Directory of Open Access Journals (Sweden)
Akio Matsumoto
2005-01-01
Full Text Available We construct a Cournot duopoly model with production externality in which reaction functions are unimodal. We consider the case of a Cournot model which has a stable equilibrium point. Then we show the existence of analytic solutions of the model. Moreover, we seek general solutions of the model in the form of nonlinear second-order difference equation.
Radiative Transfer in spheres I. Analytical Solutions
Aboughantous, C
2001-01-01
A nonsingular analytical solution for the transfer equation in a pure absorber is obtained in central symmetry and in a monochromatic radiation field. The native regular singularity of the equation is removed by applying a linear transformation to the frame of reference. Two different ap-proaches are used to carry out the solution. In the first approach the angular derivative is interpreted in an original way that made it possible to discard this derivative from the equation for all black body media without upsetting the conservation of energy. In this approach the analytic solution is expressible in terms of exponential integrals without approximations but for practical considerations the solution is presented in the form of Gauss-Legendre quadrature for quantitative evaluation of the solutions. In the second approach the angular derivative is approximated by a new set of discrete ordinates that guarantees the closer of the set of equations and the conservation of energy. The solutions from the two approache...
A Simple Analytic Solution for Tachyon Condensation
Erler, Theodore
2009-01-01
In this paper we present a new and simple analytic solution for tachyon condensation in open bosonic string field theory. Unlike the B_0 gauge solution, which requires a carefully regulated discrete sum of wedge states subtracted against a mysterious "phantom" counter term, this new solution involves a continuous integral of wedge states, and no regularization or phantom term is necessary. Moreover, we can evaluate the action and prove Sen's conjecture in a mere few lines of calculation.
Analytical solution for inviscid flow inside an evaporating sessile drop
Masoud, Hassan; Felske, James D.
2008-01-01
Inviscid flow within an evaporating sessile drop is analyzed. The field equation, E^2(Psi)=0, is solved for the stream function. The exact analytical solution is obtained for arbitrary contact angle and distribution of evaporative flux along the free boundary. Specific results and computations are presented for evaporation corresponding to both uniform flux and purely diffusive gas phase transport into an infinite ambient. Wetting and non-wetting contact angles are considered with flow patter...
Analytical solution methods for geodesic motion
Hackmann, Eva
2015-01-01
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Pleba\\'nski--Demia\\'nski type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.
Analytic solution for a quartic electron mirror
Energy Technology Data Exchange (ETDEWEB)
Straton, Jack C., E-mail: straton@pdx.edu
2015-01-15
A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirror's radius (z{sup 2}−r{sup 2}/2) to which we add a quartic term (kλz{sup 4}). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile. - Highlights: • We find the analytical solution for electron mirrors whose curvature has z4 dependence added to the usual z{sup 2} – r{sup 2}/2 terms. • The resulting Jacobi cosine-amplitude function reduces to the well-known cosh solution in the limit where the new term is 0. • This quartic term gives a mirror designer additional flexibility for eliminating spherical and chromatic aberrations. • The possibility of using these analytical results to approximately model spherical tetrode mirrors close to axis is noted.
Analytical solution for the Feynman ratchet.
Pesz, Karol; Gabryś, Barbara J; Bartkiewicz, Stanisław J
2002-12-01
A search for an analytical, closed form solution of the Fokker-Planck equation with periodic, asymmetric potentials (ratchets) is presented. It is found that logarithmic-type potential functions (related to "entropic" ratchets) allow for an approximate solution within a certain range of parameters. An expression for the net current is calculated and it is shown that the efficiency of the rocked entropic ratchet is always low.
Maximum likelihood molecular clock comb: analytic solutions.
Chor, Benny; Khetan, Amit; Snir, Sagi
2006-04-01
Maximum likelihood (ML) is increasingly used as an optimality criterion for selecting evolutionary trees, but finding the global optimum is a hard computational task. Because no general analytic solution is known, numeric techniques such as hill climbing or expectation maximization (EM), are used in order to find optimal parameters for a given tree. So far, analytic solutions were derived only for the simplest model--three taxa, two state characters, under a molecular clock. Four taxa rooted trees have two topologies--the fork (two subtrees with two leaves each) and the comb (one subtree with three leaves, the other with a single leaf). In a previous work, we devised a closed form analytic solution for the ML molecular clock fork. In this work, we extend the state of the art in the area of analytic solutions ML trees to the family of all four taxa trees under the molecular clock assumption. The change from the fork topology to the comb incurs a major increase in the complexity of the underlying algebraic system and requires novel techniques and approaches. We combine the ultrametric properties of molecular clock trees with the Hadamard conjugation to derive a number of topology dependent identities. Employing these identities, we substantially simplify the system of polynomial equations. We finally use tools from algebraic geometry (e.g., Gröbner bases, ideal saturation, resultants) and employ symbolic algebra software to obtain analytic solutions for the comb. We show that in contrast to the fork, the comb has no closed form solutions (expressed by radicals in the input data). In general, four taxa trees can have multiple ML points. In contrast, we can now prove that under the molecular clock assumption, the comb has a unique (local and global) ML point. (Such uniqueness was previously shown for the fork.).
Analytic vortex solutions on compact hyperbolic surfaces
Maldonado, R
2015-01-01
We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.
Analytic vortex solutions on compact hyperbolic surfaces
Maldonado, Rafael; Manton, Nicholas S.
2015-06-01
We construct, for the first time, abelian Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.
Can We Remove Secular Terms for Analytical Solution of Groundwater Response under Tidal Influence?
Munusamy, Selva Balaji
2016-01-01
This paper presents a secular term removal methodology based on the homotopy perturbation method for analytical solutions of nonlinear problems with periodic boundary condition. The analytical solution for groundwater response to tidal fluctuation in a coastal unconfined aquifer system with the vertical beach is provided as an example. The non-linear one-dimensional Boussinesq's equation is considered as the governing equation for the groundwater flow. An analytical solution is provided for non-dimensional Boussinesq's equation with cosine harmonic boundary condition representing tidal boundary condition. The analytical solution is obtained by using homotopy perturbation method with a virtual embedding parameter. The present approach does not require pre-specified perturbation parameter and also facilitates secular terms elimination in the perturbation solution. The solutions starting from zeroth-order up to third-order are obtained. The non-dimensional expression, $A/D_{\\infty}$ emerges as an implicit parame...
Analytic solutions of an unclassified artifact /
Energy Technology Data Exchange (ETDEWEB)
Trent, Bruce C.
2012-03-01
This report provides the technical detail for analytic solutions for the inner and outer profiles of the unclassified CMM Test Artifact (LANL Part Number 157Y-700373, 5/03/2001) in terms of radius and polar angle. Furthermore, analytic solutions are derived for the legacy Sheffield measurement hardware, also in terms of radius and polar angle, using part coordinates, i.e., relative to the analytic profile solutions obtained. The purpose of this work is to determine the exact solution for the “cosine correction” term inherent to measurement with the Sheffield hardware. The cosine correction is required in order to interpret the actual measurements taken by the hardware in terms of an actual part definition, or “knot-point spline definition,” that typically accompanies a component drawing. Specifically, there are two portions of the problem: first an analytic solution must be obtained for any point on the part, e.g., given the radii and the straight lines that define the part, it is required to find an exact solution for the inner and outer profile for any arbitrary polar angle. Next, the problem of the inspection of this part must be solved, i.e., given an arbitrary sphere (representing the inspection hardware) that comes in contact with the part (inner and outer profiles) at any arbitrary polar angle, it is required to determine the exact location of that intersection. This is trivial for the case of concentric circles. In the present case, however, the spherical portion of the profiles is offset from the defined center of the part, making the analysis nontrivial. Here, a simultaneous solution of the part profiles and the sphere was obtained.
Institute of Scientific and Technical Information of China (English)
Ling DING; Chunlei TANG
2013-01-01
The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators
Bardhan, Jaydeep P; Brune, Peter R
2012-01-01
In this paper, we present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for analytical calculations in separable geometries, we rederive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion layer and then a dilute electrolyte (modeled with the linearized Poisson--Boltzmann equation). Our main result, however, is an analytical method for calculating the reaction potential in a protein embedded in a nonlocal-dielectric solvent, the Lorentz model studied by Dogonadze and Kornyshev. The analytical method enables biophysicists to study the new nonlocal theory in a simple, computationally fast way; an open-source MATLAB implementatio...
Analytical solutions for the fractional Fisher's equation
Directory of Open Access Journals (Sweden)
H. Kheiri
2015-06-01
Full Text Available In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified Homotopy perturbation method, it is possible to get an exact solution.
Institute of Scientific and Technical Information of China (English)
苑云霞; 岳晓奎; 娄云峰
2011-01-01
The two-point boundary value problem (TPBVP) of a leader-follower spacecraft formation flying was studied. Aiming at unperturbed elliptical reference orbits, the state transfer matrix representing actual relative position and velocity was derived, and the first-order analytical solution of TPBVP is obtained, which can deal with the problems of the specified rendezvous time, fuel optimization and compromise between fuel and time, and is applicable to the periodic and non-periodic relative motion. The simulation results show that the normalized accuracy of this solution achieves 10~6 level. Furthermore, the fuel cost of relative transfer increases with eccentricity increasing, and decreases with semi-major axis increasing, and appears periodic change with initial true anomaly increasing, and decreases as the transfer time increasing.%针对无摄椭圆轨道,推导了表示真实相对位置速度的状态转移矩阵,进而推导出了相对运动两点边界值问题的一阶解析解.所得结果不仅可指定转移时间、还可在时间范围内进行全局的燃料优化或在时间和燃料两者间折中；对于周期和非周期的相对运动均适用.仿真结果表明此解的归一化精度达到10-6.进一步的仿真发现相对转移过程的燃料消耗会随目标轨道偏心率的增加而增加；随长半轴的增加而减少；随初始真近点角的增加呈现周期性变化；随着转移时间增加,燃料消耗的总趋势是减少的.
Manufactured analytical solutions for isothermal full-Stokes ice sheet models
Directory of Open Access Journals (Sweden)
A. Sargent
2010-08-01
Full Text Available We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed.
The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Comparison between analytical and numerical solution of mathematical drying model
Shahari, N.; Rasmani, K.; Jamil, N.
2016-02-01
Drying is often related to the food industry as a process of shifting heat and mass inside food, which helps in preserving food. Previous research using a mass transfer equation showed that the results were mostly concerned with the comparison between the simulation model and the experimental data. In this paper, the finite difference method was used to solve a mass equation during drying using different kinds of boundary condition, which are equilibrium and convective boundary conditions. The results of these two models provide a comparison between the analytical and the numerical solution. The result shows a close match between the two solution curves. It is concluded that the two proposed models produce an accurate solution to describe the moisture distribution content during the drying process. This analysis indicates that we have confidence in the behaviour of moisture in the numerical simulation. This result demonstrated that a combined analytical and numerical approach prove that the system is behaving physically. Based on this assumption, the model of mass transfer was extended to include the temperature transfer, and the result shows a similar trend to those presented in the simpler case.
Manufactured analytical solutions for isothermal full-Stokes ice sheet models
Directory of Open Access Journals (Sweden)
A. Sargent
2010-04-01
Full Text Available We present the detailed construction of an exact solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed.
The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.
On Analytical Solutions to Beam-Hardening
Rigaud, G.
2017-01-01
When polychromatic X-rays propagate through a material, for instance in computerized tomography (CT), low energy photons are more attenuated resulting in a "harder" beam. The beam-hardening phenomenon breaks the monochromatic radiation model based on the Radon transform giving rise to artifacts in CT reconstructions to the detriment of visual inspection and automated segmentation algorithms. We propose first a simplified analytic representation for the beam-hardening. Besides providing a general understanding of the phenomenon, this model proposes to invert the beam-hardening effect for homogeneous objects leading to classical monochromatic data. For heterogeneous objects, no analytical reconstruction of the density can be derived without more prior information. However, the beam-hardening is shown to be a smooth operation on the data and thus to preserve the encoding of the singularities of the attenuation map within the data. A microlocal analysis encourages the use of contour extraction methods to solve partially the beam-hardening effect even for heterogeneous objects. The application of both methods, exact analytical solution for homogeneous objects and feature extraction for heterogeneous ones, on real data demonstrates their relevancy and efficiency.
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.
2015-12-01
Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.
Institute of Scientific and Technical Information of China (English)
Chandaneswar Midya
2012-01-01
An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible Buid over a linearly shrinking surface is presented. The Row is permeated by an externally applied magnetic Geld normal to the plane of the flow. The equations governing the Row and concentration Reid are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is signiRcantly different from that of a stretching surface. It s found that te solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced vaJues of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications.%An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented.The flow is permeated by an externally applied magnetic field normal to the plane of the flow.The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables.Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall
Analytical Solution of Multicompartment Solute Kinetics for Hemodialysis
Directory of Open Access Journals (Sweden)
Przemysław Korohoda
2013-01-01
Full Text Available Objective. To provide an exact solution for variable-volume multicompartment kinetic models with linear volume change, and to apply this solution to a 4-compartment diffusion-adjusted regional blood flow model for both urea and creatinine kinetics in hemodialysis. Methods. A matrix-based approach applicable to linear models encompassing any number of compartments is presented. The procedure requires the inversion of a square matrix and the computation of its eigenvalues λ, assuming they are all distinct. This novel approach bypasses the evaluation of the definite integral to solve the inhomogeneous ordinary differential equation. Results. For urea two out of four eigenvalues describing the changes of concentrations in time are about 105 times larger than the other eigenvalues indicating that the 4-compartment model essentially reduces to the 2-compartment regional blood flow model. In case of creatinine, however, the distribution of eigenvalues is more balanced (a factor of 102 between the largest and the smallest eigenvalue indicating that all four compartments contribute to creatinine kinetics in hemodialysis. Interpretation. Apart from providing an exact analytic solution for practical applications such as the identification of relevant model and treatment parameters, the matrix-based approach reveals characteristic details on model symmetry and complexity for different solutes.
ANALYTICAL SOLUTION OF GROUNDWATER FLUCTUATIONS IN ESTUARINE AQUIFER
Institute of Scientific and Technical Information of China (English)
CHEN Jing; ZHOU Zhi-fang; JIA Suo-bao
2005-01-01
As a basic factor in the environment of estuary, tidal effects in the coastal aquifer have recently attracted much attention because tidal dynamic also greatly influences the solute transport in the coastal aquifer. Previous studies on tidal dynamic of coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Two-dimensional analytical solutions for groundwater level fluctuation in recent papers are localized in presenting the effect of both oceanic tides and estuarine tides in quadrantal aquifer. A two-dimensional model of groundwater fluctuations in estuarine zone in proposed in this paper. Using complex transform, the two-dimensional flow equation subject to periodic boundary condition is changed into time-independent elliptic problem. Based on Green function method, an analytical solution for groundwater fluctuations in fan-shaped aquifer is derived. The response to of groundwater tidal loading in an estuary and ocean is discussed. The result show that its more extensive application than recent studies.
Positive solutions for the beam equation under certain boundary conditions
Directory of Open Access Journals (Sweden)
Bo Yang
2005-07-01
Full Text Available We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established.
ANALYTIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
LiuXinhe
2003-01-01
Let r be a given positive number.Denote by D=D the closed disc in the complex plane C whose center is the origin and radius is r.For any subset K of C and any integer m ≥1,write A(Dm,K)={f|f:Dm→Kis a continuous map,and f|(Dm)*is analytic).For H∈A(Dm,C)(m≥2),f∈A(D,D)and z∈D,write ψH(f)(z)=H(z,f(z)……fm=1(x)).Suppose F,G∈A(D2n+1,C),and Hk,Kk∈A(Dk,C),k=2,……,n.In this paper,the system of functional equations {F(z,f(z),f2(ψHz(f)(z))…,fn(ψk2(g)(x))… gn(ψKn(g)(z)))=0 G(z,f(z),f2(ψH2(f)(z))…fn(ψHn(f)(z)),g(z),g2(ψk2(g)(x))…,gn(ψkn(g)(z)))=0(z∈D)is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A（D，D）are given.
Analytical solutions of moisture flow equations and their numerical evaluation
Energy Technology Data Exchange (ETDEWEB)
Gibbs, A.G.
1981-04-01
The role of analytical solutions of idealized moisture flow problems is discussed. Some different formulations of the moisture flow problem are reviewed. A number of different analytical solutions are summarized, including the case of idealized coupled moisture and heat flow. The evaluation of special functions which commonly arise in analytical solutions is discussed, including some pitfalls in the evaluation of expressions involving combinations of special functions. Finally, perturbation theory methods are summarized which can be used to obtain good approximate analytical solutions to problems which are too complicated to solve exactly, but which are close to an analytically solvable problem.
Approximated analytical solution to an Ebola optimal control problem
Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.
2016-11-01
An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.
Analytic solutions of a class of nonlinearly dynamic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, M-C [System Engineering Institute of Tianjin University, Tianjin, 300072 (China); Zhao, X-S; Liu, X [Tianjin University of Technology and Education, Tianjin, 300222 (China)], E-mail: mchwang123@163.com.cn, E-mail: xszhao@mail.nwpu.edu.cn, E-mail: liuxinhubei@163.com.cn
2008-02-15
In this paper, the homotopy perturbation method (HPM) is applied to solve a coupled system of two nonlinear differential with first-order similar model of Lotka-Volterra and a Bratus equation with a source term. The analytic approximate solutions are derived. Furthermore, the analytic approximate solutions obtained by the HPM with the exact solutions reveals that the present method works efficiently.
Analytical approximate solution of the cooling problem by Adomian decomposition method
Alizadeh, Ebrahim; Sedighi, Kurosh; Farhadi, Mousa; Ebrahimi-Kebria, H. R.
2009-02-01
The Adomian decomposition method (ADM) can provide analytical approximation or approximated solution to a rather wide class of nonlinear (and stochastic) equations without linearization, perturbation, closure approximation, or discretization methods. In the present work, ADM is employed to solve the momentum and energy equations for laminar boundary layer flow over flat plate at zero incidences with neglecting the frictional heating. A trial and error strategy has been used to obtain the constant coefficient in the approximated solution. ADM provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomial terms is considered and shows that the accuracy of results is increased with the increasing of Adomian polynomial terms. The velocity and thermal profiles on the boundary layer are calculated. Also the effect of the Prandtl number on the thermal boundary layer is obtained. Results show ADM can solve the nonlinear differential equations with negligible error compared to the exact solution.
Analytical solution for inviscid flow inside an evaporating sessile drop.
Masoud, Hassan; Felske, James D
2009-01-01
Inviscid flow within an evaporating sessile drop is analyzed. The field equation E;{2}psi=0 is solved for the stream function. The exact analytical solution is obtained for arbitrary contact angle and distribution of evaporative flux along the free boundary. Specific results and computations are presented for evaporation corresponding to both uniform flux and purely diffusive gas phase transport into an infinite ambient. Wetting and nonwetting contact angles are considered, with flow patterns in each case being illustrated. The limiting behaviors of small contact angle and droplets of hemispherical shape are treated. All of the above categories are considered for the cases of droplets whose contact lines are either pinned or free to move during evaporation.
Migration of radionuclides through sorbing media analytical solutions--II
Energy Technology Data Exchange (ETDEWEB)
Pigford, T.H.; Chambre, P.L.; Albert, M.
1980-10-01
This report presents analytical solutions, and the results of such solutions, for the migration of radionuclides in geologic media. Volume 1 contains analytical solutions for one-dimensional equilibrium transport in infinite media and multilayered media. One-dimensional non-equilibrium transport solutions are also included. Volume 2 contains analytical solutions for transport in a one-dimensional field flow with transverse dispersion as well as transport in multi-dimensional flow. A finite element solution of the transport of radionuclides through porous media is discussed. (DMC)
Solutions of the Einstein Constraint Equations with Apparent Horizon Boundary
Maxwell, D
2003-01-01
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method introduced by Isenberg for compact manifolds without boundary, suitably extended to accommodate semilinear boundary conditions and low regularity metrics. As a consequence of our results for manifolds with boundary, we also obtain improvements to the theory of the constraint equations on asymptotically Euclidean manifolds without boundary.
Analytical solution of basic equations set of atmospheric motion
Institute of Scientific and Technical Information of China (English)
SHI Wei-hui; SHEN Chun; WANG Yue-peng
2007-01-01
On condition that the basic equations set of atmospheric motion possesses the best stability in the smooth function classes, the structure of solution space for local analytical solution is discussed, by which the third-class initial value problem with typicaiity and application is analyzed. The calculational method and concrete expressions of analytical solution about the well-posed initial value problem of the third kind are given in the analytic function classes. Near an appointed point, the relevant theoretical and computational problems about analytical solution of initial value problem are solved completely in the meaning of local solution. Moreover, for other type of problems for determining solution, the computational method and process of their stable analytical solution can be obtained in a similar way given in this paper.
Institute of Scientific and Technical Information of China (English)
崔国忠; 张志平; 等
2002-01-01
This paper deals with the initial boundary value value problem for the Boltzmann-Poisson system ,which arises in semiconductor physics,with absorbing boundary.The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.
Analytical Solution for Stellar Density in Globular Clusters
Indian Academy of Sciences (India)
M. A. Sharaf; A. M. Sendi
2011-09-01
In this paper, four parameters analytical solution will be established for the stellar density function in globular clusters. The solution could be used for any arbitrary order of outward decrease of the cluster’s density.
Electronic states of graphene nanoribbons and analytical solutions
Directory of Open Access Journals (Sweden)
Katsunori Wakabayashi, Ken-ichi Sasaki, Takeshi Nakanishi and Toshiaki Enoki
2010-01-01
Full Text Available Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.
ON SOLUTION OF A KIND OF RIEMANN BOUNDARY VALUE PROBLEM WITH SQUARE ROOTS
Institute of Scientific and Technical Information of China (English)
路见可
2002-01-01
Solution of the Riemann boundary value problem with square roots (1.1)for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here, the work is continued without these assumptions and the problem is solved in the general case.
Analytical solutions of seawater intrusion in sloping confined and unconfined coastal aquifers
Lu, Chunhui; Xin, Pei; Kong, Jun; Li, Ling; Luo, Jian
2016-09-01
Sloping coastal aquifers in reality are ubiquitous and well documented. Steady state sharp-interface analytical solutions for describing seawater intrusion in sloping confined and unconfined coastal aquifers are developed based on the Dupuit-Forchheimer approximation. Specifically, analytical solutions based on the constant-flux inland boundary condition are derived by solving the discharge equation for the interface zone with the continuity conditions of the head and flux applied at the interface between the freshwater zone and the interface zone. Analytical solutions for the constant-head inland boundary are then obtained by developing the relationship between the inland freshwater flux and hydraulic head and combining this relationship with the solutions of the constant-flux inland boundary. It is found that for the constant-flux inland boundary, the shape of the saltwater interface is independent of the geometry of the bottom confining layer for both aquifer types, despite that the geometry of the bottom confining layer determines the location of the interface tip. This is attributed to that the hydraulic head at the interface is identical to that of the coastal boundary, so the shape of the bed below the interface is irrelevant to the interface position. Moreover, developed analytical solutions with an empirical factor on the density factor are in good agreement with the results of variable-density flow numerical modeling. Analytical solutions developed in this study provide a powerful tool for assessment of seawater intrusion in sloping coastal aquifers as well as in coastal aquifers with a known freshwater flux but an arbitrary geometry of the bottom confining layer.
Analytical solutions of the lattice Boltzmann BGK model
Zou, Q; Doolen, G D; Zou, Qisu; Hou, Shuling; Doolen, Gary D.
1995-01-01
Abstract: Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time representation of these two flows without any approximation.
A compact analytic solution describing optoacoustic phenomenon in absorbing fluid
Cundin, Luisiana; Barsalou, Norman; Voss, Shannon
2012-01-01
Derivation of an analytic, closed-form solution for Q-switched laser induced optoacoustic phenomenon in absorbing fluid media is presented. The solution assumes spherical symmetry as well for the forcing function, which represents heat deposition from Q-switched lasers. The Greens solution provided is a suitable kernel to generate more complex solutions arising in optoacoustics, optoacoustic spectroscopy, photoacoustic and photothermal problems.
Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We consider the numerical solution for the Helmholtz equation in R2 with mixed boundary conditions. The solvability of this mixed boundary value problem is established by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Numerical performances show the validity and feasibility of our method. The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.
Semi-analytic solution to planar Helmholtz equation
Directory of Open Access Journals (Sweden)
Tukač M.
2013-06-01
Full Text Available Acoustic solution of interior domains is of great interest. Solving acoustic pressure fields faster with lower computational requirements is demanded. A novel solution technique based on the analytic solution to the Helmholtz equation in rectangular domain is presented. This semi-analytic solution is compared with the finite element method, which is taken as the reference. Results show that presented method is as precise as the finite element method. As the semi-analytic method doesn’t require spatial discretization, it can be used for small and very large acoustic problems with the same computational costs.
An analytic mapping property of the Dirichlet-to-Neumann operator in Helmholtz boundary problems
DEFF Research Database (Denmark)
Karamehmedovic, Mirza
The analytic version of microlocal analysis shows that if the boundary and the Dirichlet datum of a Helmholtz boundary value problem are real-analytic, then so is the corresponding Neumann datum. However, the domain of ana-lytic continuation of the Neumann datum is, in general, unknown. We shall...... here relate, in terms of explicit estimates, the domains of analytic continua-tion of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables, and in neighbourhoods of planar pieces of the boundary. For this purpose, we shall characterise a special subspace...
Approximate analytical solution of MHD flow of an Oldroyd 8-constant fluid in a porous medium
Directory of Open Access Journals (Sweden)
Faisal Salah
2014-12-01
Full Text Available The steady flow in an incompressible, magnetohydrodynamic (MHD Oldroyd 8-constant fluid in a porous medium with the motion of an infinite plate is investigated. Using modified Darcy’s law of an Oldroyd 8-constant fluid, the equations governing the flow are modelled. The resulting nonlinear boundary value problem is solved using the homotopy analysis method (HAM. The obtained approximate analytical solutions clearly satisfy the governing nonlinear equations and all the imposed initial and boundary conditions. The convergence of the HAM solutions for different orders of approximation is demonstrated. For the Newtonian case, the approximate analytical solution via HAM is shown to be in close agreement with the exact solution. Finally, the variations of velocity field with respect to the magnetic field, porosity and non-Newtonian fluid parameters are graphically shown and discussed.
Yang, Yong; Liu, Yongzhong; Yu, Bo; Ding, Tian
2016-06-01
Volatile contaminants may migrate with carbon dioxide (CO2) injection or leakage in subsurface formations, which leads to the risk of the CO2 storage and the ecological environment. This study aims to develop an analytical model that could predict the contaminant migration process induced by CO2 storage. The analytical model with two moving boundaries is obtained through the simplification of the fully coupled model for the CO2-aqueous phase -stagnant phase displacement system. The analytical solutions are confirmed and assessed through the comparison with the numerical simulations of the fully coupled model. Then, some key variables in the analytical solutions, including the critical time, the locations of the dual moving boundaries and the advance velocity, are discussed to present the characteristics of contaminant migration in the multi-phase displacement system. The results show that these key variables are determined by four dimensionless numbers, Pe, RD, Sh and RF, which represent the effects of the convection, the dispersion, the interphase mass transfer and the retention factor of contaminant, respectively. The proposed analytical solutions could be used for tracking the migration of the injected CO2 and the contaminants in subsurface formations, and also provide an analytical tool for other solute transport in multi-phase displacement system.
Kurylyk, Barret L.; Irvine, Dylan J.
2016-02-01
This study details the derivation and application of a new analytical solution to the one-dimensional, transient conduction-advection equation that is applied to trace vertical subsurface fluid fluxes. The solution employs a flexible initial condition that allows for nonlinear temperature-depth profiles, providing a key improvement over most previous solutions. The boundary condition is composed of any number of superimposed step changes in surface temperature, and thus it accommodates intermittent warming and cooling periods due to long-term changes in climate or land cover. The solution is verified using an established numerical model of coupled groundwater flow and heat transport. A new computer program FAST (Flexible Analytical Solution using Temperature) is also presented to facilitate the inversion of this analytical solution to estimate vertical groundwater flow. The program requires surface temperature history (which can be estimated from historic climate data), subsurface thermal properties, a present-day temperature-depth profile, and reasonable initial conditions. FAST is written in the Python computing language and can be run using a free graphical user interface. Herein, we demonstrate the utility of the analytical solution and FAST using measured subsurface temperature and climate data from the Sendia Plain, Japan. Results from these illustrative examples highlight the influence of the chosen initial and boundary conditions on estimated vertical flow rates.
Hufenbach, W.; Grüber, B.; Gottwald, R.; Lepper, M.; Zhou, B.
2010-12-01
A solution method for stress concentration problems of fibre- and textile-reinforced multilayered composites with account of the influence of a circular or elliptical cut-out and of the finite outer boundary of a composite plate is presented. The method is based on complex-valued displacement functions and conformal mappings in combination with the boundary collocation and least squares methods. This allows a layer-by-layer calculation of full stress, strain, and displacement fields in a generally multilayered anisotropic plate. To verify the calculation model, extensive experimental studies have been carried out. For all the combinations of multilayered GF/PP plates, laminate lay-ups, and notch and specimen dimensions investigated so far, a very good agreement between the analytical calculations and experimental results is found to exist.
Positive Solutions for Higher Order Singular -Laplacian Boundary Value Problems
Indian Academy of Sciences (India)
Guoliang Shi; Junhong Zhang
2008-05-01
This paper investigates $2m-\\mathrm{th}(m≥ 2)$ order singular -Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2-th order singular -Laplacian BVPs on closed interval.
Pseudo almost periodic solutions to parabolic boundary value inverse problems
Institute of Scientific and Technical Information of China (English)
2008-01-01
We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.
Positive solutions and eigenvalues of nonlocal boundary-value problems
Directory of Open Access Journals (Sweden)
Jifeng Chu
2005-07-01
Full Text Available We study the ordinary differential equation $x''+lambda a(tf(x=0$ with the boundary conditions $x(0=0$ and $x'(1=int_{eta}^{1}x'(sdg(s$. We characterize values of $lambda$ for which boundary-value problem has a positive solution. Also we find appropriate intervals for $lambda$ so that there are two positive solutions.
A Comprehensive Analytical Solution of the Nonlinear Pendulum
Ochs, Karlheinz
2011-01-01
In this paper, an analytical solution for the differential equation of the simple but nonlinear pendulum is derived. This solution is valid for any time and is not limited to any special initial instance or initial values. Moreover, this solution holds if the pendulum swings over or not. The method of approach is based on Jacobi elliptic functions…
Analytical solutions of coupled-mode equations for microring resonators
Indian Academy of Sciences (India)
ZHAO C Y
2016-06-01
We present a study on analytical solutions of coupled-mode equations for microring resonators with an emphasis on occurrence of all-optical EIT phenomenon, obtained by using a cofactor. As concrete examples, analytical solutions for a $3 \\times 3$ linearly distributed coupler and a circularly distributed coupler are obtained. The former corresponds to a non-degenerate eigenvalue problem and the latter corresponds to a degenerate eigenvalue problem. For comparison and without loss of generality, analytical solution for a $4 \\times 4$ linearly distributed coupler is also obtained. This paper may be of interest to optical physics and integrated photonics communities.
Axisymmetric fundamental solutions for a finite layer with impeded boundaries
Institute of Scientific and Technical Information of China (English)
程泽海; 陈云敏; 凌道盛; 唐晓武
2003-01-01
Axisymmetrie fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit point loading and ring loading in the vertical. The solut-ions are extended to circular distributed and strip distributed normal load. The computation and analysis of set-tlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
Institute of Scientific and Technical Information of China (English)
Xiao-jing LIU; Ji-zeng WANG; Xiao-min WANG; You-he ZHOU
2014-01-01
General exact solutions in terms of wavelet expansion are obtained for multi-term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ-ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.
Dai, Hui-Hui
2011-01-01
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also causes the mathematical difficulty for obtaining analytical solutions. Based on an existing model for equilibrium states of a swollen hydrogel with a core-shell structure, this paper seeks analytical solutions of the deformations by perturbation methods for three cases, i.e. free-swelling, nearly free-swelling and general inhomogeneous swelling. Particularly for the general inhomogeneous swelling, we introduce an extended method of matched asymptotics to construct the analytical solution of the governing nonlinear second-order variable-coefficient differential equation. The analytical solution captures the boundary layer behavior of the deformation. Also, analytical formulas for the radial and hoop stretches and stresses are obtained at the two boundary surfaces of the shell, ma...
Zhang, Zhizeng; Zhao, Zhao; Li, Yongtao
2016-06-01
This paper attempts to verify the correctness of the analytical displacement solution in transversely isotropic rock mass, and to determine the scope of its application. The analytical displacement solution of a circular tunnel in transversely isotropic rock mass was derived firstly. The analytical solution was compared with the numerical solution, which was carried out by FLAC3D software. The results show that the expression of the analytical displacement solution is correct, and the allowable engineering range is that the dip angle is less than 15 degrees.
Analytical Solution for Isentropic Flows in Solids
Heuzé, Olivier
2009-12-01
In the XIXth century, Riemann gave the equations system and the exact solution for the isentropic flows in the case of the ideal gas. But to our knowledge, nothing has been done to apply it to condensed media. Many materials of practical interest, for instance metals, obey to the linear law D = c+s u, where D is the shock velocity, u the particle velocity, and c and s properties of the material. We notice that s is strongly linked to the fundamental derivative. This means that the assumption of constant fundamental derivative is useful in this case, as it was with the isentropic gamma in the Riemann solution. Then we can apply the exact Riemann solution for these materials. Although the use of the hypergeometric function is complicated in this case, we obtain a very good approximation with the development in power series.
Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
Casana, R; da Hora, E; Santos, C dos
2013-01-01
We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in Phys. Rev. D 86, 085034 (2012). Such solutions are magnetic monopoles satisfying Bogomol'nyi-Prasad-Sommerfield (BPS) equations and usual finite energy boundary conditions. Moreover, the new solutions are classified in two different types according to their capability of recovering (or not) the usual 't Hooft--Polyakov monopole. Finally, we compare the profiles of the solutions we found with the standard ones, from which we comment about the main features exhibited by the new configurations.
Generalized Analytical Solutions for Nonlinear Positive-Negative Index Couplers
Directory of Open Access Journals (Sweden)
Zh. Kudyshev
2012-01-01
Full Text Available We find and analyze a generalized analytical solution for nonlinear wave propagation in waveguide couplers with opposite signs of the linear refractive index, nonzero phase mismatch between the channels, and arbitrary nonlinear coefficients.
ANALYTICAL SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
胡建兰; 张汉林
2003-01-01
The following partial differential equations are studied: generaliz ed fifth-orderKdV equation, water wave equation, Kupershmidt equation, couples KdV equation. Theanalytical solutions to these problems via using various ansaiz es by introducing a second-order ordinary differential equation are found out.
Analytic solutions for marginal deformations in open superstring field theory
Energy Technology Data Exchange (ETDEWEB)
Okawa, Y.
2007-04-15
We extend the calculable analytic approach to marginal deformations recently developed in open bosonic string field theory to open superstring field theory formulated by Berkovits. We construct analytic solutions to all orders in the deformation parameter when operator products made of the marginal operator and the associated superconformal primary field are regular. (orig.)
New software solutions for analytical spectroscopists
Davies, Antony N.
1999-05-01
Analytical spectroscopists must be computer literate to effectively carry out the tasks assigned to them. This has often been resisted within organizations with insufficient funds to equip their staff properly, a lack of desire to deliver the essential training and a basic resistance amongst staff to learn the new techniques required for computer assisted analysis. In the past these problems were compounded by seriously flawed software which was being sold for spectroscopic applications. Owing to the limited market for such complex products the analytical spectroscopist often was faced with buying incomplete and unstable tools if the price was to remain reasonable. Long product lead times meant spectrometer manufacturers often ended up offering systems running under outdated and sometimes obscure operating systems. Not only did this mean special staff training for each instrument where the knowledge gained on one system could not be transferred to the neighbouring system but these spectrometers were often only capable of running in a stand-alone mode, cut-off from the rest of the laboratory environment. Fortunately a number of developments in recent years have substantially changed this depressing picture. A true multi-tasking operating system with a simple graphical user interface, Microsoft Windows NT4, has now been widely introduced into the spectroscopic computing environment which has provided a desktop operating system which has proved to be more stable and robust as well as requiring better programming techniques of software vendors. The opening up of the Internet has provided an easy way to access new tools for data handling and has forced a substantial re-think about results delivery (for example Chemical MIME types, IUPAC spectroscopic data exchange standards). Improved computing power and cheaper hardware now allows large spectroscopic data sets to be handled without too many problems. This includes the ability to carry out chemometric operations in
Analytical solutions for the Rabi model
Yu, Lixian; Liang, Qifeng; Chen, Gang; Jia, Suotang
2012-01-01
The Rabi model that describes the fundamental interaction between a two-level system with a quantized harmonic oscillator is one of the simplest and most ubiquitous models in modern physics. However, this model has not been solved exactly because it is hard to find a second conserved quantity besides the energy. Here we present a unitary transformation to map this unsolvable Rabi model into a solvable Jaynes-Cummings-like model by choosing a proper variation parameter. As a result, the analytical energy spectrums and wavefunctions including both the ground and the excited states can be obtained easily. Moreover, these explicit results agree well with the direct numerical simulations in a wide range of the experimental parameters. In addition, based on our obtained energy spectrums, the recent experimental observation of Bloch-Siegert in the circuit quantum electrodynamics with the ultrastrong coupling can be explained perfectly. Our results have the potential application in the solid-state quantum information...
Positive solutions of three-point boundary value problems
Institute of Scientific and Technical Information of China (English)
MIAO Ye-hong; ZHANG Ji-hui
2008-01-01
In this paper,we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian.We then study existence of solutions when the problems are in resonance cases.The proposed approach is based on the Krasnoselskii's fixed point theorem and the coincidence degree.
Axisymmetric fundamental solutions for a finite layer with impeded boundaries
Institute of Scientific and Technical Information of China (English)
程泽海; 陈云敏; 凌道盛; 唐晓武
2003-01-01
Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
Institute of Scientific and Technical Information of China (English)
Ning WANG; Kui-hua WANG; Wen-bing WU
2013-01-01
In this paper,a model named fictitious soil pile was introduced to solve the boundary coupled problem at the pile tip.In the model,the soil column between pile tip and bedrock was treated as a fictitious pile,which has the same properties as the local soil.The tip of the fictitious soil pile was assumed to rest on a rigid rock and no tip movement was allowed.In combination with the plane strain theory,the analytical solutions of vertical vibration response of piles in a frequency domain and the corresponding semi-analytical solutions in a time domain were obtained using the Laplace transforms and inverse Fourier transforms.A parametric study of pile response at the pile tip and head showed that the thickness and layering of the stratum between pile tip and bedrock have a significant influence on the complex impedances.Finally,two applications of the analytical model were presented.One is to identify the defects of the pile shaft,in which the proposed model was proved to be accurate to identify the location as well as the length of pile defects.Another application of the model is to identify the sediment thickness under the pile tip.The results showed that the sediment can lead to the decrease of the pile stiffness and increase of the damping,especially when the pile is under a low frequency load.
Analytical Solution for the Current Distribution in Multistrand Superconducting Cables
Bottura, L; Fabbri, M G
2002-01-01
Current distribution in multistrand superconducting cables can be a major concern for stability in superconducting magnets and for field quality in particle accelerator magnets. In this paper we describe multistrand superconducting cables by means of a distributed parameters circuit model. We derive a system of partial differential equations governing current distribution in the cable and we give the analytical solution of the general system. We then specialize the general solution to the particular case of uniform cable properties. In the particular case of a two-strand cable, we show that the analytical solution presented here is identical to the one already available in the literature. For a cable made of N equal strands we give a closed form solution that to our knowledge was never presented before. We finally validate the analytical solution by comparison to numerical results in the case of a step-like spatial distribution of the magnetic field over a short Rutherford cable, both in transient and steady ...
An Analytical Solution for Lateral Buckling Critical Load Calculation of Leaning-Type Arch Bridge
Directory of Open Access Journals (Sweden)
Ai-rong Liu
2014-01-01
Full Text Available An analytical solution for lateral buckling critical load of leaning-type arch bridge was presented in this paper. New tangential and radial buckling models of the transverse brace between the main and stable arch ribs are established. Based on the Ritz method, the analytical solution for lateral buckling critical load of the leaning-type arch bridge with different central angles of main arch ribs and leaning arch ribs under different boundary conditions is derived for the first time. Comparison between the analytical results and the FEM calculated results shows that the analytical solution presented in this paper is sufficiently accurate. The parametric analysis results show that the lateral buckling critical load of the arch bridge with fixed boundary conditions is about 1.14 to 1.16 times as large as that of the arch bridge with hinged boundary condition. The lateral buckling critical load increases by approximately 31.5% to 41.2% when stable arch ribs are added, and the critical load increases as the inclined angle of stable arch rib increases. The differences in the center angles of the main arch rib and the stable arch rib have little effect on the lateral buckling critical load.
Mehanee, Salah; Zhdanov, Michael
2004-12-01
Numerical modeling of the quasi-static electromagnetic (EM) field in the frequency domain in a three-dimensional (3-D) inhomogeneous medium is a very challenging problem in computational physics. We present a new approach to the finite difference (FD) solution of this problem. The FD discretization of the EM field equation is based on the balance method. To compute the boundary values of the anomalous electric field we solve for, we suggest using the fast and accurate quasi-analytical (QA) approximation, which is a special form of the extended Born approximation. We call this new condition a quasi-analytical boundary condition (QA BC). This approach helps to reduce the size of the modeling domain without losing the accuracy of calculation. As a result, a larger number of grid cells can be used to describe the anomalous conductivity distribution within the modeling domain. The developed numerical technique allows application of a very fine discretization to the area with anomalous conductivity only because there is no need to move the boundaries too far from the inhomogeneous region, as required by the traditional Dirichlet or Neumann conditions for anomalous field with boundary values equal to zero. Therefore this approach increases the efficiency of FD modeling of the EM field in a medium with complex structure. We apply the QA BC and the traditional FD (with large grid and zero BC) methods to complicated models with high resistivity contrast. The numerical modeling demonstrates that the QA BC results in 5 times matrix size reduction and 2-3 times decrease in computational time.
Big Data Security Analytic Solution using Splunk
Directory of Open Access Journals (Sweden)
P.Charishma,
2015-04-01
Full Text Available Over the past decade, usage of online applications is experiencing remarkable growth. One of the main reasons for the success of web application is its “Ease of Access” and availability on internet. The simplicity of the HTTP protocol makes it easy to steal and spoof identity. The business liability associated with protecting online information has increased significantly and this is an issue that must be addressed. According to SANSTop20, 2013 list the number one targeted server side vulnerability are Web Applications. So, this has made detecting and preventing attacks on web applications a top priority for IT companies. In this paper, a rational solution is brought to detect events on web application and provides Security intelligence, log management and extensible reporting by analyzing web server logs.
Analytic solution of simplified Cardan's shaft model
Directory of Open Access Journals (Sweden)
Zajíček M.
2014-12-01
Full Text Available Torsional oscillations and stability assessment of the homokinetic Cardan shaft with a small misalignment angle is described in this paper. The simplified mathematical model of this system leads to the linearized equation of the Mathieu's type. This equation with and without a stationary damping parameter is considered. The solution of the original differential equation is identical with those one of the Fredholm’s integral equation with degenerated kernel assembled by means of a periodic Green's function. The conditions of solvability of such problem enable the identification of the borders between stability and instability regions. These results are presented in the form of stability charts and they are verified using the Floquet theory. The correctness of oscillation results for the system with periodic stiffness is then validated by means of the Runge-Kutta integration method.
Analytical Solution of the Time Fractional Fokker-Planck Equation
Directory of Open Access Journals (Sweden)
Sutradhar T.
2014-05-01
Full Text Available A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P equation by using Adomian’s Decomposition Method (ADM. The solution is expressed in terms of Mittag- Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
AN ANALYTICAL SOLUTION FOR CALCULATING THE INITIATION OF SEDIMENT MOTION
Institute of Scientific and Technical Information of China (English)
Thomas LUCKNER; Ulrich ZANKE
2007-01-01
This paper presents an analytical solution for calculating the initiation of sediment motion and the risk of river bed movement. It thus deals with a fundamental problem in sediment transport, for which no complete analytical solution has yet been found. The analytical solution presented here is based on forces acting on a single grain in state of initiation of sediment motion. The previous procedures for calculating the initiation of sediment motion are complemented by an innovative combination of optical surface measurement technology for determining geometrical parameters and their statistical derivation as well as a novel approach for determining the turbulence effects of velocity fluctuations. This two aspects and the comparison of the solution functions presented here with the well known data and functions of different authors mainly differ the presented solution model for calculating the initiation of sediment motion from previous approaches. The defined values of required geometrical parameters are based on hydraulically laboratory tests with spheres. With this limitations the derivated solution functions permit the calculation of the effective critical transport parameters of a single grain, the calculation of averaged critical parameters for describing the state of initiation of sediment motion on the river bed, the calculation of the probability density of the effective critical velocity as well as the calculation of the risk of river bed movement. The main advantage of the presented model is the closed analytical solution from the equilibrium of forces on a single grain to the solution functions describing the initiation of sediment motion.
Transmission Line Adapted Analytical Power Charts Solution
Sakala, Japhet D.; Daka, James S. J.; Setlhaolo, Ditiro; Malichi, Alec Pulu
2016-08-01
The performance of a transmission line has been assessed over the years using power charts. These are graphical representations, drawn to scale, of the equations that describe the performance of transmission lines. Various quantities that describe the performance, such as sending end voltage, sending end power and compensation to give zero voltage regulation, may be deduced from the power charts. Usually required values are read off and then converted using the appropriate scales and known relationships. In this paper, the authors revisit this area of circle diagrams for transmission line performance. The work presented here formulates the mathematical model that analyses the transmission line performance from the power charts relationships and then uses them to calculate the transmission line performance. In this proposed approach, it is not necessary to draw the power charts for the solution. However the power charts may be drawn for the visual presentation. The method is based on applying derived equations and is simple to use since it does not require rigorous derivations.
Analytical modeling of bargaining solutions for multicast cellular services
Directory of Open Access Journals (Sweden)
Giuseppe Araniti
2013-07-01
Full Text Available Nowadays, the growing demand for group-oriented services over mobile devices has lead to the definition of new communication standards and multimedia applications in cellular systems. In this article we study the use of game theoretic solutions for these services to model and perform a trade-off analysis between fairness and efficiency in the resources allocation. More precisely, we model bargaining solutions for the multicast data services provisioning and introduce the analytical resolution for the proposed solutions.
Susuki, Yoshihiko; Hikihara Takashi
2004-01-01
This paper addresses stability boundaries in non-autonomous systems. An analytical criterion for stability boundaries in one degree of freedom (time-periodic) perturbed Hamiltonian systems was recently proposed. The criterion evaluates basin boundaries of non-resonant solutions. This paper discusses the stability boundaries with respect to the resonant solutions based on the above result and subharmonic Melnikov functions. At first one degree of freedom perturbed (time-independent) Hamiltonia...
A hybrid ICT-solution for smart meter data analytics
DEFF Research Database (Denmark)
Liu, Xiufeng; Nielsen, Per Sieverts
2016-01-01
Smart meters are increasingly used worldwide. Smart meters are the advanced meters capable of measuring energy consumption at a fine-grained time interval, e.g., every 15 min. Smart meter data are typically bundled with social economic data in analytics, such as meter geographic locations, weather...... conditions and user information, which makes the data sets very sizable and the analytics complex. Data mining and emerging cloud computing technologies make collecting, processing, and analyzing the so-called big data possible. This paper proposes an innovative ICT-solution to streamline smart meter data...... analytics. The proposed solution offers an information integration pipeline for ingesting data from smart meters, a scalable platform for processing and mining big data sets, and a web portal for visualizing analytics results. The implemented system has a hybrid architecture of using Spark or Hive for big...
Analytical solutions of the simplified Mathieu’s equation
Directory of Open Access Journals (Sweden)
Nicolae MARCOV
2016-03-01
Full Text Available Consider a second order differential linear periodic equation. The periodic coefficient is an approximation of the Mathieu’s coefficient. This equation is recast as a first-order homogeneous system. For this system we obtain analytical solutions in an explicit form. The first solution is a periodic function. The second solution is a sum of two functions, the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numeric solution. The periodic term of the second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.
Institute of Scientific and Technical Information of China (English)
KONG Jun; SONG Zhi-yao; XIN Pei; SHEN Cheng-ji
2011-01-01
Deriving analytical solutions for tide-induced groundwater fluctuations in unconfined aquifers confronts two problems:(1) As the Boussinesq equation itself contains nonlinear terms,the “secular term” would be generated in derivation,thus making perturbation solution unable to be deduced to higher order; (2) for aquifers with sloping beaches,the perturbation parameter in existing analytical solution integrating the beach slope and hydrogeological property would be sometimes larger than 1.So the application of perturbation solutions is relatively limited.Furthermore,as the beach slope decreases,the error of analytical solution would gradually increase.Given that water table over-height would increase the aquifer thickness and speed up wave propagation,this paper integrates over-height into the perturbation parameter and adjusts boundary conditions to settle the problem of “secular term” and to derive a new high-order analytical solution for nonlinear Boussinesq equation in terms of sloping beaches.Results show that the new analytical solution is more reasonable,and the analytical accuracy is obviously improved in comparison with the existing analytical solution for a gentle slope.The new analytical solution provides a theoretical basis for analyzing the propagation characteristics (e.g.,wave length and over-height variation) of tide-induced groundwater wave in unconfined aquifers,particularly those with sloping beaches.
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.
2016-09-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
Directory of Open Access Journals (Sweden)
Thiago Antonini Alves
2015-10-01
Full Text Available In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was used to change the domain into a more suitable coordinate system. Thereafter, the GITT was applied on the momentum equation to obtain the velocity field. Numerical results were obtained for quantities of practical interest, such as maximum and minimum velocity, Fanning friction factor, Poiseuille number, Hagenbach factor and hydrodynamic entry length.
An analytical model for radioactive pollutant release simulation in the atmospheric boundary layer
Energy Technology Data Exchange (ETDEWEB)
Weymar, Guilherme J.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: guicefetrs@gmail.com, E-mail: mtmbvilhena@gmail.com, E-mail: bejbodmann@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Buske, Daniela; Quadros, Regis, E-mail: danielabuske@gmail.com, E-mail: quadros99@gmail.com [Universidade Federal de Pelotas (UFPel), Capao do Leao, RS (Brazil). Programa de Pos-Graduacao em Modelagem Matematica
2013-07-01
Simulations of emission of radioactive substances in the atmosphere from the Brazilian nuclear power plant Angra 1 are a necessary tool for control and elaboration of emergency plans as a preventive action for possible accidents. In the present work we present an analytical solution for radioactive pollutant dispersion in the atmosphere, solving the time-dependent three-dimensional advection-diffusion equation. The experiment here used as a reference in the simulations consisted of the controlled releases of radioactive tritiated water vapor from the meteorological tower close to the power plant at Itaorna Beach. The wind profile was determined using experimental meteorological data and the micrometeorological parameters were calculated from empirical equations obtained in the literature. We report on a novel analytical formulation for the concentration of products of a radioactive chain released in the atmospheric boundary layer and solve the set of coupled equations for each chain radionuclide by the GILTT solution, assuming the decay of all progenitors radionuclide for each equation as source term. Further we report on numerical simulations, as an explicit but fictitious example and consider three radionuclides in the radioactive chain of Uranium 235. (author)
Periodic segregation of solute atoms in fully coherent twin boundaries.
Nie, J F; Zhu, Y M; Liu, J Z; Fang, X Y
2013-05-24
The formability and mechanical properties of many engineering alloys are intimately related to the formation and growth of twins. Understanding the structure and chemistry of twin boundaries at the atomic scale is crucial if we are to properly tailor twins to achieve a new range of desired properties. We report an unusual phenomenon in magnesium alloys that until now was thought unlikely: the equilibrium segregation of solute atoms into patterns within fully coherent terraces of deformation twin boundaries. This ordered segregation provides a pinning effect for twin boundaries, leading to a concomitant but unusual situation in which annealing strengthens rather than weakens these alloys. The findings point to a platform for engineering nano-twinned structures through solute atoms. This may lead to new alloy compositions and thermomechanical processes.
Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model
Mazaré, Pierre Emmanuel
2011-12-01
In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver. © 2011 Elsevier Ltd.
MULTIPLE SOLUTIONS TO AN ASYMPTOTICALLY LINEAR ROBIN BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
Under some weaker conditions,we prove the existence of at least two solutions to an asymptotically linear elliptic problem with Robin boundary value condition,using truncation arguments.Our results are also valid for the case of the so-called resonance at infinity.
POSITIVE SOLUTIONS TO FOURTH-ORDER NEUMANN BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, we study a class of fourth-order Neumann boundary value problem (NBVP for short). By virtue of fixed point index and the spectral theory of linear operators, the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions, which are relevant to the first eigenvalue of the corresponding linear operator.
Directory of Open Access Journals (Sweden)
M.S Uddin
2011-01-01
Full Text Available The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases.
Analytical solutions of weakly coupled map lattices using recurrence relations
Energy Technology Data Exchange (ETDEWEB)
Sotelo Herrera, Dolores, E-mail: dsh@dfmf.uned.e [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); San Martin, Jesus [Applied Maths, EUITI, UPM, Ronda de Valencia, 3-28012 Madrid (Spain); Dep. Fisica Matematica y de Fluidos, UNED, Senda del Rey 9-28040 Madrid (Spain)
2009-07-20
By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C{sup 2} function.
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
Helical tractor beam: analytical solution of Rayleigh particle dynamics.
Carretero, Luis; Acebal, Pablo; Garcia, Celia; Blaya, Salvador
2015-08-10
We analyze particle dynamics in an optical force field generated by helical tractor beams obtained by the interference of a cylindrical beam with a topological charge and a co-propagating temporally de-phased plane wave. We show that, for standard experimental conditions, it is possible to obtain analytical solutions for the trajectories of particles in such force field by using of some approximations. These solutions show that, in contrast to other tractor beams described before, the intensity becomes a key parameter for the control of particle trajectories. Therefore, by tuning the intensity value the particle can describe helical trajectories upstream and downstream, a circular trajectory in a fixed plane, or a linear displacement in the propagation direction. The approximated analytical solutions show good agreement to the corresponding numerical solutions of the exact dynamical differential equations.
On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems
DEFF Research Database (Denmark)
Karamehmedovic, Mirza
2015-01-01
We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary...
APPLICATION OF THE ANALYTICAL ELECTRON MICROSCOPE TO THE STUDY OF GRAIN BOUNDARY CHEMISTRY
Hall, E
1982-01-01
High spatial resolution X-ray spectroscopy in the analytical electron microscope (AEM) is a powerful tool for the study of changes in chemistry which occur at grain boundaries in metals and ceramics. Two major advantages are realized through the use of the AEM in these studies : the ability to obtain accurate quantitative microchemical analysis of grain boundary regions, and the capability for determining the structural and crystallographic characteristics of the boundaries on which the chemi...
Analytical solution of the simplified spherical harmonics equations in spherical turbid media
Edjlali, Ehsan; Bérubé-Lauzière, Yves
2016-10-01
We present for the first time an analytical solution for the simplified spherical harmonics equations (so-called SPN equations) in the case of a steady-state isotropic point source inside a spherical homogeneous absorbing and scattering medium. The SPN equations provide a reliable approximation to the radiative transfer equation for describing light transport inside turbid media. The SPN equations consist of a set of coupled partial differential equations and the eigen method is used to obtain a set of decoupled equations, each resembling the heat equation in the Laplace domain. The equations are solved for the realistic partial reflection boundary conditions accounting for the difference in refractive indices between the turbid medium and its environment (air) as occurs in practical cases of interest in biomedical optics. Specifically, we provide the complete solution methodology for the SP3, which is readily applicable to higher orders as well, and also give results for the SP5. This computationally easy to obtain solution is investigated for different optical properties of the turbid medium. For validation, the solution is also compared to the analytical solution of the diffusion equation and to gold standard Monte Carlo simulation results. The SP3 and SP5 analytical solutions prove to be in good agreement with the Monte Carlo results. This work provides an additional tool for validating numerical solutions of the SPN equations for curved geometries.
Horses for courses: analytical tools to explore planetary boundaries
van Vuuren, D. P.; Lucas, P. L.; Häyhä, T.; Cornell, S. E.; Stafford-Smith, M.
2015-09-01
There is a need for further integrated research on developing a set of sustainable development objectives, based on the proposed framework of planetary boundaries indicators. The relevant research questions are divided in this paper into four key categories, related to the underlying processes and selection of key indicators, understanding the impacts of different exposure levels and influence of connections between different types of impacts, a better understanding of different response strategies and the available options to implement changes. Clearly, different categories of scientific disciplines and associated models exist that can contribute to the necessary analysis, noting that the distinctions between them are fuzzy. In the paper, we both indicate how different models relate to the four categories of questions but also how further insights can be obtained by connecting the different disciplines (without necessarily fully integrating them). Research on integration can support planetary boundary quantification in a credible way, linking human drivers and social and biophysical impacts.
Modelling stellar jets with magnetospheres using as initial states analytical MHD solutions
Todorov, P; Cayatte, V; Sauty, C; Lima, J J G; Tsinganos, K
2016-01-01
In this paper we focus on the construction of stellar outflow models emerging from a polar coronal hole-type region surrounded by a magnetosphere in the equatorial regions during phases of quiescent accretion. The models are based on initial analytical solutions. We adopt a meridionally self-similar solution of the time-independent and axisymmetric MHD equations which describes effectively a jet originating from the corona of a star. We modify appropriately this solution in order to incorporate a physically consistent stellar magnetosphere. We find that the closed fieldline region may exhibit different behaviour depending on the associated boundary conditions and the distribution of the heat flux. However, the stellar jet in all final equilibrium states is very similar to the analytical one prescribed in the initial conditions. When the initial net heat flux is maintained, the magnetosphere takes the form of a dynamical helmet streamer with a quasi steady state slow magnetospheric wind. With no heat flux, a s...
MATHEMATIC MODEL AND ANALYTIC SOLUTION FOR CYLINDER SUBJECT TO UNEVEN PRESSURES
Institute of Scientific and Technical Information of China (English)
LIU Wen
2006-01-01
According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant's theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab.When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the model building of hollow cylinder and for the analytic solution of hollow cylinder with randomly uneven pressure.
ANALYTIC SOLUTION AND NUMERICAL SOLUTION TO ENDOLYMPH EQUATION USING FRACTIONAL DERIVATIVE
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper,we study the solution to the endolymph equation using the fractional derivative of arbitrary orderλ(0<λ<1).The exact analytic solution is given by using Laplace transform in terms of Mittag-Leffler functions.We then evaluate the approximate numerical solution using MATLAB.
Foam for Enhanced Oil Recovery: Modeling and Analytical Solutions
Ashoori, E.
2012-01-01
Foam increases sweep in miscible- and immiscible-gas enhanced oil recovery by decreasing the mobility of gas enormously. This thesis is concerned with the simulations and analytical solutions for foam flow for the purpose of modeling foam EOR in a reservoir. For the ultimate goal of upscaling our mo
Analytical solutions for geodesics in black hole spacetimes
Hackmann, Eva
2015-01-01
We review the analytical solution methods for the geodesic equations in Kerr-Newman-Taub-NUT-de Sitter spacetimes and its subclasses in terms of elliptic and hyperelliptic functions. A short guide to corresponding literature for general timelike and lightlike motion is also presented.
Decision Exploration Lab : A Visual Analytics Solution for Decision Management
Broeksema, Bertjan; Baudel, Thomas; Telea, Alex; Crisafulli, Paolo
2013-01-01
We present a visual analytics solution designed to address prevalent issues in the area of Operational Decision Management (ODM). In ODM, which has its roots in Artificial Intelligence (Expert Systems) and Management Science, it is increasingly important to align business decisions with business goa
Directory of Open Access Journals (Sweden)
Eskandari Jam Jafar
2014-12-01
Full Text Available In this paper, by using a semi-analytical solution based on multi-layered approach, the authors present the solutions of temperature, displacements, and transient thermal stresses in functionally graded circular hollow cylinders subjected to transient thermal boundary conditions. The cylinder has finite length and is subjected to axisymmetric thermal loads. It is assumed that the functionally graded circular hollow cylinder is composed of N fictitious layers and the properties of each layer are assumed to be homogeneous and isotropic. Time variations of the temperature, displacements, and stresses are obtained by employing series solving method for ordinary differential equation, Laplace transform techniques and a numerical Laplace inversion.
Lin, Yezhi; Liu, Yinping; Li, Zhibin
2013-01-01
The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad
Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
Pao, C. V.; Ruan, W. H.
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
An analytic solution for barotropic flow along a variable slope topography
Kuehl, Joseph J.
2014-11-01
An analytic solution is derived for the generic oceanographic situation of a barotropic current flowing along sloping topography. It is shown that the shallow water equations can be reduced to a heat-like equation in which βeffect is balanced by Ekman dissipation. For constant topography, the system is found to admit a well-known similarity solution and this solution is generalized to the case of variable topography. Several properties of the solution are explored, and an example is given for flow along the northern Gulf of Mexico slope, between the De Soto Canyon and the Mississippi Canyon. This "Topographic β-plume" solution may serve as a model for further research concerning the influence exerted by geophysical boundary layers on the interior flow via their structure and stability.
Analytical solutions for Tokamak equilibria with reversed toroidal current
Energy Technology Data Exchange (ETDEWEB)
Martins, Caroline G. L.; Roberto, M.; Braga, F. L. [Departamento de Fisica, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, Sao Paulo 12228-900 (Brazil); Caldas, I. L. [Instituto de Fisica, Universidade de Sao Paulo, 05315-970 Sao Paulo, SP (Brazil)
2011-08-15
In tokamaks, an advanced plasma confinement regime has been investigated with a central hollow electric current with negative density which gives rise to non-nested magnetic surfaces. We present analytical solutions for the magnetohydrodynamic equilibria of this regime in terms of non-orthogonal toroidal polar coordinates. These solutions are obtained for large aspect ratio tokamaks and they are valid for any kind of reversed hollow current density profiles. The zero order solution of the poloidal magnetic flux function describes nested toroidal magnetic surfaces with a magnetic axis displaced due to the toroidal geometry. The first order correction introduces a poloidal field asymmetry and, consequently, magnetic islands arise around the zero order surface with null poloidal magnetic flux gradient. An analytic expression for the magnetic island width is deduced in terms of the equilibrium parameters. We give examples of the equilibrium plasma profiles and islands obtained for a class of current density profile.
Nonlinear inertial oscillations of a multilayer eddy: An analytical solution
Dotsenko, S. F.; Rubino, A.
2008-06-01
Nonlinear axisymmetric oscillations of a warm baroclinic eddy are considered within the framework of an reduced-gravity model of the dynamics of a multilayer ocean. A class of exact analytical solutions describing pure inertial oscillations of an eddy formation is found. The thicknesses of layers in the eddy vary according to a quadratic law, and the horizontal projections of the velocity in the layers depend linearly on the radial coordinate. Owing to a complicated structure of the eddy, weak limitations on the vertical distribution of density, and an explicit form of the solution, the latter can be treated as a generalization of the exact analytical solutions of this form that were previously obtained for homogeneous and baroclinic eddies in the ocean.
ANALYTICAL SOLUTION OF FILLING AND EXHAUSTING PROCESS IN PNEUMATIC SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The filling and exhausting processes in a pneumatic system are involved with many factors,and numerical solutions of many partial differential equations are always adapted in the study of those processes, which have been proved to be troublesome and less intuitive. Analytical solutions based on loss-less tube model and average friction tube model are found respectively by using fluid net theory,and they fit the experimental results well. The research work shows that: Fluid net theory can be used to solve the analytical solution of filling and exhausting processes of pneumatic system, and the result of loss-less tube model is close to that of average friction model, so loss-less tube model is recommended since it is simpler, and the difference between filling time and exhausting time is determined by initial and final pressures, the volume of container and the section area of tube, and has nothing to do with the length of the tube.
Horses for courses: analytical tools to explore planetary boundaries
van Vuuren, Detlef P.; Lucas, Paul L.; Häyhä, Tiina; Cornell, Sarah E.; Stafford-Smith, Mark
2016-03-01
There is a need for more integrated research on sustainable development and global environmental change. In this paper, we focus on the planetary boundaries framework to provide a systematic categorization of key research questions in relation to avoiding severe global environmental degradation. The four categories of key questions are those that relate to (1) the underlying processes and selection of key indicators for planetary boundaries, (2) understanding the impacts of environmental pressure and connections between different types of impacts, (3) better understanding of different response strategies to avoid further degradation, and (4) the available instruments to implement such strategies. Clearly, different categories of scientific disciplines and associated model types exist that can accommodate answering these questions. We identify the strength and weaknesses of different research areas in relation to the question categories, focusing specifically on different types of models. We discuss that more interdisciplinary research is need to increase our understanding by better linking human drivers and social and biophysical impacts. This requires better collaboration between relevant disciplines (associated with the model types), either by exchanging information or by fully linking or integrating them. As fully integrated models can become too complex, the appropriate type of model (the racehorse) should be applied for answering the target research question (the race course).
A composite analytical solution for large break LOCA
Energy Technology Data Exchange (ETDEWEB)
Purdy, P. [Bruce Power, Tiverton, Ontario (Canada); Girard, R. [Hydro-Quebec, Quebec (Canada); Marczak, J. [Ontario Power Generation, Ontario (Canada); Taylor, D. [New Brunswick Power, Fredericton, New Brunswick (Canada); Zemdegs, R. [Candu Energy Inc., Mississauga, Ontario (Canada); Kapaklili, T. [CANDU Owner' s Group, Toronto, Ontario (Canada); Balog, G. [AMEC NSS, Ontario (Canada); Kozluk, M. [Independent Consultant (Canada); Oliva, A. [Candesco, Ontario (Canada)
2011-07-01
The Canadian CANDU Industry is implementing a composite analytical solution to demonstrate, with high confidence, adequate safety margins for Large Break Loss of Coolant Accidents (LBLOCA) in existing CANDU reactors. The approach involves consolidating a number of individual approaches in a manner that alleviates reliance on any single analytical method or activity. Using a multi-layered approach, the objective of this composite solution is to use a variety of reinforcing analytical approaches such that they complement one another to collectively form a robust solution. The composite approach involves: i) systematic reclassification of LBLOCA to beyond design basis events based on the frequency of the limiting initiating events; ii) more realistic modeling of break opening characteristics; iii) application of Best Estimate and Uncertainty (BEAU) analysis methodology to provide a more realistic representation of the margins; iv) continued application of Limit of Operating Envelope (LOE) methodology to demonstrate the adequacy of margins at the extremes of the operating envelope; v) characterizing the coolant void reactivity, with associated uncertainties; and vi) defining suitable acceptance criteria, accounting for the available experimental database and uncertainties. The approach is expected to confirm the adequacy of existing design provisions and, as such, better characterize the overall safety significance of LBLOCA in CANDU reactors. This paper describes the composite analytical approach and its development, implementation and current status. (author)
Boundary value problem for the solution of magnetic cutoff rigidities and some special applications
Edmonds, Larry
1987-01-01
Since a planet's magnetic field can sometimes provide a spacecraft with some protection against cosmic ray and solar flare particles, it is important to be able to quantify this protection. This is done by calculating cutoff rigidities. An alternate to the conventional method (particle trajectory tracing) is introduced, which is to treat the problem as a boundary value problem. In this approach trajectory tracing is only needed to supply boundary conditions. In some special cases, trajectory tracing is not needed at all because the problem can be solved analytically. A differential equation governing cutoff rigidities is derived for static magnetic fields. The presense of solid objects, which can block a trajectory and other force fields are not included. A few qualititative comments, on existence and uniqueness of solutions, are made which may be useful when deciding how the boundary conditions should be set up. Also included are topics on axially symmetric fields.
Hayek, Mohamed
2016-06-01
A general analytical model for one-dimensional transient vertical infiltration is presented. The model is based on a combination of the Brooks and Corey soil water retention function and a generalized hydraulic conductivity function. This leads to power law diffusivity and convective term for which the exponents are functions of the inverse of the pore size distribution index. Accordingly, the proposed analytical solution covers many existing realistic models in the literature. The general form of the analytical solution is simple and it expresses implicitly the depth as function of water content and time. It can be used to model infiltration through semi-infinite dry soils with prescribed water content or flux boundary conditions. Some mathematical expressions of practical importance are also derived. The general form solution is useful for comparison between models, validation of numerical solutions and for better understanding the effect of some hydraulic parameters. Based on the analytical expression, a complete inverse procedure which allows the estimation of the hydraulic parameters from water content measurements is presented.
An analytic solution of the static problem of inclined risers conveying fluid
Alfosail, Feras K.
2016-05-28
We use the method of matched asymptotic expansion to develop an analytic solution to the static problem of clamped–clamped inclined risers conveying fluid. The inclined riser is modeled as an Euler–Bernoulli beam taking into account its self-weight, mid-plane stretching, an applied axial tension, and the internal fluid velocity. The solution consists of three parts: an outer solution valid away from the two boundaries and two inner solutions valid near the two ends. The three solutions are then matched and combined into a so-called composite expansion. A Newton–Raphson method is used to determine the value of the mid-plane stretching corresponding to each applied tension and internal velocity. The analytic solution is in good agreement with those obtained with other solution methods for large values of applied tensions. Therefore, it can be used to replace other mathematical solution methods that suffer numerical limitations and high computational cost. © 2016 Springer Science+Business Media Dordrecht
Surface integrals approach to solution of some free boundary problems
Directory of Open Access Journals (Sweden)
Igor Malyshev
1988-01-01
Full Text Available Inverse problems in which it is required to determine the coefficients of an equation belong to the important class of ill-posed problems. Among these, of increasing significance, are problems with free boundaries. They can be found in a wide range of disciplines including medicine, materials engineering, control theory, etc. We apply the integral equations techniques, typical for parabolic inverse problems, to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations, as well as local existence, uniqueness, continuation of its solution, and several numerical experiments are discussed.
On the Partial Analytical Solution of the Kirchhoff Equation
Michels, Dominik L.
2015-09-01
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have the disadvantage that the quality of solutions decreases enormously with increasing temporal step sizes, which results from the numerical stiffness of the underlying partial differential equations. To prevent that, we apply a differential Thomas decomposition and a Lie symmetry analysis to derive explicit analytical solutions to specific parts of the Kirchhoff system. These solutions are general and depend on arbitrary functions, which we set up according to the numerical solution of the remaining parts. In contrast to a purely numerical handling, this reduces the numerical solution space and prevents the system from becoming unstable. The differential Kirchhoff equation describes the dynamic equilibrium of one-dimensional continua, i.e. slender structures like fibers. We evaluate the advantage of our method by simulating a cilia carpet.
Analytical exact solution of the non-linear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica
2011-07-01
Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)
Green's function solution to spherical gradiometric boundary-value problems
Martinec, Z.
2003-05-01
Three independent gradiometric boundary-value problems (BVPs) with three types of gradiometric data, {orr}, {or/,or5} and {o//mo55,o/5}, prescribed on a sphere are solved to determine the gravitational potential on and outside the sphere. The existence and uniqueness conditions on the solutions are formulated showing that the zero- and the first-degree spherical harmonics are to be removed from {or/,or5} and {o//mo55,o/5}, respectively. The solutions to the gradiometric BVPs are presented in terms of Green's functions, which are expressed in both spectral and closed spatial forms. The logarithmic singularity of the Green's function at the point `=0 is investigated for the component orr. The other two Green's functions are finite at this point. Comparisons to the paper by van Gelderen and Rummel [Journal of Geodesy (2001) 75: 1-11] show that the presented solution refines the former solution.
Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function
Institute of Scientific and Technical Information of China (English)
LIU Wen; SHAN Rui
2009-01-01
Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lamè solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.
Leray, Sarah; Engdahl, Nicholas B.; Massoudieh, Arash; Bresciani, Etienne; McCallum, James
2016-12-01
This review presents the physical mechanisms generating residence time distributions (RTDs) in hydrologic systems with a focus on steady-state analytical solutions. Steady-state approximations of the RTD in hydrologic systems have seen widespread use over the last half-century because they provide a convenient, simplified modeling framework for a wide range of problems. The concept of an RTD is useful anytime that characterization of the timescales of flow and transport in hydrologic systems is important, which includes topics like water quality, water resource management, contaminant transport, and ecosystem preservation. Analytical solutions are often adopted as a model of the RTD and a broad spectrum of models from many disciplines has been applied. Although these solutions are typically reduced in dimensionality and limited in complexity, their ease of use makes them preferred tools, specifically for the interpretation of tracer data. Our review begins with the mechanistic basis for the governing equations, highlighting the physics for generating a RTD, and a catalog of analytical solutions follows. This catalog explains the geometry, boundary conditions and physical aspects of the hydrologic systems, as well as the sampling conditions, that altogether give rise to specific RTDs. The similarities between models are noted, as are the appropriate conditions for their applicability. The presentation of simple solutions is followed by a presentation of more complicated analytical models for RTDs, including serial and parallel combinations, lagged systems, and non-Fickian models. The conditions for the appropriate use of analytical solutions are discussed, and we close with some thoughts on potential applications, alternative approaches, and future directions for modeling hydrologic residence time.
Zhao, Yu-Long; Zhang, Lie-Hui; Chen, Jun; Li, Long-Xin; Zhou, Yuan
2014-08-01
A novel mathematical model for single-phase fluid flow from unconsolidated formations to a horizontal well with the consideration of stress-sensitive permeability is presented. The model assumes the formation permeability is an exponential function of the pore pressure. Using a perturbation technique, the model is solved for either constant pressure or constant flux or infinite lateral boundary conditions with closed top and bottom boundaries. Through Laplace transformation, finite Fourier transformation and numerical inversion methods, the solutions are obtained and the pressure response curves are analyzed. The agreement between the analytical solutions in this paper and the numerical results from commercial software (Saphir) is excellent, which manifests the accuracy of the results derived in this paper.
Directory of Open Access Journals (Sweden)
Jeffrey W. Lyons
2017-01-01
Full Text Available For \\(\\alpha\\in(1,2]\\, the singular fractional boundary value problem \\[D^{\\alpha}_{0^+}x+f\\left(t,x,D^{\\mu}_{0^+}x\\right=0,\\quad 0\\lt t\\lt 1,\\] satisfying the boundary conditions \\(x(0=D^{\\beta}_{0^+}x(1=0\\, where \\(\\beta\\in(0,\\alpha-1]\\, \\(\\mu\\in(0,\\alpha-1]\\, and \\(D^{\\alpha}_{0^+}\\, \\(D^{\\beta}_{0^+}\\ and \\(D^{\\mu}_{0^+}\\ are Riemann-Liouville derivatives of order \\(\\alpha\\, \\(\\beta\\ and \\(\\mu\\ respectively, is considered. Here \\(f\\ satisfies a local Carathéodory condition, and \\(f(t,x,y\\ may be singular at the value 0 in its space variable \\(x\\. Using regularization and sequential techniques and Krasnosel'skii's fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.
Analytic Solution to Nonlinear Dynamical System of Dragon Washbasin
Institute of Scientific and Technical Information of China (English)
贾启芬; 李芳; 于雯; 刘习军; 王大钧
2004-01-01
Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinate of multi-degree-of-freedom self-excited vibration induced by dry friction of piecewise-smooth nonlinear systems is derived by means of average method, the results of which agree with those of the numerical solution. An effective and reliable analytical method investigating piecewise-smooth nonlinear systems of multi-degree-of-freedom has been given. Furthermore, this paper qualitatively analyses the curves about stationary amplitude versus rubbing velocity of hands and versus natural frequency of hands, and about angular frequency versus rubbing velocity of hands. The results provide a theoretical basis for identifying parameters of the system and the analysis of steady region.
An analytic cosmology solution of Poincaré gauge gravity
Lu, Jianbo; Chee, Guoying
2016-06-01
A cosmology of Poincaré gauge theory is developed. An analytic solution is obtained. The calculation results agree with observation data and can be compared with the ΛCDM model. The cosmological constant puzzle is the coincidence and fine tuning problem are solved naturally at the same time. The cosmological constant turns out to be the intrinsic torsion and curvature of the vacuum universe, and is derived from the theory naturally rather than added artificially. The dark energy originates from geometry, includes the cosmological constant but differs from it. The analytic expression of the state equations of the dark energy and the density parameters of the matter and the geometric dark energy are derived. The full equations of linear cosmological perturbations and the solutions are obtained.
Institute of Scientific and Technical Information of China (English)
王学彬
2016-01-01
Generalized multi‐term time‐fractional diffusion equations have been used to describe important physical phenomena .However ,studies on multi‐term time‐fractional diffusion equations with mixed boundary conditions in high dimensional conditions are still limited .In this paper ,a method of separating variables was effectively imple‐mented to solve a generalized multi‐term time‐fractional diffusion equation (GM TDE ) in a finite domain .In this equation ,the multi‐term time‐fractional derivatives were defined in the Caputo sense ,whose orders belonged to the intervals [0 ,1] ,[1 ,2] ,respectively .The space partial derivatives were classical integer order derivatives whose order were 2 .We discussed and derived the analytical solution of the GMTDE in two dimensions meeting nonhomo‐geneous mixed boundary conditions .The technique reported can be applied to other kinds of fractional differential equations with different boundary conditions .%广义多项时间分数阶扩散方程已被用于描述一些重要的物理现象，目前，有关该类方程在高维情形下满足混合边界条件的研究仍较少。利用分离变量法考虑有界区域上广义二维多项时间分数阶扩散方程，方程中关于时间变量的分数阶导数采用Caputo分数阶导数的定义，其阶分别定义在[0，1]，[1，2]。而关于空间变量的偏导数则定义为传统的整数阶导数（二阶），得到了有界区域上广义二维多项时间分数阶扩散方程满足非齐次混合边界条件的解析解。亦可用于求解其他类型的满足不同边界条件的分数阶微分方程的解析解。
Analytic solutions for unconfined groundwater flow over a stepped base
Fitts, Charles R.; Strack, Otto D. L.
1996-03-01
Two new exact solutions are presented for uniform unconfined groundwater flow over a stepped base; one for a step down in the direction of flow, the other for a step up in the direction of flow. These are two-dimensional solutions of Laplace's equation in the vertical plane, and are derived using the hodograph method and conformal mappings on Riemann surfaces. The exact solutions are compared with approximate one-dimensional solutions which neglect the resistance to vertical flow. For small horizontal hydraulic gradients typical of regional groundwater flow, little error is introduced by neglecting the vertical resistance to flow. This conclusion may be extended to two-dimensional analytical models in the horizontal plane, which neglect the vertical resistance to flow and treat the aquifer base as a series of flat steps.
Analytical Analysis and Numerical Solution of Two Flavours Skyrmion
Hadi, Miftachul; Hermawanto, Denny
2010-01-01
Two flavours Skyrmion will be analyzed analytically, in case of static and rotational Skyrme equations. Numerical solution of a nonlinear scalar field equation, i.e. the Skyrme equation, will be worked with finite difference method. This article is a more comprehensive version of \\textit{SU(2) Skyrme Model for Hadron} which have been published at Journal of Theoretical and Computational Studies, Volume \\textbf{3} (2004) 0407.
Molecular clock fork phylogenies: closed form analytic maximum likelihood solutions.
Chor, Benny; Snir, Sagi
2004-12-01
Maximum likelihood (ML) is increasingly used as an optimality criterion for selecting evolutionary trees, but finding the global optimum is a hard computational task. Because no general analytic solution is known, numeric techniques such as hill climbing or expectation maximization (EM) are used in order to find optimal parameters for a given tree. So far, analytic solutions were derived only for the simplest model-three-taxa, two-state characters, under a molecular clock. Quoting Ziheng Yang, who initiated the analytic approach,"this seems to be the simplest case, but has many of the conceptual and statistical complexities involved in phylogenetic estimation."In this work, we give general analytic solutions for a family of trees with four-taxa, two-state characters, under a molecular clock. The change from three to four taxa incurs a major increase in the complexity of the underlying algebraic system, and requires novel techniques and approaches. We start by presenting the general maximum likelihood problem on phylogenetic trees as a constrained optimization problem, and the resulting system of polynomial equations. In full generality, it is infeasible to solve this system, therefore specialized tools for the molecular clock case are developed. Four-taxa rooted trees have two topologies-the fork (two subtrees with two leaves each) and the comb (one subtree with three leaves, the other with a single leaf). We combine the ultrametric properties of molecular clock fork trees with the Hadamard conjugation to derive a number of topology dependent identities. Employing these identities, we substantially simplify the system of polynomial equations for the fork. We finally employ symbolic algebra software to obtain closed formanalytic solutions (expressed parametrically in the input data). In general, four-taxa trees can have multiple ML points. In contrast, we can now prove that each fork topology has a unique(local and global) ML point.
N Level System with RWA and Analytical Solutions Revisited
Fujii, K; Kato, R; Wada, Y; Fujii, Kazuyuki; Higashida, Kyoko; Kato, Ryosuke; Wada, Yukako
2003-01-01
In this paper we consider a model of an atom with n energy levels interacting with n(n-1)/2 external (laser) fields which is a natural extension of two level system, and assume the rotating wave approximation (RWA) from the beginning. We revisit some construction of analytical solutions (which correspond to Rabi oscillations) of the model in the general case and examine it in detail in the case of three level system.
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)
1997-12-31
This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)
Development of CAD implementing the algorithm of boundary elements’ numerical analytical method
Directory of Open Access Journals (Sweden)
Yulia V. Korniyenko
2015-03-01
Full Text Available Up to recent days the algorithms for numerical-analytical boundary elements method had been implemented with programs written in MATLAB environment language. Each program had a local character, i.e. used to solve a particular problem: calculation of beam, frame, arch, etc. Constructing matrices in these programs was carried out “manually” therefore being time-consuming. The research was purposed onto a reasoned choice of programming language for new CAD development, allows to implement algorithm of numerical analytical boundary elements method and to create visualization tools for initial objects and calculation results. Research conducted shows that among wide variety of programming languages the most efficient one for CAD development, employing the numerical analytical boundary elements method algorithm, is the Java language. This language provides tools not only for development of calculating CAD part, but also to build the graphic interface for geometrical models construction and calculated results interpretation.
Hayek, Mohamed; Kosakowski, Georg; Churakov, Sergey
2011-07-01
We present exact analytical solutions for a one-dimensional diffusion problem coupled with the precipitation-dissolution reaction ? and feedback of porosity change. The solutions are obtained in the form of traveling waves and describe spatial and temporal evolutions of solute concentration, porosity, and mineral distribution for a set of initial and boundary conditions. The form of the solutions limits the choice of admissible boundary conditions, which might be difficult to adapt in natural systems, and thus, the solutions are of limited use for such a system. The main application of the derived solutions is therefore the benchmarking of numerical reactive transport codes for systems with strong porosity change. To test the performance of numerical codes, numerical solutions obtained by using a global implicit finite volume technique are compared to the analytical solutions. Good agreement is obtained between the analytical solutions and the numerical solutions when a sufficient spatial discretization resolves the spatial concentration gradients at any time. In the limit of fast kinetics (local equilibrium), steep concentration fronts cannot be resolved in a numerical discretization schema.
Analytical solution for multilayer plates using general layerwise plate theory
Directory of Open Access Journals (Sweden)
Vuksanović Đorđe M.
2005-01-01
Full Text Available This paper deals with closed-form solution for static analysis of simply supported composite plate, based on generalized laminate plate theory (GLPT. The mathematical model assumes piece-wise linear variation of in-plane displacement components and a constant transverse displacement through the thickness. It also include discrete transverse shear effect into the assumed displacement field, thus providing accurate prediction of transverse shear stresses. Namely, transverse stresses satisfy Hook's law, 3D equilibrium equations and traction free boundary conditions. With assumed displacement field, linear strain-displacement relation, and constitutive equations of the lamina, equilibrium equations are derived using principle of virtual displacements. Navier-type closed form solution of GLPT, is derived for simply supported plate, made of orthotropic laminae, loaded by harmonic and uniform distribution of transverse pressure. Results are compared with 3D elasticity solutions and excellent agreement is found.
An Analytical Solution of Partially Penetrating Hydraulic Fractures in a Box-Shaped Reservoir
Directory of Open Access Journals (Sweden)
He Zhang
2015-01-01
Full Text Available This paper presents a new method to give an analytical solution in Laplace domain directly that is used to describe pressure transient behavior of partially penetrating hydraulic fractures in a box-shaped reservoir with closed boundaries. The basic building block of the method is to solve diffusivity equation with the integration of Dirac function over the distance that is presented for the first time. Different from the traditional method of using the source solution and Green’s function presented by Gringarten and Ramey, this paper uses Laplace transform and Fourier transform to solve the diffusivity equation and the analytical solution obtained is accurate and simple. The effects of parameters including fracture height, fracture length, the position of the fracture, and reservoir width on the pressure and pressure derivative are fully investigated. The advantage of the analytical solution is easy to incorporate storage coefficient and skin factor. It can also reduce the amount of computation and compute efficiently and quickly.
Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods
Eom, Hyo J
2004-01-01
Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As such, Electromagnetic Wave Theory for Boundary-Value Problems is intended to help students enhance analytic skills by solving pertinent boundary-value problems. In particular, the techniques of Fourier transform, mode matching, and residue calculus are utilized to solve some canonical scattering and radiation problems.
Similarity Solutions of Marangoni Convection Boundary Layer Flow with Gravity and External Pressure
Institute of Scientific and Technical Information of China (English)
张艳; 郑连存
2014-01-01
This study is focused on a steady dissipative layer, which is generated by Marangoni convection flow over the surface resulted from an imposed temperature gradient, coupled with buoyancy effects due to gravity and external pressure. A model is proposed with Marangoni condition in the boundary conditions at the interface. The similarity equations are determined and approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Padé approximant technique. For the cases that buoyancy force is favorable or unfavor-able to Marangoni flow, the features of flow and temperature fields are investigated in terms of Marangoni mixed convection parameter and Prantl number.
JOVIAN STRATOSPHERE AS A CHEMICAL TRANSPORT SYSTEM: BENCHMARK ANALYTICAL SOLUTIONS
Energy Technology Data Exchange (ETDEWEB)
Zhang Xi; Shia Runlie; Yung, Yuk L., E-mail: xiz@gps.caltech.edu [Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 (United States)
2013-04-20
We systematically investigated the solvable analytical benchmark cases in both one- and two-dimensional (1D and 2D) chemical-advective-diffusive systems. We use the stratosphere of Jupiter as an example but the results can be applied to other planetary atmospheres and exoplanetary atmospheres. In the 1D system, we show that CH{sub 4} and C{sub 2}H{sub 6} are mainly in diffusive equilibrium, and the C{sub 2}H{sub 2} profile can be approximated by modified Bessel functions. In the 2D system in the meridional plane, analytical solutions for two typical circulation patterns are derived. Simple tracer transport modeling demonstrates that the distribution of a short-lived species (such as C{sub 2}H{sub 2}) is dominated by the local chemical sources and sinks, while that of a long-lived species (such as C{sub 2}H{sub 6}) is significantly influenced by the circulation pattern. We find that an equator-to-pole circulation could qualitatively explain the Cassini observations, but a pure diffusive transport process could not. For slowly rotating planets like the close-in extrasolar planets, the interaction between the advection by the zonal wind and chemistry might cause a phase lag between the final tracer distribution and the original source distribution. The numerical simulation results from the 2D Caltech/JPL chemistry-transport model agree well with the analytical solutions for various cases.
Institute of Scientific and Technical Information of China (English)
周登; 张澄
2002-01-01
The principle of the minimum energy dissipation rate is applied to toroidal plasmas with a coaxial direct current helicity injection. The relaxed states are analysed based on the analytical solutions of the resulting Euler-Lagrangian equations. Three typical states are found. The relaxed states are close to the Taylor state if the ratio of current density to magnetic field on the boundary is small enough. The states will deviate from the Taylor state when the ratio increases, but when it approaches a critical value the central part of relaxed plasmas may approach a force free state, and above the critical value both current and magnetic field may reverse in the central part.
Institute of Scientific and Technical Information of China (English)
HUANG De-jin; DING Hao-jiang; CHEN Wei-qiu
2007-01-01
The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation.The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.
Numerical Methods and the Solution of Boundary Value Problems.
1979-12-01
York: The Macmillan Company, 1967. 6. Arfken G. Mathematical Methods for Physicists. New York: Academic Press, 1966. 7. Crandall, S.H. -Engineering...one and two-dimensions. 118 Bibliography 1. Hildebrand, F.B. Methods of Applied Mathematics . New York: Prentice-Hall, Inc., 1952. 2. Hajdin, J. and D...ANUO 1 MERICAL METHODS AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS. (Li weC 79 6 N NELSON UMCLmsZPI I FlTI#WIpwfl-? ii. II.1Ilh Ŗ" MEN Iiii/ I~v I
Numerical solution of fuzzy boundary value problems using Galerkin method
Indian Academy of Sciences (India)
SMITA TAPASWINI; S CHAKRAVERTY; JUAN J NIETO
2017-01-01
This paper proposes a new technique based on Galerkin method for solving nth order fuzzy boundary value problem. The proposed method has been illustrated by considering three different cases depending upon the sign of coefficients with benchmark example problems. To show the applicability of the proposed method, an application problem related to heat conduction has also been studied. The results obtained by the proposed methods are compared with the exact solution and other existing methods for demonstrating the validity and efficiency of the present method.
Institute of Scientific and Technical Information of China (English)
Wei-An Yao; Xiao-Fei Hu; Feng Xiao
2011-01-01
This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found...
Solution of MHD problems with mixed-type boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Antimirov, M.IA.
1985-06-01
The introduction of artificial anisotropy of the dynamic viscosity in one of the subregions in which the solution is sought is utilized to derive an approximation method for MHD problems with mixed-type boundary conditions. The method is demonstrated through two problems: slow rotation of a disk and motion of a finite-width infinitely long plate in an infinite volume of a conducting fluid. The velocity and magnetic field solutions are obtained in the form of integrals of Bessel functions, and the torque is found. It is shown that when the Hartmann number approaches infinity the torque of a convex body of revolution in a longitudinal magnetic field is equal to that of a disk lying at the centerline section of the body.
Off-shell amplitudes as boundary integrals of analytically continued Wilson line slope
Kotko, Piotr; Stasto, Anna M
2016-01-01
One of the methods to calculate tree-level multi-gluon scattering amplitudes is to use the Berends-Giele recursion relation involving off-shell currents or off-shell amplitudes. As shown in recent works using for example the light-front perturbation theory, solutions to these recursions naturally collapse into gauge invariant and gauge-dependent components, at least for some helicity configurations. In this work, we show that such structure is helicity independent and emerges from analytic properties of matrix elements of Wilson line operators, where the slope of the straight gauge path is shifted in certain complex direction. This is similar to the procedure leading to the Britto-Cachazo-Feng-Witten (BCFW) recursion, however we apply a complex shift of the Wilson line slope instead of shifting an external momentum. While the boundary integrals over the complex shift in BCFW procedure vanish for certain deformations, here they are non-zero and are equal to the off-shell amplitudes.
Solutions from boundary condition changing operators in open string field theory
Kiermaier, Michael; Soler, Pablo
2010-01-01
We construct analytic solutions of open string field theory using boundary condition changing (bcc) operators. We focus on bcc operators with vanishing conformal weight such as those for regular marginal deformations of the background. For any Fock space state phi, the component string field of the solution Psi exhibits a remarkable factorization property: it is given by the matter three-point function of phi with a pair of bcc operators, multiplied by a universal function that only depends on the conformal weight of phi. This universal function is given by a simple integral expression that can be computed once and for all. The three-point functions with bcc operators are thus the only needed physical input of the particular open string background described by the solution. We illustrate our solution with the example of the rolling tachyon profile, for which we prove convergence analytically. The form of our solution, which involves bcc operators instead of explicit insertions of the marginal operator, can b...
A general solution for vertical-drain consolidation with impeded drainage boundaries
Institute of Scientific and Technical Information of China (English)
付崔伟; 雷国辉
2016-01-01
An analytical solution is derived from the generalized governing equations of equal-strain consolidation with vertical drains under multi-ramp surcharge preloading. The hydraulic boundary conditions at both top and bottom of the consolidating soil are modelled as impeded drainage. The impeded drainage is described by using the third type boundary condition with a characteristic factor of drainage efficiency. Fully drained and undrained boundary conditions can also be modelled by applying an infinite and a zero characteristic factor, respectively. Simultaneous radial and vertical flow conditions are considered, together with the effects of drain resistance and smear. An increase in total stress due to multi-ramp loading is reasonably modelled as a function of both time and depth. A solution to calculate excess pore-water pressure at any arbitrary point in soil is derived, and the overall average degree of consolidation is obtained. It shows that the proposed solution can be used to analyze not only vertical-drain consolidation but also one-dimensional consolidation under either one-way or two-way vertical drainage conditions. The characteristic factors of drainage efficiency of top and bottom boundaries have a potentially important influence on consolidation. The boundary may be considered fully drained when the characteristic factor is greater than 100 and fully undrained when the characteristic factor is less than 0.1. The stress distribution along depth induced by the surcharge loading has a limited effect on the overall average degree of consolidation. However, it has a significant effect on the dissipation of excess pore-water pressure.
Analytic solution to a class of integro-differential equations
Directory of Open Access Journals (Sweden)
Xuming Xie
2003-03-01
Full Text Available In this paper, we consider the integro-differential equation $$ epsilon^2 y''(x+L(xmathcal{H}(y=N(epsilon,x,y,mathcal{H}(y, $$ where $mathcal{H}(y[x]=frac{1}{pi}(Pint_{-infty}^{infty} frac{y(t}{t-x}dt$ is the Hilbert transform. The existence and uniqueness of analytic solution in appropriately chosen space is proved. Our method consists of extending the equation to an appropriately chosen region in the complex plane, then use the Contraction Mapping Theorem.
Institute of Scientific and Technical Information of China (English)
范天佑; 郭玉翠
1997-01-01
The mathematical theory of elasticity for planar pentagonal quasicrystals is developed and some analytic solutions for a class of mixed boundary-value problems (corresponding to a Griffith crack) of the theory are offered.An alternate procedure and a direct integral approach are proposed.Some analytical solutions are constructed and the stress and displacement fields of a Griffith crack in the quasicrystals are determined.A basis for further studying the mechanical behavior of the material related to planar defects is provided.
Analytic solution of differential equation for gyroscope's motions
Tyurekhodjaev, Abibulla N.; Mamatova, Gulnar U.
2016-08-01
Problems of motion of a rigid body with a fixed point are one of the urgent problems in classical mechanics. A feature of this problem is that, despite the important results achieved by outstanding mathematicians in the last two centuries, there is still no complete solution. This paper obtains an analytical solution of the problem of motion of an axisymmetric rigid body with variable inertia moments in resistant environment described by the system of nonlinear differential equations of L. Euler, involving the partial discretization method for nonlinear differential equations, which was built by A. N. Tyurekhodjaev based on the theory of generalized functions. To such problems belong gyroscopic instruments, in particular, and especially gyroscopes.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Finding the internal-friction peak of grain boundary anelastic relaxation was one of the important breakthroughs in the study of internal friction in the last century.But the micro-mechanism of grain boundary anelastic relaxations is still obscure.Based on the observations of the grain boundary seg-regation or depletion of solute induced by an applied stress,the following micro-mechanism was suggested:grain-boundaries will work as sources to emit vacancies when a compressive stress is exerted on them and as sinks to absorb vacancies when a tensile stress is exerted,inducing grain-boundary depletion or segregation of solute,respectively.The equations of vacancy and solute con-centrations at grain boundaries were established under the equilibrium of grain-boundary anelastic relaxation.With these the kinetic equations were established for grain boundary segregation and depletion during the grain boundary relaxation progress.
Fayolle, Guy; Malyshev, Vadim
2017-01-01
This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows spec...
The Analytic Solution of the s-Process for Heavy Element
Institute of Scientific and Technical Information of China (English)
2002-01-01
In this paper, we investigate the net-work equation of s-process. After divide the s-process into twostandard forms, we get the analytic solution of the net-work equation. With our analytic solution, we
On the global existence and uniqueness of solutions to the nonstationary boundary layer system
Institute of Scientific and Technical Information of China (English)
ZHANG; Jianwen; ZHAO; Junning
2006-01-01
In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.
New chemical evolution analytical solutions including environment effects
Spitoni, E
2015-01-01
In the last years, more and more interest has been devoted to analytical solutions, including inflow and outflow, to study the metallicity enrichment in galaxies. In this framework, we assume a star formation rate which follows a linear Schmidt law, and we present new analytical solutions for the evolution of the metallicity (Z) in galaxies. In particular, we take into account environmental effects including primordial and enriched gas infall, outflow, different star formation efficiencies, and galactic fountains. The enriched infall is included to take into account galaxy-galaxy interactions. Our main results can be summarized as: i) when a linear Schmidt law of star formation is assumed, the resulting time evolution of the metallicity Z is the same either for a closed-box model or for an outflow model. ii) The mass-metallicity relation for galaxies which suffer a chemically enriched infall, originating from another evolved galaxy with no pre-enriched gas, is shifted down in parallel at lower Z values, if co...
Analytic solutions of tunneling time through smooth barriers
Xiao, Zhi; Huang, Hai
2016-03-01
In the discussion of temporary behaviors of quantum tunneling, people usually like to focus their attention on rectangular barrier with steep edges, or to deal with smooth barrier with semi-classical or even numerical calculations. Very few discussions on analytic solutions of tunneling through smooth barrier appear in the literature. In this paper, we provide two such examples, a semi-infinite long barrier V ( x ) = /A 2 [ 1 + tanh ( x / a ) ] and a finite barrier V(x) = A sech2(x/a). To each barrier, we calculate the associated phase time and dwell time after obtaining the analytic solution. The results show that, different from rectangular barrier, phase time or dwell time does increase with the length parameter a controlling the effective extension of the barrier. More interestingly, for the finite barrier, phase time or dwell time exhibits a peak in k-space. A detailed analysis shows that this interesting behavior can be attributed to the strange tunneling probability Ts(k), i.e., Ts(k) displays a unit step function-like profile Θ(k - k0), especially when a is large, say, a ≫ 1/κ, 1/k. And k 0 ≡ √{ m A } / ħ is exactly where the peak appears in phase or dwell time k-spectrum. Thus only those particles with k in a very narrow interval around k0 are capable to dwell in the central region of the barrier sufficiently long.
Analytical Solution of Projectile Motion with Quadratic Resistance and Generalisations
Ray, Shouryya
2013-01-01
The paper considers the motion of a body under the influence of gravity and drag of the surrounding fluid. Depending on the fluid mechanical regime, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body relative to the fluid. The case of quadratic drag is substantially more complex than the linear case, as it nonlinearly couples both components of the momentum equation, and no explicit analytic solution is known for a general trajectory. After a detailed account of the literature, the paper provides such a solution in form of a series expansion. This result is discussed in detail and related to other approaches previously proposed. In particular, it is shown to yield certain approximate solutions proposed in the literature as limiting cases. The solution technique employs a strategy to reduce systems of ordinary differential equations with a triangular dependence of the right-hand side on the vector of unknowns to a single equation in an auxiliary variable....
Sharma, Pankaj; Parashar, Sandeep Kumar
2016-05-01
The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d15 effect. In piezoelectric actuators, the potential use of d15 effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d31 and d33. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton`s principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.
Institute of Scientific and Technical Information of China (English)
Fang-fang LI; Jing LIU; Kai YUE
2009-01-01
Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temper-ature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
Existence of solutions to boundary value problem of fractional differential equations with impulsive
Directory of Open Access Journals (Sweden)
Weihua JIANG
2016-12-01
Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.
Directory of Open Access Journals (Sweden)
A. Acker
1995-06-01
Full Text Available classical solution of a Bernoulli-type free boundary problem for the $p$-Laplace equation, $ 1 < p < infty $. In addition, we prove the existence of a classical solution in $N$ dimensions when $p = 2$ and, for $ 1 < p < infty $, results on uniqueness and starlikeness of the free boundary and continuous dependence on the fixed boundary and on the free boundary data. Finally, as an application of the trial free boundary method, we prove (also for $ 1 < p < infty $ that the free boundary is convex when the fixed boundary is convex.
Renormalization-group symmetries for solutions of nonlinear boundary value problems
Kovalev, V F
2008-01-01
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...
Dual solution of Casson fluid over a porous medium: Exact solutions with extra boundary condition
Khan, Najeeb Alam; Khan, Sidra
2016-12-01
In this article we calculate the exact solution of the steady flow of non-Newtonian Casson fluid, over a stretching/shrinking sheet. The governing partial differential equations (PDEs) are transformed into ordinary differential equation (ODE) by using similarity transformation and then solved analytically by utilizing the exact solution. The closed form unique solution is obtained in the case of stretching sheet whereas for shrinking sheet unique and dual solutions are obtained. Influences of Casson fluid and suction/injection parameter on dimensionless velocity function are discussed and plotted graphically; also the effects of skin friction coefficient are presented in graphical form. Comparisons of current solutions with previous study are also made for the verification of the present study.
Capacity of the circular plate condenser: analytical solutions for large gaps between the plates
Rao, T. V.
2005-11-01
A solution of Love's integral equation (Love E R 1949 Q. J. Mech. Appl. Math. 2 428), which forms the basis for the analysis of the electrostatic field due to two equal circular co-axial parallel conducting plates, is considered for the case when the ratio, τ, of distance of separation to radius of the plates is greater than 2. The kernel of the integral equation is expanded into an infinite series in odd powers of 1/τ and an approximate kernel accurate to {\\cal O}(\\tau^{-(2N+1)}) is deduced therefrom by terminating the series after an arbitrary but finite number of terms, N. The approximate kernel is rearranged into a degenerate form and the integral equation with this kernel is reduced to a system of N linear equations. An explicit analytical solution is obtained for N = 4 and the resulting analytical expression for the capacity of the circular plate condenser is shown to be accurate to {\\cal O}(\\tau^{-9}) . Analytical expressions of lower orders of accuracy with respect to 1/τ are deduced from the four-term (i.e., N = 4) solution and predictions (of capacity) from the expressions of different orders of accuracy (with respect to 1/τ) are compared with very accurate numerical solutions obtained by solving the linear system for large enough N. It is shown that the {\\cal O}(\\tau^{-9}) approximation predicts the capacity extremely well for any τ >= 2 and an {\\cal O}(\\tau^{-3}) approximation gives, for all practical purposes, results of adequate accuracy for τ >= 4. It is further shown that an approximate solution, applicable for the case of large distances of separation between the plates, due to Sneddon (Sneddon I N 1966 Mixed Boundary Value Problems in Potential Theory (Amsterdam: North-Holland) pp 230-46) is accurate to {\\cal O}(\\tau^{-6}) for τ >= 2.
Institute of Scientific and Technical Information of China (English)
吴勃英
2001-01-01
This paper gives a analytic solution of a boundary value problemof partial differential equation of the second order in the form of series on a reproducing kernel space H02(D). This series solution possesses following characteristics:1. Truncating the series, the analytic numerical solution can be obtained. 2.when in creasing the number of the node, the error of the analytic numerical solution is monotone decreasing in the sense of the norm on H02 (D) space.
Analytical solution of Boussinesq equations as a model of wave generation
Wiryanto, L. H.; Mungkasi, S.
2016-02-01
When a uniform stream on an open channel is disturbed by existing of a bump at the bottom of the channel, the surface boundary forms waves growing splitting and propagating. The model of the wave generation can be a forced Korteweg de Vries (fKdV) equation or Boussinesq-type equations. In case the governing equations are approximated from steady problem, the fKdV equation is obtained. The model gives two solutions representing solitary-like wave, with different amplitude. However, phyically there is only one profile generated from that process. Which solution is occured, we confirm from unsteady model. The Boussinesq equations are proposed to determine the stabil solution of the fKdV equation. From the linear and steady model, its solution is developed to determine the analytical solution of the unsteady equations, so that it can explain the physical phenomena, i.e. the process of the wave generation, wave splitting and wave propagation. The solution can also determine the amplitude and wave speed of the waves.
Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow
Directory of Open Access Journals (Sweden)
Milićev Snežana S.
2016-01-01
Full Text Available The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn≤0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy. [Projekat Ministarstva nauke Republike Srbije, br. 35046 i 174014
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
FORECAST OF WATER TEMPERATURE IN RESERVOIR BASED ON ANALYTICAL SOLUTION
Institute of Scientific and Technical Information of China (English)
JI Shun-wen; ZHU Yue-ming; QIANG Sheng; ZENG Deng-feng
2008-01-01
The water temperature in reservoirs is difficult to be predicted by numerical simulations. In this article, a statistical model of forecasting the water temperature was proposed. In this model, the 3-D thermal conduction-diffusion equations were converted into a system consisting of 2-D equations with the Fourier expansion and some hypotheses. Then the statistical model of forecasting the water temperature was developed based on the analytical solution to the 2-D thermal equations. The simplified statistical model can elucidate the main physical mechanism of the temperature variation much more clearly than the numerical simulation with the Navier-Stokes equations. Finally, with the presented statistical model, the distribution of water temperature in the Shangyoujiang reservoir was determined.
Analytic solution of Hubbell's model of local community dynamics
McKane, A; Sole, R; Kane, Alan Mc; Alonso, David; Sole, Ricard
2003-01-01
Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model i.e.a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution -- also called the zero-sum multinomial -- is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.
Pseudo analytical solution to time periodic stiffness systems
Institute of Scientific and Technical Information of China (English)
Wang Yan-Zhong; Zhou Yuan-Zi
2011-01-01
An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.
An analytic solution to asymmetrical bending problem of diaphragm coupling
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Because rigidity of either hub or rim of diaphragm coupling is much greater than that of the disk, and asymmetrical bending is under the condition of high speed revolution, an assumption is made that each circle in the middle plane before deforma-tion keeps its radius unchanged after deformation, but the plane on which the circle lies has a varying deflecting angle. Based on this assumption, and according to the principle of energy variation, the corresponding Euler's equation can be obtained, which has the primary integral. By neglecting some subsidiary factors, an analytic solution is obtained. Applying these formulas to a hyperbolic model of diaphragm, the results show that the octahedral shear stress varies less along either radial or thickness direction, but fluctu-ates greatly and periodically along circumferential direction. Thus asymmetrical bending significantly affects the material's fatigue.
Measurement of Actinides in Molybdenum-99 Solution Analytical Procedure
Energy Technology Data Exchange (ETDEWEB)
Soderquist, Chuck Z. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Weaver, Jamie L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2015-11-01
This document is a companion report to a previous report, PNNL 24519, Measurement of Actinides in Molybdenum-99 Solution, A Brief Review of the Literature, August 2015. In this companion report, we report a fast, accurate, newly developed analytical method for measurement of trace alpha-emitting actinide elements in commercial high-activity molybdenum-99 solution. Molybdenum-99 is widely used to produce ^{99m}Tc for medical imaging. Because it is used as a radiopharmaceutical, its purity must be proven to be extremely high, particularly for the alpha emitting actinides. The sample of ^{99}Mo solution is measured into a vessel (such as a polyethylene centrifuge tube) and acidified with dilute nitric acid. A gadolinium carrier is added (50 µg). Tracers and spikes are added as necessary. Then the solution is made strongly basic with ammonium hydroxide, which causes the gadolinium carrier to precipitate as hydrous Gd(OH)_{3}. The precipitate of Gd(OH)_{3} carries all of the actinide elements. The suspension of gadolinium hydroxide is then passed through a membrane filter to make a counting mount suitable for direct alpha spectrometry. The high-activity ^{99}Mo and ^{99m}Tc pass through the membrane filter and are separated from the alpha emitters. The gadolinium hydroxide, carrying any trace actinide elements that might be present in the sample, forms a thin, uniform cake on the surface of the membrane filter. The filter cake is first washed with dilute ammonium hydroxide to push the last traces of molybdate through, then with water. The filter is then mounted on a stainless steel counting disk. Finally, the alpha emitting actinide elements are measured by alpha spectrometry.
A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
Alikhanov, A A
2011-01-01
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
LIMIT BEHAVIOUR OF SOLUTIONS TO EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
LI Fengquan
2002-01-01
In this paper, we discuss the limit behaviour of solutions to equivalued surface boundary value problem for parabolic equations when the equivalued surface boundary shrinks to a point and the space dimension of the domain is two or more.
Mayrhofer, Arno; Violeau, Damien; Ferrand, Martin
2013-01-01
The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which implies exact energy conservation. It will be shown that this property holds only in the limit of the continuous SPH approximation, whereas in the discrete SPH formulation it is only approximately true, leading to numerical noise. This noise, interpreted as form of "turbulence", is treated using an additional volume diffusion term in the continuity equation which we show is equivalent to an approximate Riemann solver. Subsequently two extensions to the boundary conditions are presented. The first dealing with a variable driving force when imposing a volume flux in a periodic flow and the second showing a generalization of the wall boundary condition to Robin type and arbitrary-order interpolation. Two modifications for free-surface flows are presented for the volume diffusio...
Analytical solutions for elastic binary nanotubes of arbitrary chirality
Jiang, Lai; Guo, Wanlin
2016-09-01
Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young's modulus and Poisson's ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III-V and II-VI group elements.
Analytical solutions for elastic binary nanotubes of arbitrary chirality
Jiang, Lai; Guo, Wanlin
2016-12-01
Analytical solutions for the elastic properties of a variety of binary nanotubes with arbitrary chirality are obtained through the study of systematic molecular mechanics. This molecular mechanics model is first extended to chiral binary nanotubes by introducing an additional out-of-plane inversion term into the so-called stick-spiral model, which results from the polar bonds and the buckling of binary graphitic crystals. The closed-form expressions for the longitudinal and circumferential Young's modulus and Poisson's ratio of chiral binary nanotubes are derived as functions of the tube diameter. The obtained inversion force constants are negative for all types of binary nanotubes, and the predicted tube stiffness is lower than that by the former stick-spiral model without consideration of the inversion term, reflecting the softening effect of the buckling on the elastic properties of binary nanotubes. The obtained properties are shown to be comparable to available density functional theory calculated results and to be chirality and size sensitive. The developed model and explicit solutions provide a systematic understanding of the mechanical performance of binary nanotubes consisting of III-V and II-VI group elements.
General analytical solutions for DC/AC circuit network analysis
Rubido, Nicolás; Baptista, Murilo S
2014-01-01
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm's law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that o...
Editorial: Special Issue on Analytical and Approximate Solutions for Numerical Problems
Directory of Open Access Journals (Sweden)
Walailak Journal of Science and Technology
2014-08-01
iteration must be minimum (set as a condition. Suppose, if an exact solution is possible analytically and if the requirement is an exact solution then there is no advantage of numerical method. The main intention of this special issue is to provide an analytical and approximate solution for some numerical problems of ordinary differential equations (ODEs. Furthermore, it focuses on constructing new numerical methods and algorithms for ODEs including mathematical analysis and its behaviour. Particularly, with a study of well-posedness initial value problems and boundary value problems for a first/second order differential equations and system of such equations are also carried out for better understanding. Sometimes, it is not easy to be a good numerical analyst, since, as in other branches of mathematics, because it takes considerable skill and experience to be able to leap nimbly to and fro from the general and abstract to the particular and practical. Moreover, numerical analysis is well motivated and employs many important mathematical concepts. There are numerous research opportunities which are open and available in the field of numerical analysis, thus end user can easily find topics for research and venues for presenting their results. Indeed, researchers can gain sufficient knowledge to be able to identify some area of study, and as they become more and more familiar with different algorithms, they can easily develop applications for research problems in numerous fields. Researchers were able to explore in greater detail some topic that interested them and to see first-hand the importance of computation and analysis in real world applications. Some of the applications of numerical methods are computer graphics (root finding, interpolation, curve fitting, optimization, ODE solver, PDE solver, finite element method such as physics-based animation, geometry modelling; computer vision (optimization, curve fitting, linear equations, such as stereo vision, shape from
POLYNOMIAL SOLUTIONS TO PIEZOELECTRIC BEAMS(Ⅱ)--ANALYTICAL SOLUTIONS TO TYPICAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
DING Hao-jiang; JIANG Ai-min
2005-01-01
For the orthotropic piezoelectric plane problem, a series of piezoelectric beams is solved and the corresponding analytical solutions are obtained with the trialand-error method on the basis of the general solution in the case of three distinct eigenvalues, in which all displacements, electrical potential, stresses and electrical displacements are expressed by three displacement functions in terms of harmonic polynomials. These problems are cantilever beam with cross force and point charge at free end, cantilever beam and simply-supported beam subjected to uniform loads on the upper and lower surfaces, and cantilever beam subjected to linear electrical potential.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.
Concerning an analytical solution of some families of Kepler’s transcendental equation
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2016-03-01
Full Text Available The problem of finding an analytical solution of some families of Kepler transcendental equation is studied in some detail, by the Special Trans Functions Theory – STFT. Thus, the STFT mathematical approach in the form of STFT iterative methods with a novel analytical solutions are presented. Structure of the STFT solutions, numerical results and graphical simulations confirm the validity of the basic principle of the STFT. In addition, the obtained analytical results are compared with the calculated values of other analytical methods for alternative proving its significance. Undoubtedly, the proposed novel analytical approach implies qualitative improvement in comparison with conventional numerical and analytical methods.
THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS
Institute of Scientific and Technical Information of China (English)
Zhongwei SI; Jinyuan DU
2013-01-01
Let R0,n be the real Clifford algebra generated by e1,e2,…,en satisfying eiej +ejei =-2δij,i,j =1,2,…,n.e0 is the unit element.Let Ω be an open set.A function f is called left generalized analytic in Ω if f satisfies the equation Lf =0,(0.1)where L =q0e0(δ)x0 + q1e1(δ)x1 + … +qnen(δ)xn,qi ＞ 0,i =0,1,…,n.In this article,we first give the kernel function.for the generalized analytic function.Further,the Hilbert boundary value problem for generalized analytic functions in Rn+1+ will be investigated.
Leble, Sergey
2013-01-01
The model under consideration is based on approximate analytical solution of two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations. Approximations are based on the typical for natural convection assumptions: the fluid noncompressibility and Bousinesq approximation. We also assume that ortogonal to the plate component (x) of velocity is neglectible small. The solution of the boundary problem is represented as a Taylor Series in $x$ coordinate for velocity and temperature which introduces functions of vertical coordinate (y), as coefficients of the expansion. The correspondent boundary problem formulation depends on parameters specific for the problem: Grashoff number, the plate height (L) and gravity constant. The main result of the paper is the set of equations for the coefficient functions for example choice of expansion terms number. The nonzero velocity at the starting point of a flow appears in such approach as a development of convecntional boundary layer theory formulation.
Institute of Scientific and Technical Information of China (English)
XIAZhi
2004-01-01
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
Messaris, Gerasimos A. T.; Hadjinicolaou, Maria; Karahalios, George T.
2016-08-01
The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the
GLOBAL SOLUTIONS TO AN INITIAL BOUNDARY VALUE PROBLEM FOR THE MULLINS EQUATION
Institute of Scientific and Technical Information of China (English)
Hans-Dieter Alber; Zhu Peicheng
2007-01-01
In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L∞(Ω)-norm, as time tends to infinity.
The BV solution of the parabolic equation with degeneracy on the boundary
Directory of Open Access Journals (Sweden)
Zhan Huashui
2016-12-01
Full Text Available Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.
Food Adulteration: From Vulnerability Assessment to New Analytical Solutions.
Cavin, Christophe; Cottenet, Geoffrey; Blancpain, Carine; Bessaire, Thomas; Frank, Nancy; Zbinden, Pascal
2016-01-01
Crises related to the presence of melamine in milk or horse meat in beef have been a wake-up call to the whole food industry showing that adulteration of food raw materials is a complex issue. By analysing the situation, it became clear that the risk-based approach applied to ensure the safety related to chemical contaminants in food is not adequate for food fraud. Therefore, a specific approach has been developed to evaluate adulteration vulnerabilities within the food chain. Vulnerabilities will require the development of new analytical solutions. Fingerprinting methodologies can be very powerful in determining the status of a raw material without knowing the identity of each constituent. Milk adulterated by addition of adulterants with very different chemical properties could be detected rapidly by Fourier-transformed mid-infrared spectroscopy (FT-mid-IR) fingerprinting technology. In parallel, a fast and simple multi-analytes liquid-chromatography tandem mass-spectrometry (LC/MS-MS) method has been developed to detect either high levels of nitrogen-rich compounds resulting from adulteration or low levels due to accidental contamination either in milk or in other sensitive food matrices. To verify meat species authenticity, DNA-based methods are preferred for both raw ingredients and processed food. DNA macro-array, and more specifically the Meat LCD Array have showed efficient and reliable meat identification, allowing the simultaneous detection of 32 meat species. While the Meat LCD Array is still a targeted approach, DNA sequencing is a significant step towards an untargeted one.
Energy Technology Data Exchange (ETDEWEB)
Gazzaniga, G.; Sacchi, G. [Istituto di Analisi Numerica, Pavia (Italy)
1995-12-01
Different Domain Decomposition techniques for the solution of elliptic boundary-value problems are considered. The results of the implementation on a parallel distributed memory architecture are discussed.
Starn, J. J.
2013-12-01
Particle tracking often is used to generate particle-age distributions that are used as impulse-response functions in convolution. A typical application is to produce groundwater solute breakthrough curves (BTC) at endpoint receptors such as pumping wells or streams. The commonly used semi-analytical particle-tracking algorithm based on the assumption of linear velocity gradients between opposing cell faces is computationally very fast when used in combination with finite-difference models. However, large gradients near pumping wells in regional-scale groundwater-flow models often are not well represented because of cell-size limitations. This leads to inaccurate velocity fields, especially at weak sinks. Accurate analytical solutions for velocity near a pumping well are available, and various boundary conditions can be imposed using image-well theory. Python can be used to embed these solutions into existing semi-analytical particle-tracking codes, thereby maintaining the integrity and quality-assurance of the existing code. Python (and associated scientific computational packages NumPy, SciPy, and Matplotlib) is an effective tool because of its wide ranging capability. Python text processing allows complex and database-like manipulation of model input and output files, including binary and HDF5 files. High-level functions in the language include ODE solvers to solve first-order particle-location ODEs, Gaussian kernel density estimation to compute smooth particle-age distributions, and convolution. The highly vectorized nature of NumPy arrays and functions minimizes the need for computationally expensive loops. A modular Python code base has been developed to compute BTCs using embedded analytical solutions at pumping wells based on an existing well-documented finite-difference groundwater-flow simulation code (MODFLOW) and a semi-analytical particle-tracking code (MODPATH). The Python code base is tested by comparing BTCs with highly discretized synthetic steady
Grain boundary structure and solute segregation in titanium-doped sapphire bicrystals
Energy Technology Data Exchange (ETDEWEB)
Taylor, Seth T.
2002-05-17
Solute segregation to ceramic grain boundaries governs material processing and microstructure evolution, and can strongly influence material properties critical to engineering performance. Understanding the evolution and implications of grain boundary chemistry is a vital component in the greater effort to engineer ceramics with controlled microstructures. This study examines solute segregation to engineered grain boundaries in titanium-doped sapphire (Al2O3) bicrystals, and explores relationships between grain boundary structure and chemistry at the nanometer scale using spectroscopic and imaging techniques in the transmission electron microscope (TEM). Results demonstrate dramatic changes in solute segregation stemming from small fluctuations in grain boundary plane and structure. Titanium and silicon solute species exhibit strong tendencies to segregate to non-basal and basal grain boundary planes, respectively. Evidence suggests that grain boundary faceting occurs in low-angle twis t boundaries to accommodate nonequilibrium solute segregation related to slow specimen cooling rates, while faceting of tilt grain boundaries often occurs to expose special planes of the coincidence site lattice (CSL). Moreover, quantitative analysis of grain boundary chemistry indicates preferential segregation of charged defects to grain boundary dislocations. These results offer direct proof that static dislocations in ionic materials can assume a net charge, and emphasize the importance of interactions between charged point, line, and planar defects in ionic materials. Efforts to understand grain boundary chemistry in terms of space charge theory, elastic misfit and nonequilibrium segregation are discussed for the Al2O3 system.
Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Nemat Nyamoradi
2013-01-01
Full Text Available We consider a system of boundary value problems for fractional differential equation given by D0+βϕp(D0+αu(t=λ1a1(tf1(u(t,v(t, t∈(0,1, D0+βϕp(D0+αv(t=λ2a2(tf2(u(t,v(t, t∈(0,1, where 1<α, β≤2, 2<α+β≤4, λ1, λ2 are eigenvalues, subject either to the boundary conditions D0+αu(0=D0+αu(1=0, u(0=0, D0+β1u(1-Σi=1m-2a1i D0+β1u(ξ1i=0, D0+αv(0=D0+αv(1=0, v(0=0, D0+β1v(1-Σi=1m-2a2i D0+β1v(ξ2i=0 or D0+αu(0=D0+αu(1=0, u(0=0, D0+β1u(1-Σi=1m-2a1i D0+β1u(ξ1i=ψ1(u, D0+αv(0=D0+αv(1=0, v(0=0, D0+β1v(1-Σi=1m-2a2i D0+β1v(ξ2i=ψ2(v, where 0<β1<1, α-β1-1≥0 and ψ1, ψ2:C([0,1]→[0, ∞ are continuous functions. The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems. As an application, an example is given to demonstrate some of main results.
An analytical solution to patient prioritisation in radiotherapy based on utilitarian optimisation.
Ebert, M A; Li, W; Jennings, L
2014-03-01
The detrimental impact of a radiotherapy waiting list can in part be compensated by patient prioritisation. Such prioritisation is phrased as an optimisation problem where the probability of local control for the overall population is the objective to be maximised and a simple analytical solution derived. This solution is compared with a simulation of a waiting list for the same population of patients. It is found that the analytical solution can provide an optimal ordering of patients though cannot explicitly constrain optimal waiting times. The simulation-based solution was undertaken using both the analytical solution and a numerical optimisation routine for daily patient ordering. Both solutions provided very similar results with the analytical approach reducing the calculation time of the numerical solution by several orders of magnitude. It is suggested that treatment delays due to resource limitations and resulting waiting lists be incorporated into treatment optimisation and that the derived analytical solution provides a mechanism for this to occur.
Approximate analytic solutions to the NPDD: Short exposure approximations
Close, Ciara E.; Sheridan, John T.
2014-04-01
There have been many attempts to accurately describe the photochemical processes that take places in photopolymer materials. As the models have become more accurate, solving them has become more numerically intensive and more 'opaque'. Recent models incorporate the major photochemical reactions taking place as well as the diffusion effects resulting from the photo-polymerisation process, and have accurately described these processes in a number of different materials. It is our aim to develop accessible mathematical expressions which provide physical insights and simple quantitative predictions of practical value to material designers and users. In this paper, starting with the Non-Local Photo-Polymerisation Driven Diffusion (NPDD) model coupled integro-differential equations, we first simplify these equations and validate the accuracy of the resulting approximate model. This new set of governing equations are then used to produce accurate analytic solutions (polynomials) describing the evolution of the monomer and polymer concentrations, and the grating refractive index modulation, in the case of short low intensity sinusoidal exposures. The physical significance of the results and their consequences for holographic data storage (HDS) are then discussed.
Electromechanics: An analytic solution for graded biological cell.
Chan, Kin Lok; Yu, K. W.
2007-03-01
Electromechanics of graded material has been established recently to study the effective response of inhomogeneous graded spherical particles under an external ac electric field.[1, 2]Such particles having a complex dielectric profile varies along the radius of the particles. The gradation in the colloidal particles is modeled by assuming both the dielectric and conductivity vary along the radius. More precisely, both the dielectric and conductivity function are assumed to be a isotopic linear function dependence on the radius variable r, namely, ɛ(r)=ɛ(0)+A1r, σ(r)=σ(0)+A2r.In this talk, we will present the exact analytical solutions of the dipole moment of such particle in terms of the hypergeometric functions, and the effective electric response in dilute limit. Moreover, we applied the dielectric dispersion spectral representation (DDSR) to study the Debye Behavior of the cell. Our exact results may be applied to graded biological cell suspensions, as their interior must be inhomogeneous in nature. [1] En-Bo Wei, L. Dong, K. W. Yu, Journal of Applied Physics 99, 054101(2006) [2] L. Dong, Mikko Karttunen, K. W. Yu, Phys. Rev. E, Vol. 72, art. no. 016613 (2005)
New analytic solutions for modeling vertical gravity gradient anomalies
Kim, Seung-Sep; Wessel, Paul
2016-05-01
Modern processing of satellite altimetry for use in marine gravimetry involves computing the along-track slopes of observed sea-surface heights, projecting them into east-west and north-south deflection of the vertical grids, and using Laplace's equation to algebraically obtain a grid of the vertical gravity gradient (VGG). The VGG grid is then integrated via overlapping, flat Earth Fourier transforms to yield a free-air anomaly grid. Because of this integration and associated edge effects, the VGG grid retains more short-wavelength information (e.g., fracture zone and seamount signatures) that is of particular importance for plate tectonic investigations. While modeling of gravity anomalies over arbitrary bodies has long been a standard undertaking, similar modeling of VGG anomalies over oceanic features is not commonplace yet. Here we derive analytic solutions for VGG anomalies over simple bodies and arbitrary 2-D and 3-D sources. We demonstrate their usability in determining mass excess and deficiency across the Mendocino fracture zone (a 2-D feature) and find the best bulk density estimate for Jasper seamount (a 3-D feature). The methodologies used herein are implemented in the Generic Mapping Tools, available from gmt.soest.hawaii.edu.
Acceleration of multiple solution of a boundary value problem involving a linear algebraic system
Gazizov, Talgat R.; Kuksenko, Sergey P.; Surovtsev, Roman S.
2016-06-01
Multiple solution of a boundary value problem that involves a linear algebraic system is considered. New approach to acceleration of the solution is proposed. The approach uses the structure of the linear system matrix. Particularly, location of entries in the right columns and low rows of the matrix, which undergo variation due to the computing in the range of parameters, is used to apply block LU decomposition. Application of the approach is considered on the example of multiple computing of the capacitance matrix by method of moments used in numerical electromagnetics. Expressions for analytic estimation of the acceleration are presented. Results of the numerical experiments for solution of 100 linear systems with matrix orders of 1000, 2000, 3000 and different relations of variated and constant entries of the matrix show that block LU decomposition can be effective for multiple solution of linear systems. The speed up compared to pointwise LU factorization increases (up to 15) for larger number and order of considered systems with lower number of variated entries.
Analytical solutions of heat transfer for laminar flow in rectangular channels
Directory of Open Access Journals (Sweden)
Rybiński Witold
2014-12-01
Full Text Available The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type. The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s perimeter is related to the asymptotic case of channel’s wall thermal resistance: infinite in the axial direction and zero in the peripheral one. It represents typical conditions in a minichannel heat exchanger made of metal.
Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition
Institute of Scientific and Technical Information of China (English)
Zifei SHEN; Chenyin QIAN
2009-01-01
The authors study the p(x)-Laplacian equations with nonlinear boundary condition.By using the variational method,under appropriate assumptions on the perturbation terms f1(x,u),f2(x,u) and h1(x),h2(x),such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively,the existence and multiplicity of solutions are obtained.The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.
Semi-analytic Solution of Steady Temperature Fields During Thin Plate Welding
Institute of Scientific and Technical Information of China (English)
DAI Yao; TAN Wei; SUN Qi; SUN Chang-qing
2006-01-01
Usually, it is very difficult to find out an analytical solution to thermal conduction problems during high temperature welding. Therefore, as an important numerical approach, the method of lines (MOLs) is introduced to solve the temperature field characterized by high gradients. The basic idea of the method is to semi-discretize the governing equation of the problem into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method, by which the thermal boundary condition with high gradients are directly embodied in formulation. Thus the temperature field can be obtained by solving the ODEs. As a numerical example, the variation of an axisymmetrical temperature field along the plate thickness can be obtained.
STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
闫振亚; 张鸿庆
2001-01-01
The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.
Mehdi Delkhosh; Mohammad Delkhosh
2012-01-01
Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011). In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011;...
EXISTENCE OF TRIPLE POSITIVE SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
We apply a fixed point theorem to verify the existence of at least three positive solutions to a multi-point boundary value problem with p-Laplacian. Existence criteria which ensure the existence of triple positive solutions are established.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
Guedda, Mohamed
2008-01-01
The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\\infty x^{-1}). The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examenin detail new exact solutions. The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties o...
Solutions to a hyperbolic system of conservation laws on two boundaries
Institute of Scientific and Technical Information of China (English)
JIA Zhi; YAO Ai-di
2009-01-01
This paper studies the interaction of elementary waves including delta-shock waves on two boundaries for a hyperbolic system of conservation laws. The solutions of the initial-boundary value problem for the system are constructively obtained. In the problem the initial-boundary data are in piecewise constant states.
Qualitative behavior of axial-symmetric solutions of elliptic free boundary problems
Directory of Open Access Journals (Sweden)
Andrew F. Acker
1997-01-01
Full Text Available axial-symmetric solutions and qualitative geometric properties of the free boundary are compared to those of the fixed boundary for the axial and radial directions. Counterexamples obtained previously by the first author show that our results cannot hold in the same generality as those for similar free boundary problems in R^2.
Approximate analytical solutions to the condensation-coagulation equation of aerosols
Smith, Naftali; Svensmark, Henrik
2015-01-01
We present analytical solutions to the steady state injection-condensation-coagulation equation of aerosols in the atmosphere. These solutions are appropriate under different limits but more general than previously derived analytical solutions. For example, we provide an analytic solution to the coagulation limit plus a condensation correction. Our solutions are then compared with numerical results. We show that the solutions can be used to estimate the sensitivity of the cloud condensation nuclei number density to the nucleation rate of small condensation nuclei and to changes in the formation rate of sulfuric acid.
An analytical solution for light field modes in waveguides with nonideal cladding
Arslanov, N M; Moiseev, S A
2015-01-01
We have obtained an analytical solution for the dispersion relation of the light field modes in the nanowaveguide structure. The solution has been analyzed for the planar waveguide with metamaterial claddings and dielectric core. The analytical solution is valid within the broadband spectral range and is confirmed by existing numerical calculations. The developed theoretical approach opens vast possibilities for the analytical investigations of the light fields in the various waveguides.
Solution of Moving Boundary Space-Time Fractional Burger’s Equation
Directory of Open Access Journals (Sweden)
E. A.-B. Abdel-Salam
2014-01-01
Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.
Energy Technology Data Exchange (ETDEWEB)
Li Xicheng; Xu Mingyu [Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100 (China); Wang Shaowei [Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (China)], E-mail: xichengli@yahoo.com.cn
2008-04-18
In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given.
EXISTENCE OF SOLUTIONS TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.
Approximate analytical solution for the isothermal Lane Emden equation in a spherical geometry
Soliman, Moustafa Aly; Al-Zeghayer, Yousef
2015-10-01
This paper obtains an approximate analytical solution for the isothermal Lane-Emden equation that models a self-gravitating isothermal sphere. The approximate solution is obtained by perturbation methods in terms of small and large distance parameters. The approximate solution is compared with the numerical solution. The approximate solution obtained is valid for all values of the distance parameter.
Existence and non-uniqueness of similarity solutions of a boundary-layer problem
Hussaini, M. Y.; Lakin, W. D.
1986-01-01
A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.
Existence and non-uniqueness of similarity solutions of a boundary layer problem
Hussaini, M. Y.; Lakin, W. D.
1984-01-01
A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.
Directory of Open Access Journals (Sweden)
Kulish Vladimir V.
2004-01-01
Full Text Available This paper presents an integral solution of the generalized one-dimensional equation of energy transport with the convective term.The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders. Confluent hypergeometric functions, known as Whittaker's functions, appear in the course of the solution procedure upon applying the Laplace transform to the original transport equation.The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the transported property (e.g., temperature, mass, momentum, etc. and its flux.The solution is valid everywhere within the domain, including the domain boundary.
EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A THREE-POINT BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper, we are concerned with the existence and nonexistence of positive solutions to a three-point boundary value problems. By Krasnoselskii's fixed point theorem in Banach space, we obtain sufficient conditions for the existence and non-existence of positive solutions to the above three-point boundary value problems.
Energy Technology Data Exchange (ETDEWEB)
Petracca, S. [Salerno Univ. (Italy)
1996-08-01
Debye potentials, the Lorentz reciprocity theorem, and (extended) Leontovich boundary conditions can be used to obtain simple and accurate analytic estimates of the longitudinal and transverse coupling impedances of (piecewise longitudinally uniform) multi-layered pipes with non simple transverse geometry and/or (spatially inhomogeneous) boundary conditions. (author)
Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations
Kanoglu, U.; Aydin, B.
2014-12-01
The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV
Generalized solutions of initial-boundary value problems for second-order hyperbolic systems
Alexeyeva, L. A.; Zakir'yanova, G. K.
2011-07-01
The method of boundary integral equations is developed as applied to initial-boundary value problems for strictly hyperbolic systems of second-order equations characteristic of anisotropic media dynamics. Based on the theory of distributions (generalized functions), solutions are constructed in the space of generalized functions followed by passing to integral representations and classical solutions. Solutions are considered in the class of singular functions with discontinuous derivatives, which are typical of physical problems describing shock waves. The uniqueness of the solutions to the initial-boundary value problems is proved under certain smoothness conditions imposed on the boundary functions. The Green's matrix of the system and new fundamental matrices based on it are used to derive integral analogues of the Gauss, Kirchhoff, and Green formulas for solutions and solving singular boundary integral equations.
Positive Solutions of Singular Boundary Value Problem of Negative Exponent Emden–Fowler Equation
Indian Academy of Sciences (India)
Yuxia Wang; Xiyu Liu
2003-05-01
This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden–Fowler equation. A necessary and sufficient condition for the existence of [0, 1] positive solutions as well as 1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.
Analytic Solution for Magnetohydrodynamic Stagnation Point Flow towards a Stretching Sheet
Institute of Scientific and Technical Information of China (English)
DING Qi; ZHANG Hong-Qing
2009-01-01
A steady two-dimensional magnetohydrodynamic stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The analytic solution is obtained by homotopy analysis method. Theconvergence region is computed and the feature of the solution is discussed.
On analytic solutions of wave equations in regular coordinate systems on Schwarzschild background
Philipp, Dennis
2015-01-01
The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual Schwarzschild, Eddington-Finkelstein, Painleve-Gullstrand and Kruskal-Szekeres coordinates. In the first three cases, but not in the last one, it is possible to separate a harmonic time-dependence. Then the resulting radial equations belong to the class of confluent Heun equations, i.e., we can identify one irregular and two regular singularities. Using the generalized Riemann scheme we collect properties of all the singular points and construct analytic (local) solutions in terms of the standard confluent Heun function HeunC, Frobenius and asymptotic Thome series. We study the Eddington-Finkelstein case in detail and obtain a solution that is regular at the black hole horizon. This solution satisfies causal boundary conditions, i.e., it describes purely ingoing radiation at $r=2M$. ...
Positive solutions of some nonlocal boundary value problems
Directory of Open Access Journals (Sweden)
Gennaro Infante
2003-01-01
employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.
Approximate analytic solutions of stagnation point flow in a porous medium
Kumaran, V.; Tamizharasi, R.; Vajravelu, K.
2009-06-01
An efficient and new implicit perturbation technique is used to obtain approximate analytical series solution of Brinkmann equation governing the two-dimensional stagnation point flow in a porous medium. Analytical approximate solution of the classical two-dimensional stagnation point flow is obtained as a limiting case. Also, it is shown that the obtained higher order series solutions agree well with the computed numerical solutions.
Directory of Open Access Journals (Sweden)
Taha Aziz
2013-01-01
Full Text Available The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.
Troch, P.A.A.; Loon, van A.H.; Hilberts, A.G.J.
2004-01-01
This technical note presents an analytical solution to the linearized hillslope-storage Boussinesq equation for subsurface flow along complex hillslopes with exponential width functions and discusses the application of analytical solutions to storage-based subsurface flow equations in catchment stud
Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution
Directory of Open Access Journals (Sweden)
Longhua Zhao
2016-11-01
Full Text Available To investigate the translation of a compound particle in a highly viscous, incompressible fluid, we carry out an analytic study on flow past a fixed spherical compound particle. The spherical object is considered to have a rigid kernel covered with a fluid coating. The fluid within the coating has a different viscosity from that of the surrounding fluid and is immiscible with the surrounding fluid. The inertia effect is negligible for flows both inside the coating and outside the object. Thus, flows are in the Stokes regime. Taking advantage of the symmetry properties, we reduce the problem in two dimensions and derive the explicit formulae of the stream function in the polar coordinates. The no-slip boundary condition for the rigid kernel and the no interfacial mass transfer and force equilibrium conditions at fluid interfaces are considered. Two extreme cases: the uniform flow past a sphere and the uniform flow past a fluid drop, are reviewed. Then, for the fluid coating the spherical object, we derive the stream functions and investigate the flow field by the contour plots of stream functions. Contours of stream functions show circulation within the fluid coating. Additionally, we compare the drag and the terminal velocity of the object with a rigid sphere or a fluid droplet. Moreover, the extended results regarding the analytical solution for a compound particle with a rigid kernel and multiple layers of fluid coating are reported.
Guo, Y.; Xia, C.; Keppens, R.; Valori, G.
2016-09-01
We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov-Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax-Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.
Analytical mechanics solutions to problems in classical physics
Merches, Ioan
2014-01-01
Fundamentals of Analytical Mechanics Constraints Classification Criteria for Constraints The Fundamental Dynamical Problem for a Constrained Particle System of Particles Subject to Constraints Lagrange Equations of the First KindElementary Displacements Generalities Real, Possible and Virtual Displacements Virtual Work and Connected Principles Principle of Virtual WorkPrinciple of Virtual Velocities Torricelli's Principle Principles of Analytical Mechanics D'alembert's Principle Configuration Space Generalized Forces Hamilton's Principle The Simple Pendulum Problem Classical (Newtonian) Formal
Exact Solution for Perk－Schultz Model with Boundary Impurities *
Institute of Scientific and Technical Information of China (English)
LI Guang-Liang; YUE Rui-Hong; SHI Kang-Jie; HOU Bo-Yu
2001-01-01
The Perk-Schultz model with SUq(m｜n) spin boundary impurities is constructed by dressing the c-number reflecting K-matrix with the local L-matrix which acts non-trivially on an impurity Hilbert space. The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method (m ≠ n). When m ＝ 1,n ＝ 2, our results come back to that of supersymmetric t - J model with SUq(1｜2) spin boundary impurities.
Directory of Open Access Journals (Sweden)
R. T. Al-Khairy
2009-01-01
source, whose capacity is given by (,=((1−− while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.
Indian Academy of Sciences (India)
Zehra Pinar; Abhishek Dutta; Guido Bény; Turgut Öziş
2015-01-01
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation of a nonlinear PBE with appropriately chosen parameters is taken to be analogous to the description of the dynamic behaviour of the particulate processes. For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation and breakage, (2) when aggregation can dominate and (3) breakage can dominate, are selected and solved for their corresponding analytical solutions. The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the solution approach proposed via AEM is flexible and therefore more efficient than the analytical approach used in the literature.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
On analytical solutions of the generalized Boussinesq equation
Kudryashov, Nikolay A.; Volkov, Alexandr K.
2016-06-01
Extended Boussinesq equation for the description of the Fermi-Pasta-Ulam problem is studied. It is analysed with the Painlevé test. It is shown, that the equation does not pass the Painlevé test, although necessary conditions for existence of the meromorphic solution are carried out. Method of the logistic function is introduced for Solitary wave solutions of the considered equation. Elliptic solutions for studied equation are constructed and discussed.
Reproduction of solutions in the plane problem on motion of a free-boundary fluid
Karabut, E. A.; Zhuravleva, E. N.
2016-07-01
This study is devoted to finding exact solutions of the plane unsteady problem on the motion of an ideal incompressible free-boundary fluid. A certain procedure of reproduction making it possible to obtain a two-parametrical family of new exact solutions from one known solution is proposed.
Boundary Element Method Solution in the Time Domain For a Moving Time-Dependent Force
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Kirkegaard, Poul Henning; Rasmussen, K. M.
2001-01-01
satisfy the radiation conditions exactly. In this paper a model based on the BEM is formulated for the solution of the mentioned problem. A numerical solution is obtained for the 2D plane strain case, and comparison is made with the results obtained from a corresponding FEM solution with an impedance...... absorbing boundary condition....
Analytic continuation of solutions of some nonlinear convolution partial differential equations
Directory of Open Access Journals (Sweden)
Hidetoshi Tahara
2015-01-01
Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.
Explicit Analytical Solutions of Coupled Fluid Flow Transfer Equation in Heterogeneous Porous Media
Institute of Scientific and Technical Information of China (English)
张娜; 蔡睿贤
2002-01-01
Explicit analytical solutions are presented for the coupled fluid flow transfer equation in heterogeneous porous media. These analytical solutions are useful for their description of actual flow fields and as benchmark solutions to check the rapidly developing numerical calculations and to study various computational methods such as the discrete approximations of the governing equations and grid generation methods. In addition, some novel mathematical methods are used in the analyses.
Aljoufi, Mona D.; Ebaid, Abdelhalim
2016-12-01
The exact solutions of a nonlinear differential equations system, describing the boundary layer flow over a stretching sheet with a convective boundary condition and a slip effect have been obtained in this paper. This problem has been numerically solved by using the shooting method in literature. The aim of the current paper is to check the accuracy of these published numerical results. This goal has been achieved via first obtaining the exact solutions of the governing nonlinear differential equations and then, by comparing them with the approximate numerical results reported in literature. The effects of the physical parameters on the flow field and the temperature distribution have been re-investigated through the new exact solutions. The main advantage of the current paper is the simple computational approach that has been introduced to analyze exactly the present physical problem. This simple analytical approach can be further applied to investigate similar problems. Although no remarkable differences have been detected between the current figures and those obtained in literature, the authors believe that if some numerical calculations were available for the fluid velocity and the temperature in literature then the convergence criteria and the accuracy of the shooting method used in Ref. [15] can be validated in view of the current exact expressions.
Analytical Applications of Electrified Interfaces Between Two Immiscible Solutions
1993-04-07
electrode potentiostate needed for the iwork is described. Experimental techniques involving potentiometry , polarography with dropping electrode...convert any potentiostat to the 4-electrode potentiostat needed for the work is described. Experimental techniques involving potentiometry , polarography...potentiostat input. Analytical applications Potentiometry Potentiometric measurements on ITIES are related to the principle of ionl selective electrodes (ISE
An analytical model for the amplitude of lee waves forming on the boundary layer inversion
Sachsperger, Johannes; Serafin, Stefano; Stiperski, Ivana; Grubišić, Vanda
2016-04-01
Lee waves are horizontally propagating gravity waves with a typical wavelength of 5-15 km that may be generated when stratified flow is lifted over a mountain. A frequently observed type of such waves is that of interfacial lee waves. Those develop, similar to surface waves on a free water surface, when the upstream flow features a density discontinuity. Such conditions are often present for example at the capping inversion in boundary layer flow. The dynamics of interfacial lee waves can be described concisely with linear interfacial gravity wave theory. However, while this theoretical framework accurately describes the wavelength, it fails to properly predict the amplitude of lee waves. It is well known that large amplitude lee waves may lead to low-level turbulence, which poses a potential hazard for aviation. Therefore, this property of interfacial lee waves deserves further attention. In this study, we develop a simple analytical model for the amplitude of lee waves forming on the boundary layer inversion. This model is based on the energetics of two-layer flow. We obtain an expression for the wave amplitude by equating the energy loss across an internal jump with the energy radiation through lee waves. The verification of the result with water tank experiments of density-stratified two-layer flow over two-dimensional topography from the HYDRALAB campaign shows good agreement between theory and observations. This new analytical model may be useful in determining potential hazards of interfacial lee waves with negligible computational cost as compared to numerical weather prediction models.
Zhao, Yuqing; Zhang, You-Kuan; Liang, Xiuyu
2016-08-01
A semi-analytical solution was presented for groundwater flow due to pumping in a leaky sloping fault-zone aquifer surrounded by permeable matrices. The flow in the aquifer was descried by a three-dimensional flow equation, and the flow in the upper and lower matrix blocks are described by a one-dimensional flow equation. A first-order free-water surface equation at the outcrop of the fault-zone aquifer was used to describe the water table condition. The Laplace domain solution was derived using Laplace transform and finite Fourier transform techniques and the semi-analytical solutions in the real time domain were evaluated using the numerical inverse Laplace transform method. The solution was in excellent agreement with Theis solution combined with superposition principle as well as the solution of Huang et al. (2014). It was found that the drawdown increases as the sloping angle of the aquifer increases in early time and the impact of the angle is insignificant after pumping for a long time. The free-water surface boundary as additional source recharges the fault aquifer and significantly affect the drawdown at later time. The surrounding permeable matrices have a strong influence on drawdown but this influence can be neglected when the ratio of the specific storage and the ratio of the hydraulic conductivity of the matrices to those of the fault aquifer are less than 0.001.
Existence of Positive Solutions for Higher Order Boundary Value Problem on Time Scales
Institute of Scientific and Technical Information of China (English)
XIE DA-PENG; LIU YANG; SUN MING-ZHE; Li Yong
2013-01-01
In this paper,we investigate the existence of positive solutions of a class higher order boundary value problems on time scales.The class of boundary value problems educes a four-point (or three-point or two-point) boundary value problems,for which some similar results are established.Our approach relies on the Krasnosel'skii fixed point theorem.The result of this paper is new and extends previously known results.
Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales
Directory of Open Access Journals (Sweden)
Topal SGulsan
2009-01-01
Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
On the Solutions of Some Boundary Value Problems for the General Kdv Equation
Energy Technology Data Exchange (ETDEWEB)
Ignatyev, M. Yu., E-mail: mikkieram@gmail.com [Saratov State University, Department of Mathematics (Russian Federation)
2014-12-15
This paper is concerned with a class of partial differential equations, which are linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary conditions of a certain special form is studied. We construct some class of solutions of the problem using the inverse spectral method.
Directory of Open Access Journals (Sweden)
Hongxia Fan
2011-01-01
Full Text Available By means of the fixed point theory of strict set contraction operators, we establish a new existence theorem on multiple positive solutions to a singular boundary value problem for second-order impulsive differential equations with periodic boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.
Vdovichenko, I. I.; Yakovlev, M. Ya; Vershinin, A. V.; Levin, V. A.
2016-11-01
One of the key problems of mechanics of composite materials is an estimation of effective properties of composite materials. This article describes the algorithms for numerical evaluation of the effective thermal conductivity and thermal expansion of composites. An algorithm of effective thermal conductivity evaluation is based on sequential solution of boundary problems of thermal conductivity with different boundary conditions (in the form of the temperature on the boundary) on representative volume element (RVE) of composite with subsequent averaging of the resulting vector field of heat flux. An algorithm of effective thermal expansion evaluation is based on the solution of the boundary problem of elasticity (considering the thermal expansion) on a RVE of composite material with subsequent averaging of a resulting strain tensor field. Numerical calculations were performed with the help of Fidesys Composite software module of CAE Fidesys using the finite element method. The article presents the results of numerical calculations of the effective coefficients of thermal conductivity and thermoelasticity for two types of composites (single-layer fiber and particulate materials) in comparison with the analytical estimates. The comparison leads to the conclusion about the correctness of algorithms and program developed.
Explicit analytical wave solutions of unsteady 1D ideal gas flow with friction and heat transfer
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Several families of algebraically explicit analytical wavesolutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families of standing wave solutions and one standing wave solution. \\{Among\\} them, the former four solution families contain arbitrary functions, so actually there are infinite analytical wave solutions having been derived. Besides their very important theoretical meaning, such analytical wave solutions can guide the development of some new equipment, and can be the benchmark solutions to promote the development of computational fluid dynamics. For example, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve the numerical computation skills such as differential schemes, grid generation ways and so on.
LIMIT BEHAVIOUR OF SOLUTIONS TO EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
LiFengquan
2002-01-01
In this paper,we discuss the limit behaviour of solutions to equivalued surface boundayr value problem for parabolic equatiopns when the equivalued surface boundary shriks to a point and the space dimension of the domain is two or more.
MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
Yang Liu; Shen Chunfang
2009-01-01
Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green's function of these problems are also given.
EXISTENCE AND ITERATION OF POSITIVE SYMMETRIC SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we consider the existence of symmetric solutions to a nonlinear second order multi-point boundary value problem,and establish corresponding iterative schemes based on the monotone iterative method.
ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
SunYan; XuBenlong; SunYongping
2005-01-01
By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.
Institute of Scientific and Technical Information of China (English)
LiHongyu; SunJingxian
2005-01-01
By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions,we prove the existence of positive solution of the problem.
Directory of Open Access Journals (Sweden)
Johnny Henderson
2016-01-01
Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.
Existence and uniqueness of solutions for a Neumann boundary-value problem
Directory of Open Access Journals (Sweden)
Safia Benmansour
2011-09-01
Full Text Available In this article, we show the existence and uniqueness of positive solutions for perturbed Neumann boundary-value problems of second-order differential equations. We use a fixed point theorem for general $alpha$-concave operators.
Brahim Tellab; Kamel Haouam
2016-01-01
In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.
Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems
Directory of Open Access Journals (Sweden)
Moulay Rchid Sidi Ammi
2013-01-01
Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.
MULTIPLE POSITIVE SOLUTIONS TO FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,using the Krasnaselskii's fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value problems is considered.
Directory of Open Access Journals (Sweden)
Mehdi Delkhosh
2012-01-01
Full Text Available Many applications of various self-adjoint differential equations, whose solutions are complex, are produced (Arfken, 1985; Gandarias, 2011; and Delkhosh, 2011. In this work we propose a method for the solving some self-adjoint equations with variable change in problem, and then we obtain a analytical solutions. Because this solution, an exact analytical solution can be provided to us, we benefited from the solution of numerical Self-adjoint equations (Mohynl-Din, 2009; Allame and Azal, 2011; Borhanifar et al. 2011; Sweilam and Nagy, 2011; Gülsu et al. 2011; Mohyud-Din et al. 2010; and Li et al. 1996.
Holota, Petr; Nesvadba, Otakar
2014-05-01
In geodesy mathematical techniques for gravity field studies that rest on the concept of the so-called classical solution of boundary value problems, have a rather traditional position. Nevertheless, the range of the tools for treating problems in this field is much wider. For instance the concept of the weak solution met with a considerable attention. From this point of view the approach is associated with constructing the respective integral kernels or Green's function in case we consider the classical solution concept or with the choice and constructing basis functions in case we are lucking for the weak solution of the problem. Within the tools considered we discuss also the use of reproducing kernels. In both the cases (classical or weak) the construction of the apparatus above represents and important technical step. It is not elementary, but for a number of fundamental boundary value problems the solution is known, in particular in the case of a spherical solution domain. The sphere, however, is rather far from the real shape of the Earth, which is interpreted here in terms of a functional analytic norm. The distance has a negative effect on any attempt to reach the solution of the boundary value problems considered (and to bridge the departure of the Earth's surface from the sphere) by an iteration procedure based on a successive application of a solution technique developed for the spherical boundary. From this point of view the construction of the integral kernels and basis functions for an oblate ellipsoid of revolution means a step closer towards reality. In this contribution we on the one hand give an overview of the results already achieved and subsequently develop the topic. The summation of series of ellipsoidal harmonics is one of the key problems in this connection. Hypergeometric functions and series are applied too. We also show where the use of Legendre elliptic integrals adds to the solution of the problem. It is interesting that they do not
Analytic Solution of Strongly Coupling Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
LIAO Jin-Feng; ZHUANG Peng-Fei
2004-01-01
A recently developed expansion method for analytically solving the ground states of strongly coupling Schrodinger equations by Friedberg,Lee,and Zhao is extended to excited states and applied to power-law central forces for which scaling properties are proposed.As examples for application of the extended method,the Hydrogen atom problem is resolved and the low-lying states of Yukawa potential are approximately obtained.
Analytic solutions of transcendental equations with application to automatics
Directory of Open Access Journals (Sweden)
Górecki Henryk
2016-12-01
Full Text Available In the paper the extremal dynamic error x(τ and the moment of time τ are considered. The extremal value of dynamic error gives information about accuracy of the system. The time τ gives information about velocity of transient. The analytical formulae enable design of the system with prescribed properties. These formulae are calculated due to the assumption that x(τ is a function of the roots s1, ..., sn of the characteristic equation.
Yang, Jianwen
2012-04-01
A general analytical solution is derived by using the Laplace transformation to describe transient reactive silica transport in a conceptualized 2-D system involving a set of parallel fractures embedded in an impermeable host rock matrix, taking into account of hydrodynamic dispersion and advection of silica transport along the fractures, molecular diffusion from each fracture to the intervening rock matrix, and dissolution of quartz. A special analytical solution is also developed by ignoring the longitudinal hydrodynamic dispersion term but remaining other conditions the same. The general and special solutions are in the form of a double infinite integral and a single infinite integral, respectively, and can be evaluated using Gauss-Legendre quadrature technique. A simple criterion is developed to determine under what conditions the general analytical solution can be approximated by the special analytical solution. It is proved analytically that the general solution always lags behind the special solution, unless a dimensionless parameter is less than a critical value. Several illustrative calculations are undertaken to demonstrate the effect of fracture spacing, fracture aperture and fluid flow rate on silica transport. The analytical solutions developed here can serve as a benchmark to validate numerical models that simulate reactive mass transport in fractured porous media.
A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries
Institute of Scientific and Technical Information of China (English)
Yuxi Zheng
2003-01-01
We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.
GLOBAL BEHAVIOR OF POSITIVE SOLUTIONS TO A KIND OF THREE-POINT BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, using the fixed-point index theorems and the cone theory we study the structure of the positive solutions to a kind of second-order three-point boundary value problems. We obtain the result which guarantee that the positive solution set of the three-point boundary value problem has a continuum, which means that there exists a nonempty, closed and connected subset.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper,authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order.They first give the well posedness of general discontinuous boundary value problems,reduce the discontinuousboundary value problems to a variation problem,and then find the numerical solutions ofabove problem by the finite element method.Finally authors give some error-estimates of the foregoing numerical solutions.
Analytical solutions of the electrostatically actuated curled beam problem
Younis, Mohammad I.
2014-07-24
This works presents analytical expressions of the electrostatically actuated initially deformed cantilever beam problem. The formulation is based on the continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximation. In such cases, multi-mode reduced order models are shown to yield accurate results. © 2014 Springer-Verlag Berlin Heidelberg.
Institute of Scientific and Technical Information of China (English)
TsuiChih－Ya
1992-01-01
A set of new gasdynamic functions with varying specific heat are deriveo for the first time.An original analytical solution of normal shock waves is owrked out therewith.This solution is thereafter further improved by not involving total temperature,Illustrative examples of comparison are given,including also some approximate solutions to show the orders of their errors.
Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads
Institute of Scientific and Technical Information of China (English)
陈江英; 丁皓江; 侯鹏飞
2003-01-01
In this paper, the axisymmetric general solutions of transversely isotropic magnetoelectroelastic media are expressed with four harmonic displacement functions at first. Then, based on the solutions, the analytical three-dimensional solutions are provided for a simply supported magnetoelectroelastic circular plate subjected to uniform loads. Finally, the example of circular plate is presented.
Verhoest, N.E.C.; Pauwels, V.R.N.; Troch, P.A.; Troch, De F.P.
2002-01-01
This paper presents two analytical solutions of the linearized Boussinesq equation for an inclined aquifer, drained by ditches, subjected to a constant recharge rate. These solutions are based on different initial conditions. First, the transient solution is obtained for an initially fully saturated
Analytical solution for electromagnetic scattering from a sphere of uniaxial left-handed material
Institute of Scientific and Technical Information of China (English)
GENG You-lin; HE Sai-ling
2006-01-01
Based on the analytical solution of electromagnetic scattering by a uniaxial anisotropic sphere in the spectral domain,an analytical solution to the electromagnetic scattering by a uniaxial left-handed materials (LHMs) sphere is obtained in terms of spherical vector wave functions in a uniaxial anisotropic LHM medium. The expression of the analytical solution contains only some one-dimensional integral which can be calculated easily. Numerical results show that Mie series of plane wave scattering by an isotropic LHM sphere is a special case of the present method. Some numerical results of electromagnetic scattering ofa uniaxial anisotropic sphere by a plane wave are given.
Global existence and blowup of solutions to a free boundary problem for mutualistic model
Institute of Scientific and Technical Information of China (English)
KIM; KwangIk
2010-01-01
This article is concerned with a system of semilinear parabolic equations with a free boundary,which arises in a mutualistic ecological model.The local existence and uniqueness of a classical solution are obtained.The asymptotic behavior of the free boundary problem is studied.Our results show that the free problem admits a global slow solution if the inter-specific competitions are strong,while if the inter-specific competitions are weak there exist the blowup solution and global fast solution.
Directory of Open Access Journals (Sweden)
Mohammad Zamani Nejad
2014-01-01
Full Text Available Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT. These equations are in the form of a set of general differential equations. Given that the cylinder is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM is also presented and good agreement was found.
Institute of Scientific and Technical Information of China (English)
马西奎; 韩社教
2002-01-01
Based on the multipole expansion theory of the potential, a satisfactory interpretation is put forward of the exact nature of the approximations of asymptotic boundary condition (called the ABC) techniques for the numerical solutions of open-boundary static electromagnetic-field problems, and a definite physical meaning is bestowed on ABC, which provide a powerful theoretical background for laying down the operating rules and the key to the derivation of asymptotic boundary conditions. This paper is also intended to reveal the shortcomings of the conventional higher-order ABC, and at the same time to give the concept of a new type of higher-order ABC, and to present a somewhat different formulation of the new nth-order ABC. In order to test its feasibility, several simple problems of electrostatic potentials are analyzed. The results are found to be much better than those of conventional higher-order ABCs.
Directory of Open Access Journals (Sweden)
Nelly S. Khapilova
2015-10-01
Full Text Available We present the analytical solution of the axisymmetric mixed problem for the isotropic half-space with the surface fixed elastically outside the circular area of the application of a distributed load. In the solution of the problem, the transition procedure from a distributed load to the concentrated force has been justified. A compact form of the exact analytical solution of the problem on the concentrated force applied to the half-space with the surface fixed elastically was obtained. In the specific case when the proportionality factor of normal stresses and displacements vanishing under the condition of the elastic fixing of the boundary, the constructed analytical solution was shown to coincide with the well-known Boussinesq formulae.
Palaniappan, D.
2009-04-01
An exact solution for a magnetostatic boundary value problem involving two fused (overlapping) spheres placed in a field generated by an axial magnetic point dipole is constructed based on the image method. The basic idea is illustrated for two unequal superconducting spheres intersecting with a vertex angle π /2 and the analytical solution for the scalar magnetic potential satisfying the Neumann boundary condition at the surface is derived. The image solution for a dipole-twin-sphere configuration consists of three image dipoles—one inside each sphere and the third inside a pseudo-/virtual sphere—all located at the respective inverse points inside the superconducting two-sphere assembly. The levitation force acting on the two-sphere superconducting surface is also calculated for the overlapping geometry. These exact results can be used as a benchmark for testing numerical algorithms for overlapping spherical superconductors. Our simple approach also offers clues for solving the Neumann boundary value problem for vertex angles π /n, n is an integer, and other related superconducting geometries.
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
Directory of Open Access Journals (Sweden)
Asterios Pantokratoras
2008-01-01
Full Text Available Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of 0∘C≤≤8∘C, where water density is nearly parabolic. Except for their use as benchmarking means for testing the numerical solution of the Navier-Stokes equations, the presented exact solutions with EMHD forces have use in flow separation control in aeronautics and hydronautics, whereas the MHD results have applications in process metallurgy and fusion technology. These analytical solutions are valid for flows with strong suction.
Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach
Directory of Open Access Journals (Sweden)
Panos K. Palamides
2012-01-01
Full Text Available We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness of the solutions funnel (Kneser's Theorem, combined with the corresponding vector field.
Three dimensional boundary element solutions for eddy current nondestructive evaluation
Yang, Ming; Song, Jiming; Nakagawa, Norio
2014-02-01
The boundary integral equations (BIE) method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations. It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture mechanics. The eddy current problem is formulated by the BIE and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The three dimensional arbitrarily shaped objects are described by a number of triangular patches. The Stratton-Chu formulation is specialized for the conductive medium. The equivalent electric and magnetic surface currents are expanded in terms of Rao-Wilton-Glisson (RWG) vector basis function while the normal component of magnetic field is expanded in terms of the pulse basis function. Also, a low frequency approximation is applied in the external medium. Additionally, we introduce Auld's impedance formulas to calculate impedance variation. There are very good agreements between numerical results and those from theory and/or experiments for a finite cross-section above a wedge.
Singular boundary method using time-dependent fundamental solution for scalar wave equations
Chen, Wen; Li, Junpu; Fu, Zhuojia
2016-11-01
This study makes the first attempt to extend the meshless boundary-discretization singular boundary method (SBM) with time-dependent fundamental solution to two-dimensional and three-dimensional scalar wave equation upon Dirichlet boundary condition. The two empirical formulas are also proposed to determine the source intensity factors. In 2D problems, the fundamental solution integrating along with time is applied. In 3D problems, a time-successive evaluation approach without complicated mathematical transform is proposed. Numerical investigations show that the present SBM methodology produces the accurate results for 2D and 3D time-dependent wave problems with varied velocities c and wave numbers k.
Zhu, C
2003-01-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
Energy Technology Data Exchange (ETDEWEB)
Zhu, Changjiang; Duan, Renjun [Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People' s Republic of China (China)
2003-02-28
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Directory of Open Access Journals (Sweden)
Mohammed Guedda
2007-05-01
Full Text Available This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point. In particular, we shall examine in detail the behavior of $f$ near the blow-up point.
Unbounded Periodic Solutions to Serrin's Overdetermined Boundary Value Problem
Fall, Mouhamed Moustapha; Minlend, Ignace Aristide; Weth, Tobias
2017-02-01
We study the existence of nontrivial unbounded domains {Ω} in RN such that the overdetermined problem {-Δ u = 1 quad in Ω}, quad u = 0, quad partial_{ν} u = const quad on partial Ω admits a solution u. By this, we complement Serrin's classification result from 1971, which yields that every bounded domain admitting a solution of the above problem is a ball in RN. The domains we construct are periodic in some variables and radial in the other variables, and they bifurcate from a straight (generalized) cylinder or slab. We also show that these domains are uniquely self Cheeger relative to a period cell for the problem.
General Analytical Solutions of Scalar Field Cosmology with Arbitrary Potential
Dimakis, N; Zampeli, Adamantia; Paliathanasis, Andronikos; Christodoulakis, T; Terzis, Petros A
2016-01-01
We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. The case for both spatially flat and non flat are studied first in the presence of only the scalar field and subsequently with the addition of non interacting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature.
Institute of Scientific and Technical Information of China (English)
Jing ZHU; Lian-cun ZHENG; Xin-xin ZHANG
2009-01-01
This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method(HAM).It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters.
A Quantum Dot with Spin-Orbit Interaction--Analytical Solution
Basu, B.; Roy, B.
2009-01-01
The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.
The analyticity of solutions to a class of degenerate elliptic equations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In the present paper,the analyticity of solutions to a class of degenerate elliptic equations is obtained.A kind of weighted norms are introduced and under such norms some degenerate elliptic operators are of weak coerciveness.
Institute of Scientific and Technical Information of China (English)
侯进军
2007-01-01
@@ 1 Seed Selection Genetic Programming In Genetic Programming, each tree in population shows an algebraic or surmounting expression, and each algebraic or surmounting expression shows an approximate analytic solution to differential equations.
Approximation analytical solutions for a unified plasma sheath model by double decomposition method
Institute of Scientific and Technical Information of China (English)
FangJin－Qing
1998-01-01
A unified plasma sheath model and its potential equation are proposed.Any higher-order approximation analytical solutions for the unified plasma sheath potential equation are derived by double decomposition method.
Analytical solutions for transport processes fluid mechanics, heat and mass transfer
Brenn, Günter
2017-01-01
This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field. .
Directory of Open Access Journals (Sweden)
Partner L. Ndlovu
2013-01-01
Full Text Available Explicit analytical expressions for the temperature profile, fin efficiency, and heat flux in a longitudinal fin are derived. Here, thermal conductivity and heat transfer coefficient depend on the temperature. The differential transform method (DTM is employed to construct the analytical (series solutions. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other, whereas heat transfer coefficient is only given by the power law. The analytical solutions constructed by the DTM agree very well with the exact solutions even when both the thermal conductivity and the heat transfer coefficient are given by the power law. The analytical solutions are obtained for the problems which cannot be solved exactly. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated and explained.
Application of Analytic Solution in Relative Motion to Spacecraft Formation Flying in Elliptic Orbit
Cho, Hancheol; Park, Sang-Young; Choi, Kyu-Hong
2008-09-01
The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.
RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Reinhard Hochmuth
2002-01-01
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0＜σ＜∞ and (1+σ)-1＜τ＜∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
Analytic method for solitary solutions of some partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya@firat.edu.tr
2007-10-22
In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation.
General scalar-tensor cosmology: analytical solutions via noether symmetry
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza
2017-02-01
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system.
Sun, Tao; Morgan, Hywel; Green, Nicolas G.
2007-10-01
Analysis of the movement of particles in a nonuniform field requires accurate knowledge of the electric field distribution in the system. This paper describes a method for analytically solving the electric field distribution above interdigitated electrode arrays used for dielectrophoresis (DEP) and traveling wave dielectrophoresis (twDEP), using the Schwarz-Christoffel mapping method. The electric field solutions are used to calculate the dielectrophoretic force in both cases, and the traveling wave dielectrophoretic force and the electrorotational torque for the twDEP case. This method requires no approximations and can take into account the Neumann boundary condition used to represent an insulating lid and lower substrate. The analytical results of the electric field distributions are validated for different geometries by comparison with numerical simulations using the finite element method.
An Analytical Solution for Acoustic Emission Source Location for Known P Wave Velocity System
Directory of Open Access Journals (Sweden)
Longjun Dong
2014-01-01
Full Text Available This paper presents a three-dimensional analytical solution for acoustic emission source location using time difference of arrival (TDOA measurements from N receivers, N⩾5. The nonlinear location equations for TDOA are simplified to linear equations, and the direct analytical solution is obtained by solving the linear equations. There are not calculations of square roots in solution equations. The method solved the problems of the existence and multiplicity of solutions induced by the calculations of square roots in existed close-form methods. Simulations are included to study the algorithms' performance and compare with the existing technique.
Analytical solution based on stream-aquifer interactions in partially penetrating streams
Institute of Scientific and Technical Information of China (English)
Yong HUANG; Zhi-fang ZHOU; Zhong-bo YU
2010-01-01
An analytical solution of drawdown caused by pumping was developed for an aquifer partially penetrated by two streams.The proposed analytical solution modifies Hunt's analytical solution and considers the effects of stream width and the interaction of two streams on drawdown.Advantages of the solution include its simple structure,consisting of the Theis well function and parameters of aquifer and streambed semipervious material.The calculated results show that the proposed analytical solution agrees with a previously developed acceptable solution and the errors between the two solutions are equal to zero without consideration of the effect of stream width.Also,deviations between the two analytical solutions incrcase with stream width.Four cases were studied to examine the effect of two streams on drawdown,assuming that some parameters were changeable,and other parameters were constant,such as the stream width,the distance between the stream and the pumping well,the stream recharge rate,and the leakage coefficient of streambed semipervious material.
Analytic study of solutions for the Born-Infeld equation in nonlinear electrodynamics
Gao, Hui; Xu, Tianzhou; Fan, Tianyou; Wang, Gangwei
2017-03-01
The Born-Infeld equation is an important nonlinear partial differential equation in theoretical and mathematical physics. The Lie group method is used for simplifying the nonlinear partial differential equation, which is partly solved, in which there are some difficulties; to overcome the difficulties, we develop a power series method, and find the solutions in analytic form. In the mean time, a wave propagation (traveling wave) method is developed for solving the equation, and analytic solutions are also constructed.
Analytical solutions for the slow neutron capture process of heavy element nucleosynthesis
Institute of Scientific and Technical Information of China (English)
Wu Kai-Su
2009-01-01
In this paper,the network equation for the slow neutron capture process (s-process) of heavy element nucleosynthesis is investigated. Dividing the s-process network reaction chains into two standard forms and using the technique of matrix decomposition,a group of analytical solutions for the network equation are obtained. With the analytical solutions,a calculation for heavy element abundance of the solar system is carried out and the results are in good agreement with the astrophysical measurements.
An analytical solution in the complex plane for the luminosity distance in flat cosmology
Zaninetti, L
2016-01-01
We present an analytical solution for the luminosity distance in spatially flat cosmology with pressureless matter and the cosmological constant. The complex analytical solution is made of a real part and a negligible imaginary part. The real part of the luminosity distance allows finding the two parameters $H_0$ and $\\om$. A simple expression for the distance modulus for SNs of type Ia is reported in the framework of the minimax approximation.
Solution of the quantum initial value problem with transparent boundary conditions
Puga, A.; Miller, B. N.
2013-01-01
Many systems of interest at the forefront of technological development, for example, in quantum computation, consist of weakly interacting elements that obey quantum mechanics. A challenge for modern theoretical physics is to develop a systematic methodology for approaching these "open" quantum systems. In particular, applied mathematicians have formulated the method of transparent boundary conditions (TBCs) to model interacting quantum systems of infinite extent. Here, we consider a particular application of TBCs to the escape of a particle from a one-dimensional infinite well when one of the bounding barriers is extinguished. We analytically obtain the exact time-dependent wave function by a Green's function method and then show that a numerical solution based on the TBC method is in excellent agreement. This work was motivated by an experiment carried out at the University of Texas on escape from a gravitational wedge billiard. Physicists have used billiards to understand and explore both classical and quantum chaos. Although the original experiment was carried out in the classical regime, current work is probing lower temperatures, where a quantum mechanical formulation is required.
Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations
Kudryashov, N. A.
2015-01-01
The method of the logistic function is presented for finding exact solutions of nonlinear differential equations. The application of the method is illustrated by using the nonlinear ordinary differential equation of the fourth order. Analytical solutions obtained by this method are presented. These solutions are expressed via exponential functions.logistic function, nonlinear wave, nonlinear ordinary differential equation, Painlev´e test, exact solution
An analytic solution to LO coupled DGLAP evolution equations: a new pQCD tool
Block, Martin M; Ha, Phuoc; McKay, Douglas W
2010-01-01
We have analytically solved the LO pQCD singlet DGLAP equations using Laplace transform techniques. Newly-developed highly accurate numerical inverse Laplace transform algorithms allow us to write fully decoupled solutions for the singlet structure function F_s(x,Q^2)and G(x,Q^2) as F_s(x,Q^2)={\\cal F}_s(F_{s0}(x), G_0(x)) and G(x,Q^2)={\\cal G}(F_{s0}(x), G_0(x)). Here {\\cal F}_s and \\cal G are known functions of the initial boundary conditions F_{s0}(x) = F_s(x,Q_0^2) and G_{0}(x) = G(x,Q_0^2), i.e., the chosen starting functions at the virtuality Q_0^2. For both G and F_s, we are able to either devolve or evolve each separately and rapidly, with very high numerical accuracy, a computational fractional precision of O(10^{-9}). Armed with this powerful new tool in the pQCD arsenal, we compare our numerical results from the above equations with the published MSTW2008 and CTEQ6L LO gluon and singlet F_s distributions, starting from their initial values at Q_0^2=1 GeV^2 and 1.69 GeV^2, respectively, using their ...
Analytic Solutions of Three-Level Dressed-Atom Model
Institute of Scientific and Technical Information of China (English)
WANG Zheng-Ling; YIN Jian-Ping
2004-01-01
On the basis of the dressed-atom model, the general analytic expressions for the eigenenergies, eigenstates and their optical potentials of the A-configuration three-level atom system are derived and analysed. From the calculation of dipole matrix element of different dressed states, we obtain the spontaneous-emission rates in the dressed-atom picture. We find that our general expressions of optical potentials for the three-level dressed atom can be reduced to the same as ones in previous references under the approximation of a small saturation parameter. We also analyse the dependences of the optical potentials of a three-level 85Rb atom on the laser detuning and the dependences of spontaneous-emission rates on the radial position in the dark hollow beam, and discuss the probability (population) evolutions of dressed-atomic eigenstates in three levels in the hollow beam.
Methods for estimating uncertainty in factor analytic solutions
Directory of Open Access Journals (Sweden)
P. Paatero
2013-08-01
Full Text Available EPA PMF version 5.0 and the underlying multilinear engine executable ME-2 contain three methods for estimating uncertainty in factor analytic models: classical bootstrap (BS, displacement of factor elements (DISP, and bootstrap enhanced by displacement of factor elements (BS-DISP. The goal of these methods is to capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. It is shown that the three methods complement each other: depending on characteristics of the data set, one method may provide better results than the other two. Results are presented using synthetic data sets, including interpretation of diagnostics, and recommendations are given for parameters to report when documenting uncertainty estimates from EPA PMF or ME-2 applications.
Analytical solutions for space charge fields in TPC drift volumes
Rossegger, S; Schnizer, B
2011-01-01
At high particle rates and high multiplicities, Time Projection Chambers can suffer from field distortions due to slow moving ions that accumulate within the drift volume. These variations modify the electron trajectory along the drift path, affecting the tracking performance of the detector. In order to calculate the track distortions due to an arbitrary space charge distribution in a TPC, novel representations of the Green's function for a TPC-like geometry were worked out. This analytical approach permits accurate predictions of track distortions due to an arbitrary space charge distribution (by solving the Langevin equation) as well as the possibility to benchmark common numerical methods to calculate such space charge fields. (C) 2011 Elsevier B.V. All rights reserved.
EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.
EXISTENCE THEOREM ABOUT MULTIPLE POSITIVE SOLUTIONS TO p-LAPLACIAN BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,we apply a fixed point theorem to verify the existence of multiple positive solutions to a p-Laplacian boundary value problem.Sufficient conditions are established which guarantee the existence of multiple positive solutions to the problem.
EXISTENCE OF SOLUTIONS TO 2m-ORDER PERIODIC BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions.
On the Existence of Positive Solutions ofSingular Second Order BoundaryValue Problems
Institute of Scientific and Technical Information of China (English)
LIHe-cheng
2004-01-01
This paper deals with the existence of positive solutions of the equation u"+f(t,u)=0 with linear boundary conditions. We show the existence of at least onepositive solution if f is neither superlinear nor sublinear on u by a simple application of afixed point Theorem in cones.
Directory of Open Access Journals (Sweden)
Jiqiang Jiang
2012-01-01
Full Text Available We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper,we study the existence and approximation of solution to boundary value problems for impulsive differential equations with delayed arguments.Sufficient conditions are established for the existence of a unique solution or extremal ones to the given problem.A monotone iterative technique is applied.
Institute of Scientific and Technical Information of China (English)
徐西安
2004-01-01
In this paper, we first obtain some New results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.
The Method of Subsuper Solutions for Weighted p(r-Laplacian Equation Boundary Value Problems
Directory of Open Access Journals (Sweden)
Zhimei Qiu
2008-10-01
Full Text Available This paper investigates the existence of solutions for weighted p(r-Laplacian ordinary boundary value problems. Our method is based on Leray-Schauder degree. As an application, we give the existence of weak solutions for p(x-Laplacian partial differential equations.
Institute of Scientific and Technical Information of China (English)
Shanying Zhu
2009-01-01
This paper deals with the existence of positive solutions to the singular second-order periodic boundary value problem, We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.
Symbolic Iterative Solution of Boundary Value Problems for Partial Differential Equations
Semiyari, Hamid
2016-01-01
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is easy to implement, computationally efficient, and it is highly accurate. The output of the method is a function that approximates the exact solution.
Analytical solution for wave-induced response of isotropic poro-elastic seabed
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
By use of separation of variables,the governing equations describing the Biot consolidation model is firstly transformed into a complex coefficient linear homogeneous ordinary differential equation,and the general solution of the horizontal displacement of seabed is constructed by employing a complex wave number,thus,all the explicit analytical solutions of the Biot consolidation model are determined. By comparing with the experimental results and analytical solution of Yamamoto etc. and the analytical solution of Hsu and Jeng,the validity and superiority of the suggested solution are verified. After investigating the influence of seabed depth on the wave-induced response of isotropic poro-elastic seabed based on the present theory,it can be concluded that the influence depth of wave-induced hydrodynamic pressure in the seabed is equal to the wave length.
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares
2015-07-01
This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)
Directory of Open Access Journals (Sweden)
Paulo Rangel Rios
2009-06-01
Full Text Available Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA. In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.
On the Poynting-Robertson Effect and Analytical Solutions
Klacka, J
2000-01-01
Solutions of the two-body problem with the simultaneous action of the solar electromagnetic radiation in the form of the Poynting-Robertson effect are discussed. Special attention is devoted to pseudo-circular orbits and terminal values of osculating elements. The obtained results complete those of Klacka and Kaufmannova (1992) and Breiter and Jackson (1998). Terminal values of osculating elements presented in Breiter and Jackson (1998) are of no physical sense due to the fact that relativistic equation of motion containing only first order of $\\vec{v}/c$ was used in the paper.
Directory of Open Access Journals (Sweden)
A. Malvandi
2014-01-01
Full Text Available Steady two-dimensional boundary layer flow of a nanofluid past a nonlinear stretching sheet is investigated analytically using the Homotopy Analysis Method (HAM. The employed model for nanofluid includes twocomponent four-equation non-homogeneous equilibrium model that incorporates the effects of Brownian motion ( Nb , thermophoresis ( Nt and Lewis number ( Le simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via the similarity variables. Analytical results are in best agreements with those existing in the literatures. The outcomes signify the decreasing trend of heat transfer rate with thermophoresis, Brownian motion and Lewis number. However, concentration rate has a sensitive behavior with parameters, especially the Brownian motion and thermophoresis parameters. Also, the weak points of numerical methods in such problems have been mentioned and the efficiency of HAM, as an alternative approach, in solving these kinds of nonlinear coupled problems has been shown.
Valent, Tullio
1988-01-01
In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be sides being quite spontaneous, allows us to consider a great many inter esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...
Analytic solutions for degenerate Raman-coupled model
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Ming; Yu Ya-Fei
2008-01-01
The Raman-coupled interaction between an atom and a single mode of a cavity field is studied. For the cases in which a light field is initially in a coherent state and in a thermal state separately, we have derived the analytic expressions for the time evolutions of atomic population difference W, modulus B of the Bloch vector, and entropy E. We find that the time evolutions of these quantities are periodic with a period of e. The maxima of W and B appear at the scaled interaction time points (τ) = κπ(κ =0, 1, 2,...). At these time points, E = 0, which shows that the atom and the field are not entangled. Between these time points, E ≠ 0, which means that the atom and the field are entangled. When the field is initially in a coherent state, near the maxima, the envelope of W is a Gaussian function with a variance of 1/(4(-n)) ((-n) is the mean number of photons). Under the envelope, W oscillates at a frequency of (-n)/e.When the field is initially in a thermal state, near the maxima, W is a Lorentz function with a width of 1/(-n).
Approximate analytical solutions for excitation and propagation in cardiac tissue
Greene, D'Artagnan; Shiferaw, Yohannes
2015-04-01
It is well known that a variety of cardiac arrhythmias are initiated by a focal excitation in heart tissue. At the single cell level these currents are typically induced by intracellular processes such as spontaneous calcium release (SCR). However, it is not understood how the size and morphology of these focal excitations are related to the electrophysiological properties of cardiac cells. In this paper a detailed physiologically based ionic model is analyzed by projecting the excitation dynamics to a reduced one-dimensional parameter space. Based on this analysis we show that the inward current required for an excitation to occur is largely dictated by the voltage dependence of the inward rectifier potassium current (IK 1) , and is insensitive to the detailed properties of the sodium current. We derive an analytical expression relating the size of a stimulus and the critical current required to induce a propagating action potential (AP), and argue that this relationship determines the necessary number of cells that must undergo SCR in order to induce ectopic activity in cardiac tissue. Finally, we show that, once a focal excitation begins to propagate, its propagation characteristics, such as the conduction velocity and the critical radius for propagation, are largely determined by the sodium and gap junction currents with a substantially lesser effect due to repolarizing potassium currents. These results reveal the relationship between ion channel properties and important tissue scale processes such as excitation and propagation.
Analysing an Analytical Solution Model for Simultaneous Mobility
Directory of Open Access Journals (Sweden)
Md. Ibrahim Chowdhury
2013-12-01
Full Text Available Current mobility models for simultaneous mobility h ave their convolution in designing simultaneous movement where mobile nodes (MNs travel randomly f rom the two adjacent cells at the same time and also have their complexity in the measurement of th e occurrences of simultaneous handover. Simultaneou s mobility problem incurs when two of the MNs start h andover approximately at the same time. As Simultaneous mobility is different for the other mo bility pattern, generally occurs less number of tim es in real time; we analyze that a simplified simultaneou s mobility model can be considered by taking only symmetric positions of MNs with random steps. In ad dition to that, we simulated the model using mSCTP and compare the simulation results in different sce narios with customized cell ranges. The analytical results shows that with the bigger the cell sizes, simultaneous handover with random steps occurrences become lees and for the sequential mobility (where initial positions of MNs is predetermined with ran dom steps, simultaneous handover is more frequent.
An Analytical Solution for Cylindrical Concrete Tank on Deformable Soil
Directory of Open Access Journals (Sweden)
Shirish Vichare
2010-07-01
Full Text Available Cylindrical concrete tanks are commonly used in wastewater treatment plants. These are usually clarifier tanks. Design codes of practice provide methods to calculate design forces in the wall and raft of such tanks. These methods neglect self-weight of tank material and assume extreme, namely ‘fixed’ and ‘hinged’ conditions for the wall bottom. However, when founded on deformable soil, the actual condition at the wall bottom is neither fixed nor hinged. Further, the self-weight of the tank wall does affect the design forces. Thus, it is required to offer better insight of the combined effect of deformable soil and bottom raft stiffness on the design forces induced in such cylindrical concrete tanks. A systematic analytical method based on fundamental equations of shells is presented in this paper. Important observations on variation of design forces across the wall and the raft with different soil conditions are given. Set of commonly used tanks, are analysed using equations developed in the paper and are appended at the end.
Institute of Scientific and Technical Information of China (English)
Hong Xia; LIU Tao PAN
2007-01-01
This paper is concerned with an initial boundary value problem for strictly convex conser-vation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial valuemethod to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includesthe following new interaction type: an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the invis-cidsolution is bounded by O (1/2)in1-norm; otherwise, as in the initial value problem, the L1-error bound is O ( | ln ε | ).
General Scalar-Tensor cosmology: Analytical solutions via Noether symmetry
Masaeli, Erfan; Sepangi, Hamid Reza
2016-01-01
We analyze the cosmology of a general Scalar-Tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galileon gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which dynamics of the system allow transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the mo...
Analytic crack solutions for tilt fields around hydraulic fractures
Energy Technology Data Exchange (ETDEWEB)
Warpinski, N.R.
2000-01-05
The recent development of downhole tiltmeter arrays for monitoring hydraulic fractures has provided new information on fracture growth and geometry. These downhole arrays offer the significant advantages of being close to the fracture (large signal) and being unaffected by the free surface. As with surface tiltmeter data, analysis of these measurements requires the inversion of a crack or dislocation model. To supplement the dislocation models of Davis [1983], Okada [1992] and others, this work has extended several elastic crack solutions to provide tilt calculations. The solutions include constant-pressure 2D, penny-shaped, and 3D-elliptic cracks and a 2D-variable-pressure crack. Equations are developed for an arbitrary inclined fracture in an infinite elastic space. Effects of fracture height, fracture length, fracture dip, fracture azimuth, fracture width and monitoring distance on the tilt distribution are given, as well as comparisons with the dislocation model. The results show that the tilt measurements are very sensitive to the fracture dimensions, but also that it is difficult to separate the competing effects of the various parameters.
Super stellar clusters with a bimodal hydrodynamic solution: an Approximate Analytic Approach
Wünsch, R; Palous, J; Tenorio-Tagle, G
2007-01-01
We look for a simple analytic model to distinguish between stellar clusters undergoing a bimodal hydrodynamic solution from those able to drive only a stationary wind. Clusters in the bimodal regime undergo strong radiative cooling within their densest inner regions, which results in the accumulation of the matter injected by supernovae and stellar winds and eventually in the formation of further stellar generations, while their outer regions sustain a stationary wind. The analytic formulae are derived from the basic hydrodynamic equations. Our main assumption, that the density at the star cluster surface scales almost linearly with that at the stagnation radius, is based on results from semi-analytic and full numerical calculations. The analytic formulation allows for the determination of the threshold mechanical luminosity that separates clusters evolving in either of the two solutions. It is possible to fix the stagnation radius by simple analytic expressions and thus to determine the fractions of the depo...
Numerical solution of an edge flame boundary value problem
Shields, Benjamin; Freund, Jonathan; Pantano, Carlos
2016-11-01
We study edge flames for modeling extinction, reignition, and flame lifting in turbulent non-premixed combustion. An adaptive resolution finite element method is developed for solving a strained laminar edge flame in the intrinsic moving frame of reference of a spatially evolving shear layer. The variable-density zero Mach Navier-Stokes equations are used to solve for both advancing and retreating edge flames. The eigenvalues of the system are determined simultaneously (implicitly) with the scalar fields using a Schur complement strategy. A homotopy transformation over density is used to transition from constant- to variable-density, and pseudo arc-length continuation is used for parametric tracing of solutions. Full details of the edge flames as a function of strain and Lewis numbers will be discussed. This material is based upon work supported [in part] by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.
Existence of solutions for critical elliptic systems with boundary singularities
Directory of Open Access Journals (Sweden)
Jianfu Yang
2013-04-01
Full Text Available This article concerns the existence of positive solutions to the nonlinear elliptic system involving critical Hardy-Sobolev exponent $$displaylines{ -Delta u= frac{2lambdaalpha}{alpha+eta} frac{u^{alpha-1} v^eta}{|pi(x|^s}- u^p, quad hbox{in } Omega,cr -Delta v= frac{2lambdaeta}{alpha+eta} frac{u^alpha v^{eta-1}}{|pi(x|^s}- v^p, quad hbox{in } Omega,cr u>0,quad v>0, quad hbox{in } Omega,cr u=v=0, quad hbox{on } partialOmega, }$$ where $Ngeq 4$ and $Omega$ is a $C^1$ bounded domain in $mathbb{R}^N$, $01$, $lambda>0$ and $1leq p
Institute of Scientific and Technical Information of China (English)
ZHOU Xiao-ping; LING Tong-hua
2006-01-01
The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.
Cutting solid figures by plane - analytical solution and spreadsheet implementation
Benacka, Jan
2012-07-01
In some secondary mathematics curricula, there is a topic called Stereometry that deals with investigating the position and finding the intersection, angle, and distance of lines and planes defined within a prism or pyramid. Coordinate system is not used. The metric tasks are solved using Pythagoras' theorem, trigonometric functions, and sine and cosine rules. The basic problem is to find the section of the figure by a plane that is defined by three points related to the figure. In this article, a formula is derived that gives the positions of the intersection points of such a plane and the figure edges, that is, the vertices of the section polygon. Spreadsheet implementations of the formula for cuboid and right rectangular pyramids are presented. The user can check his/her graphical solution, or proceed if he/she is not able to complete the section.
Nonlinear Helicons ---an analytical solution elucidating multi-scale structure
Abdelhamid, Hamdi M
2016-01-01
The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here we elucidate an intrinsic multi-scale property embodied by the combination of dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.
Some analytical properties of solutions of differential equations of noninteger order
Directory of Open Access Journals (Sweden)
S. M. Momani
2004-01-01
Full Text Available The analytical properties of solutions of the nonlinear differential equations x(α(t=f(t,x, α∈ℝ, 0<α≤1 of noninteger order have been investigated. We obtained two results concerning the frame curves of solutions. Moreover, we proved a result on differential inequality with fractional derivatives.
Analytical solutions for spin response functions in model storage rings with Siberian Snakes
Energy Technology Data Exchange (ETDEWEB)
Mane, S.R. [Convergent Computing Inc., P.O. Box 561, Shoreham, NY 11786 (United States)], E-mail: srmane@optonline.net
2009-03-01
I present analytical solutions for the spin response functions for radial field rf dipole spin flippers in models of storage rings with one Siberian Snake or two diametrically opposed orthogonal Siberian Snakes. The solutions can serve as benchmarks tests for computer programs. The spin response functions can be used to calculate the resonance strengths for radial field rf dipole spin flippers in storage rings.
Plasma flow structures as analytical solution of a magneto-hydro-dynamic model with pressure
Paccagnella, R.
2012-03-01
In this work starting from a set of magnetohydrodynamic (MHD) equations that describe the dynamical evolution for the pressure driven resistive/interchange modes in a magnetic confinement system, global solutions for the plasma flow relevant for toroidal pinches like tokamaks and reversed field pinches (RFPs) are derived. Analytical solutions for the flow stream function associated with the dominant modes are presented.
Institute of Scientific and Technical Information of China (English)
Li Ta-tsien(李大潜); Peng Yue-Jun
2003-01-01
Abstract We prove that the C0 boundedness of solution impliesthe global existence and uniqueness of C1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C1 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.
Jin, Guoyong; Su, Zhu
2015-01-01
This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.
Analytical Structuring of Periodic and Regular Cascading Solutions in Self-Pulsing Lasers
Directory of Open Access Journals (Sweden)
Belkacem Meziane
2008-01-01
Full Text Available A newly proposed strong harmonic-expansion method is applied to the laser-Lorenz equations to analytically construct a few typical solutions, including the first few expansions of the well-known period-doubling cascade that characterizes the system in its self-pulsing regime of operation. These solutions are shown to evolve in accordance with the driving frequency of the permanent solution that we recently reported to illustrate the system. The procedure amounts to analytically construct the signal Fourier transform by applying an iterative algorithm that reconstitutes the first few terms of its development.
Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading
Institute of Scientific and Technical Information of China (English)
XIE Kang-he; QI Tian; DONG Ya-qin
2006-01-01
This paper presents an analytical solution for one-dimensional consolidation of soft soil under some common types of cyclic loading such as trapezoidal cyclic loading, based on the assumptions proposed by Davis and Raymond (1965) that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of the soil and that the distribution of initial effective stress is constant with depth. It is verified by the existing analytical solutions in special cases. Using the solution obtained, some diagrams are prepared and the relevant consolidation behavior is investigated.
Institute of Scientific and Technical Information of China (English)
CAI; Ruixian(蔡睿贤); ZHANG; Na(张娜)
2002-01-01
Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model an improved Darcy model describing the natural convection in porous media. Besides their important theoretical meaning (for example, to analyze the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions to promoting the develop ment of computational heat and mass transfer. For instance, we can use them to check the accuracy,convergence and effectiveness of various numerical computational methods and to improve numerical calculation skills such as differential schemes and grid generation ways.
Salama, Amgad
2013-09-01
In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.
Indian Academy of Sciences (India)
Ajay Manglik
2005-04-01
During the solidification of a lava lake heat is released convectively from the top surface as well as conductively into the country rock from the base, leading to non-uniform solidification. The upper solidified layer grows at a faster rate than the lower solidified layer. Similarly, solidification of magma intrusion within the crust is also non-uniform due to the presence of thermal gradient in the crust. Available analytical solution for solidification of a melt layer assumes only symmetric cooling about the centre of the layer. In the present work a moving boundary solution for thermal evolution and non-uniform solidification of a melt layer incorporating time-varying contact temperature conditions at both of its boundaries is developed. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in the time domain, and is validated with available analytical solutions for simple cases and a semi-analytical solution for the case involving temperature gradient in the country rock. This solution can be used to analyse solidification of lava lakes and magma intrusions experiencing time-dependent temperature variation at their contacts with the country rock.
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
2015-03-31
to the Helmholtz Equationin the Presence of Boundary Singularities Problems of time-harmonic wave propagation arise in important fields of study...to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable- coecient inhomogeneous Helmholtz equation in... Helmholtz Equationin the Presence of Boundary Singularities Report Title Problems of time-harmonic wave propagation arise in important fields of study
Institute of Scientific and Technical Information of China (English)
SU XIN-WEI
2011-01-01
This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects. The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in [B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems, 3(2009), 251258].
Rahmouni, Lyes; Cools, Kristof; Andriulli, Francesco P
2016-01-01
In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages in several real case scenarios. Unfortunately however, it is widely reported that the accuracy of standard BEM schemes is limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly discretized EEG forward problems, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several ...
Matching of analytical and numerical solutions for neutron stars of arbitrary rotation
Energy Technology Data Exchange (ETDEWEB)
Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)
2009-10-01
We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.
Directory of Open Access Journals (Sweden)
Soheil Salahshour
2015-02-01
Full Text Available In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville or a solution with increasing length of their support (Hukuhara difference. Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
Directory of Open Access Journals (Sweden)
Ilmārs Grants
2016-06-01
Full Text Available Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Grants, Ilmārs; Bojarevičs, Andris; Gerbeth, Gunter
2016-06-01
Powerful forces arise when a pulse of a magnetic field in the order of a few tesla diffuses into a conductor. Such pulses are used in electromagnetic forming, impact welding of dissimilar materials and grain refinement of solidifying alloys. Strong magnetic field pulses are generated by the discharge current of a capacitor bank. We consider analytically the penetration of such pulse into a conducting half-space. Besides the exact solution we obtain two simple self-similar approximate solutions for two sequential stages of the initial transient. Furthermore, a general solution is provided for the external field given as a power series of time. Each term of this solution represents a self-similar function for which we obtain an explicit expression. The validity range of various approximate analytical solutions is evaluated by comparison to the exact solution.
Institute of Scientific and Technical Information of China (English)
CAI; Ruixian; GOU; Chenhua
2006-01-01
This paper presents two algebraically explicit analytical solutions for the incompressible unsteady rotational flow of Oldroyd-B type in an annular pipe. The first solution is derived with the common method of separation of variables. The second one is deduced with the method of separation of variables with addition developed in recent years. The first analytical solution is of clear physical meaning and both of them are fairly simple and valuable for the newly developing computational fluid dynamics. They can be used as the benchmark solutions to verify the applicability of the existing numerical computational methods and to inspire new differencing schemes, grid generation ways, etc. Moreover, a steady solution for the generalized second grade rheologic fluid flow is also presented. The correctness of these solutions can be easily proven by substituting them into the original governing equation.
Solution matching for a three-point boundary-value problem on atime scale
Directory of Open Access Journals (Sweden)
Martin Eggensperger
2004-07-01
Full Text Available Let $mathbb{T}$ be a time scale such that $t_1, t_2, t_3 in mathbb{T}$. We show the existence of a unique solution for the three-point boundary value problem $$displaylines{ y^{DeltaDeltaDelta}(t = f(t, y(t, y^Delta(t, y^{DeltaDelta}(t, quad t in [t_1, t_3] cap mathbb{T},cr y(t_1 = y_1, quad y(t_2 = y_2, quad y(t_3 = y_3,. }$$ We do this by matching a solution to the first equation satisfying a two-point boundary conditions on $[t_1, t_2] cap mathbb{T}$ with a solution satisfying a two-point boundary conditions on $[t_2, t_3] cap mathbb{T}$.
A fully nonlinear iterative solution method for self-similar potential flows with a free boundary
Iafrati, Alessandro
2013-01-01
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied under the assumptions of an ideal and incompressible fluid with negligible gravity and surface tension effects. The approach is based on a pseudo time stepping procedure, which uses a boundary integral equation method for the solution of the Laplace problem governing the velocity potential at each iteration. In order to demonstrate the flexibility and the capabilities of the approach, several applications are presented: the classical wedge entry problem, which is also used for a validation of the approach, the block sliding along an inclined sea bed, the vertical water entry of a flat plate and the ditching of an inclined plate. The solution procedure is also applied to cases in which the body surface is either porous or perforated. Comparisons with numerical or experimental d...
Analytic solution of Riccati equations occurring in open-loop Nash multiplayer differential games
Directory of Open Access Journals (Sweden)
L. Jódar
1992-01-01
Full Text Available In this paper we present explicit analytic solutions of coupled Riccati matrix differential systems appearing in open-loop Nash games. Two different cases are considered. Firstly, by means of appropriate algebraic transformations the problem is decoupled so that an explicit solution of the problem is available. The second is based on the existence of a solution of a rectangular Riccati type algebraic matrix equation associated with the problem.
Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures.
Kominis, Y
2006-06-01
A phase space method is employed for the construction of analytical solitary wave solutions of the nonlinear Kronig-Penney model in a photonic structure. This class of solutions is obtained under quite generic conditions, while the method is applicable to a large variety of systems. The location of the solutions on the spectral band gap structure as well as on the low dimensional space of system's conserved quantities is studied, and robust solitary wave propagation is shown.
Kharin, Stanislav N.; Sarsengeldin, Merey M.; Nouri, Hassan
2016-08-01
On the base of the Holm model, we represent two phase spherical Stefan problem and its analytical solution, which can serve as a mathematical model for diverse thermo-physical phenomena in electrical contacts. Suggested solution is obtained from integral error function and its properties which are represented in the form of series whose coefficients have to be determined. Convergence of solution series is proved.
Abrupt PN junctions: Analytical solutions under equilibrium and non-equilibrium
Khorasani, Sina
2016-08-01
We present an explicit solution of carrier and field distributions in abrupt PN junctions under equilibrium. An accurate logarithmic numerical method is implemented and results are compared to the analytical solutions. Analysis of results shows reasonable agreement with numerical solution as well as the depletion layer approximation. We discuss extensions to the asymmetric junctions. Approximate relations for differential capacitance C-V and current-voltage I-V characteristics are also found under non-zero external bias.
Analytical Solution for the SU(2)Hedgehog Skyrmion and Static Properties of Nucleons
Institute of Scientific and Technical Information of China (English)
JIA Duo-Jie; WANG Xiao-Wei; LIU Feng
2010-01-01
@@ An analytical solution for symmetric Skyrmion is proposed for the SU(2)Skyrme model,which takes the form of the hybrid form of a kink-like solution,given by the instanton method.The static properties of nucleons is then computed within the framework of collective quantization of the Skyrme model,in a good agreement with that given by the exact numeric solution.The comparisons with the previous results as well as the experimental values are also presented.
An analytical dynamo solution for large-scale magnetic fields of galaxies
Chamandy, Luke
2016-01-01
We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parameterized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the `no-$z$' approximation and the dynamical $\\alpha$-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted onto galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure (RM) datasets. Further, we explore the properties of our numerical solut...
High-Order Accurate Solutions to the Helmholtz Equation in the Presence of Boundary Singularities
Britt, Darrell Steven, Jr.
Problems of time-harmonic wave propagation arise in important fields of study such as geological surveying, radar detection/evasion, and aircraft design. These often involve highfrequency waves, which demand high-order methods to mitigate the dispersion error. We propose a high-order method for computing solutions to the variable-coefficient inhomogeneous Helmholtz equation in two dimensions on domains bounded by piecewise smooth curves of arbitrary shape with a finite number of boundary singularities at known locations. We utilize compact finite difference (FD) schemes on regular structured grids to achieve highorder accuracy due to their efficiency and simplicity, as well as the capability to approximate variable-coefficient differential operators. In this work, a 4th-order compact FD scheme for the variable-coefficient Helmholtz equation on a Cartesian grid in 2D is derived and tested. The well known limitation of finite differences is that they lose accuracy when the boundary curve does not coincide with the discretization grid, which is a severe restriction on the geometry of the computational domain. Therefore, the algorithm presented in this work combines high-order FD schemes with the method of difference potentials (DP), which retains the efficiency of FD while allowing for boundary shapes that are not aligned with the grid without sacrificing the accuracy of the FD scheme. Additionally, the theory of DP allows for the universal treatment of the boundary conditions. One of the significant contributions of this work is the development of an implementation that accommodates general boundary conditions (BCs). In particular, Robin BCs with discontinuous coefficients are studied, for which we introduce a piecewise parameterization of the boundary curve. Problems with discontinuities in the boundary data itself are also studied. We observe that the design convergence rate suffers whenever the solution loses regularity due to the boundary conditions. This is
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
The numerical solution of the boundary inverse problem for a parabolic equation
Vasil'ev, V. V.; Vasilyeva, M. V.; Kardashevsky, A. M.
2016-10-01
Boundary inverse problems occupy an important place among the inverse problems of mathematical physics. They are connected with the problems of diagnosis, when additional measurements on one of the borders or inside the computational domain are necessary to restore the boundary regime in the other border, inaccessible to direct measurements. The boundary inverse problems belong to a class of conditionally correct problems, and therefore, their numerical solution requires the development of special computational algorithms. The paper deals with the solution of the boundary inverse problem for one-dimensional second-order parabolic equations, consisting in the restoration of boundary regime according to measurements inside the computational domain. For the numerical solution of the inverse problem it is proposed to use an analogue of a computational algorithm, proposed and developed to meet the challenges of identification of the right side of the parabolic equations in the works P.N.Vabishchevich and his students based on a special decomposition of solving the problem at each temporal layer. We present and discuss the results of a computational experiment conducted on model problems with quasi-solutions, including with random errors in the input data.
Joekar-Niasar, V.
2013-01-25
Upscaling electroosmosis in porous media is a challenge due to the complexity and scale-dependent nonlinearities of this coupled phenomenon. "Pore-network modeling" for upscaling electroosmosis from pore scale to Darcy scale can be considered as a promising approach. However, this method requires analytical solutions for flow and transport at pore scale. This study concentrates on the development of analytical solutions of flow and transport in a single rectangular channel under combined effects of electrohydrodynamic forces. These relations will be used in future works for pore-network modeling. The analytical solutions are valid for all regimes of overlapping electrical double layers and have the potential to be extended to nonlinear Boltzmann distribution. The innovative aspects of this study are (a) contribution of overlapping of electrical double layers to the Stokes flow as well as Nernst-Planck transport has been carefully included in the analytical solutions. (b) All important transport mechanisms including advection, diffusion, and electromigration have been included in the analytical solutions. (c) Fully algebraic relations developed in this study can be easily employed to upscale electroosmosis to Darcy scale using pore-network modeling. © 2013 Springer Science+Business Media Dordrecht.
Directory of Open Access Journals (Sweden)
Ying Wang
2015-03-01
Full Text Available In this article, we study the existence of multiple positive solutions for singular semipositone boundary-value problem (BVP with integral boundary conditions on infinite intervals. By using the properties of the Green's function and the Guo-Krasnosel'skii fixed point theorem, we obtain the existence of multiple positive solutions under conditions concerning the nonlinear functions. The method in this article can be used for a large number of problems. We illustrate the validity of our results with an example in the last section.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
Directory of Open Access Journals (Sweden)
FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics
Directory of Open Access Journals (Sweden)
A. Barari
2008-01-01
Full Text Available Variational iteration method (VIM is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM. The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.
Kuiper, Logan K
2016-01-01
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
Algebraically explicit analytical solutions of two-buoyancy natural convection in porous media
Institute of Scientific and Technical Information of China (English)
CAI Ruixian; ZHANG Na; LIU Weiwei
2003-01-01
Analytical solutions of governing equations of various physical phenomena have their own irreplaceable theoretical meaning. In addition, they can also be the benchmark solutions to verify the outcomes and codes of numerical solution, and to develop various numerical methods such as their differencing schemes and grid generation skills as well. In order to promote the development of the discipline of natural convection, three simple algebraically explicit analytical solution sets are derived for a non-linear simultaneous partial differential equation set with five dependent unknown variables, which represents the natural convection in porous media with both temperature and concentration gradients. An extraordinary method separating variables with addition is applied in this paper to deduce solutions.
Acker, A.
We give an analytical proof of the existence of convex classical solutions for the (convex) Prandtl-Batchelor free boundary problem in fluid dynamics. In this problem, a convex vortex core of constant vorticity μ >0 is embedded in a closed irrotational flow inside a closed, convex vessel in ℜ 2. The unknown boundary of the vortex core is a closed curve Γ along which (v+)^2-(v^-)^2=Λ , where v+ and v- denote, respectively, the exterior and interior flow-speeds along Γ and Λ is a given constant. Our existence results all apply to the natural multidimensional mathematical generalization of the above problem. The present existence theorems are the only ones available for the Prandtl-Batchelor problem for Λ >0, because (a) the author's prior existence treatment was restricted to the case where Λ <0, and because (b) there is no analytical existence theory available for this problem in the non-convex case, regardless of the sign of Λ .
Analytical solution of the Gross-Neveu model at finite density
Thies, M
2003-01-01
Recent numerical calculations have shown that the ground state of the Gross-Neveu model at finite density is a crystal. Guided by these results, we can now present the analytical solution to this problem in terms of elliptic functions. The scalar potential is the superpotential of the non-relativistic Lame Hamiltonian. This model can also serve as analytically solvable toy model for a relativistic superconductor in the Larkin-Ovchinnikov-Fulde-Ferrell phase.
Institute of Scientific and Technical Information of China (English)
LIU Hong-Zhun; PAN Zu-Liang; LI Peng
2006-01-01
In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.
Analytic Solutions of a Polynomial-Like Iterative Functional Equation near Resonance
Institute of Scientific and Technical Information of China (English)
LIU Ling Xia; SI Jian Guo
2009-01-01
In this paper existence of local analytic solutions of a polynomial-like iterative functional equation is studied. As well as in previous work, we reduce this problem with the Schroder transformation to finding analytic solutions of a functional equation without iteration of the unknown function f. For technical reasons, in previous work the constant α given in the Schr(o)der transformation, i.e., the eigenvalue of the linearized f at its fixed point O, is required to fulfill that α is off the unit circle S1 or lies on the circle with the Diophantine condition. In this paper,we obtain results of analytic solutions in the case of α at resonance, i.e., at a root of the unity and the case of α near resonance under the Brjuno condition.
Existence of positive solutions to a Laplace equation with nonlinear boundary condition
Kim, C.-G.; Liang, Z.-P.; Shi, J.-P.
2015-12-01
The positive solutions of a Laplace equation with a superlinear nonlinear boundary condition on a bounded domain are studied. For higher-dimensional domains, it is shown that non-constant positive solutions bifurcate from a branch of trivial solutions at a sequence of bifurcation points, and under additional conditions on nonlinearity, the existence of a non-constant positive solution for any sufficiently large parameter value is proved by using variational approach. It is also proved that for one-dimensional domain, there is only one bifurcation point, all non-constant positive solutions lie on the bifurcating curve, and for large parameter values, there exist at least two non-constant positive solutions. For a special case, there are exactly two non-constant positive solutions.
Corrected Analytical Solution of the Generalized Woods-Saxon Potential for Arbitrary $\\ell$ States
Bayrak, O
2015-01-01
The bound state solution of the radial Schr\\"{o}dinger equation with the generalized Woods-Saxon potential is carefully examined by using the Pekeris approximation for arbitrary $\\ell$ states. The energy eigenvalues and the corresponding eigenfunctions are analytically obtained for different $n$ and $\\ell$ quantum numbers. The obtained closed forms are applied to calculate the single particle energy levels of neutron orbiting around $^{56}$Fe nucleus in order to check consistency between the analytical and Gamow code results. The analytical results are in good agreement with the results obtained by Gamow code for $\\ell=0$.
The “2T” ion-electron semi-analytic shock solution for code-comparison with xRAGE: A report for FY16
Energy Technology Data Exchange (ETDEWEB)
Ferguson, Jim Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-10-05
This report documents an effort to generate the semi-analytic "2T" ion-electron shock solution developed in the paper by Masser, Wohlbier, and Lowrie, and the initial attempts to understand how to use this solution as a code-verification tool for one of LANL's ASC codes, xRAGE. Most of the work so far has gone into generating the semi-analytic solution. Considerable effort will go into understanding how to write the xRAGE input deck that both matches the boundary conditions imposed by the solution, and also what physics models must be implemented within the semi-analytic solution itself to match the model assumptions inherit within xRAGE. Therefore, most of this report focuses on deriving the equations for the semi-analytic 1D-planar time-independent "2T" ion-electron shock solution, and is written in a style that is intended to provide clear guidance for anyone writing their own solver.
The “2T” ion-electron semi-analytic shock solution for code-comparison with xRAGE: A report for FY16
Energy Technology Data Exchange (ETDEWEB)
Ferguson, Jim Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-10-05
This report documents an effort to generate the semi-analytic "2T" ion-electron shock solution developed in the paper by Masser, Wohlbier, and Lowrie [1], and the initial attempts to understand how to use this solution as a code-verification tool for one of LANL's ASC codes, xRAGE. Most of the work so far has gone into generating the semi-analytic solution. Considerable effort will go into understanding how to write the xRAGE input deck that both matches the boundary conditions imposed by the solution, and also what physics models must be implemented within the semi-analytic solution itself to match the model assumptions inherit within xRAGE. Therefore, most of this report focuses on deriving the equations for the semi-analytic 1D-planar time-independent "2T" ion-electron shock solution, and is written in a style that is intended to provide clear guidance for anyone writing their own solver.
Positive solutions for a nonlinear periodic boundary-value problem with a parameter
Directory of Open Access Journals (Sweden)
Jingliang Qiu
2012-08-01
Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams
2014-01-01
This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the effi...
Analytical solution for the free vibration analysis of delaminated Timoshenko beams.
Jafari-Talookolaei, Ramazan-Ali; Abedi, Maryam
2014-01-01
This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology.
Institute of Scientific and Technical Information of China (English)
WANG Chun-ling; HUANG Yi; JIA Ji-hong
2007-01-01
The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semiinfinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented.
An analytical solution to the equation of motion for the damped nonlinear pendulum
DEFF Research Database (Denmark)
Johannessen, Kim
2014-01-01
An analytical approximation of the solution to the differential equation describing the oscillations of the damped nonlinear pendulum at large angles is presented. The solution is expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic modulus. The analytical...... of the damped nonlinear pendulum is presented, and it is shown that the period of oscillation is dependent on time. It is established that, in general, the period is longer than that of a linearized model, asymptotically approaching the period of oscillation of a damped linear pendulum....
AN EXACT ANALYTICAL SOLUTION FOR THE INTERSTELLAR MAGNETIC FIELD IN THE VICINITY OF THE HELIOSPHERE
Energy Technology Data Exchange (ETDEWEB)
Röken, Christian [Universität Regensburg, Fakultät für Mathematik, Regensburg (Germany); Kleimann, Jens; Fichtner, Horst, E-mail: christian.roeken@mathematik.uni-regensburg.de, E-mail: jk@tp4.rub.de, E-mail: hf@tp4.rub.de [Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Institut für Theoretische Physik IV, Bochum (Germany)
2015-06-01
An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The three-dimensional field structure close to the heliopause is calculated as a solution of the induction equation under the assumption that it is frozen into a prescribed plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. The usefulness of this analytical solution as an approximation to self-consistent magnetic field configurations obtained numerically from the full MHD equations is illustrated by quantitative comparisons.
Seidi, M.; Behnia, S.; Khodabakhsh, R.
2014-09-01
Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expectation values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.
ANALYTICAL SOLUTION OF BENDING-COMPRESSION COLUMN USING DIFFERENT TENSION-COMPRESSION MODULUS
Institute of Scientific and Technical Information of China (English)
姚文娟; 叶志明
2004-01-01
Based on elastic theory of different tension-compression modulus, the analytical solution was deduced for bending-compression column subject to combined loadings by the flowing coordinate system and phased integration method. The formulations for the neutral axis, stress, strain and displacement were developed, the finite element program was compiled for calculation, and the comparison between the result of finite element and analytical solution were given too. Finally, compare and analyze the result of different modulus and the same modulus, obtain the difference of two theories in result, and propose the reasonable suggestion for the calculation of this structure.
An Analytic and Optimal Inverse Kinematic Solution for a 7-DOF Space Manipulator
Institute of Scientific and Technical Information of China (English)
WANG Yingshi; SUN Lei; YAN Wenbin; LIU Jingtai
2014-01-01
An analytic inverse kinematic solution is presented for a 7-DOF (degree of freedom) redundant space manipu-lator. The proposed method can obtain all the feasible solutions in the global joint space, which are denoted by a joint angle parameter. Meanwhile, both the singularity problem and the joint limits are considered in detail. Besides, an optimization approach is provided to get one near optimal inverse kinematic solution from all the feasible solutions. The proposed method can reduce effectively the computational complexity, so that it can be applied online. Finally, the method’s validity is shown by kinematic simulations.
Institute of Scientific and Technical Information of China (English)
CAI Ruixian; ZHANG Na
2004-01-01
The analytical solutions of unsteady heat conduction with variable thermal properties(thermal conductivity,density and specific heat are functions of temperature or coordinates)are meaningful in theory.In addition,they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes,grid generation methods and so forth.Such solutions in rectangular coordinates have been derived by the authors.Some other solutions for 1-D and 2-D axisymmetrical heat conduction in cylin drical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.
Institute of Scientific and Technical Information of China (English)
M J UDDIN; O Anwar BG; M N UDDIN; A I Md ISMAIL
2016-01-01
A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, tempera- ture and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excelle- nt correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bio- reactor diffusion flows and high-temperature chemical materials processing systems.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper investigates the existence of positive solutions to systems of second order nonlocal boundary value problems with first order derivatives, in which the nonlinear term is not required to be continuous and involves first order derivatives. The main tool used in this paper is a fixed point index theory in a cone.
Positive solutions of multi-point boundary value problem of fractional differential equation
Directory of Open Access Journals (Sweden)
De-xiang Ma
2015-07-01
Full Text Available By means of two fixed-point theorems on a cone in Banach spaces, some existence and multiplicity results of positive solutions of a nonlinear fractional differential equation boundary value problem are obtained. The proofs are based upon some properties of Green’s function, which are also the key of the paper.
L^p-continuity of solutions to parabolic free boundary problems
Directory of Open Access Journals (Sweden)
Abdeslem Lyaghfouri
2015-07-01
Full Text Available In this article, we consider a class of parabolic free boundary problems. We establish some properties of the solutions, including L^infinity-regularity in time and a monotonicity property, from which we deduce strong L^p-continuity in time.
POSITIVE SOLUTIONS TO A SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM ON TIME SCALES
Institute of Scientific and Technical Information of China (English)
Liu Yang; Chunfang Shen
2009-01-01
By a fixed point theorem in a cone,the existence of at least three positive solutions to a class of second-order multi-point boundary value problem for dynamic equation on time scales with the nonlinear term depends on the first order derivative is studied.
Directory of Open Access Journals (Sweden)
Jian Liu
2013-09-01
Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.
EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.
NONTRIVIAL SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarantee the existence of nontrivial solutions are obtained. We use the topological degree to prove our main results.
Variational solution about over-determined geodetic boundary value problem and its related theories
Institute of Scientific and Technical Information of China (English)
2007-01-01
A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.
EXISTENCE OF SOLUTIONS TO A CLASS OF NONLINEAR n-DIMENSIONAL DISCRETE BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,using the critical point theory,we obtain a new result on the existence of the solutions to a class of n-dimensional discrete boundary value problems.Results obtained extend or improve the existing ones.
Institute of Scientific and Technical Information of China (English)
KANG Ping; YAO Jianli
2009-01-01
In this paper, we investigate the existence of symmetric solutions of singular nonlocal boundary value problems for systems of differential equations. Our analysis relies on a nonlinear alternative of Leray - schauder type. Our results presented here unify, generalize and significantly improve many known results in the literature.
Directory of Open Access Journals (Sweden)
Mohamed Jleli
2014-01-01
Full Text Available A class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.
Institute of Scientific and Technical Information of China (English)
Yaohong LI; Xiaoyan ZHANG
2013-01-01
In this paper,we consider boundary value problems for systems of nonlinear thirdorder differential equations.By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem,the existence of multiple positive solutions is obtained.As application,we give some examples to demonstrate our results.
Existence of Two Solutions of Nonlinear m-Point Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
任景莉; 葛渭高
2003-01-01
Sufficient conditions for the existence of at least two positive solutions of a nonlinear m-points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.
Pérez Guerrero, J. S.; Skaggs, T. H.
2010-08-01
SummaryMathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-dispersion equation with distance-dependent coefficients. An integrating factor is employed to obtain a transport equation that has a self-adjoint differential operator, and a solution is found using the generalized integral transform technique (GITT). It is demonstrated that an analytical expression for the integrating factor exists for several transport equation formulations of practical importance in groundwater transport modeling. Unlike nearly all solutions available in the literature, the current solution is developed for a finite spatial domain. As an illustration, solutions for the particular case of a linearly increasing dispersivity are developed in detail and results are compared with solutions from the literature. Among other applications, the current analytical solution will be particularly useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.
General Analytical Solution of Transverse Vibration For Orthotropic Rectangular Thin Plates
Institute of Scientific and Technical Information of China (English)
HUANG; Yan; ZHANG; Xiao-jin
2002-01-01
A general solution of differential equation for transverse displacement function of orthotropic rectangular thin plates in free vibration is established in this paper. It can be used to solve the vibration problem of plate with arbitrary boundaries. As an example, the frequencies of a composite laminated plate with four free edges have been solved. The result as compared with the experiment is satisfactory.
Gaury, Benoit; Haney, Paul M.
2016-12-01
Analytical expressions are presented for the dark current-voltage relation J(V) of a pn+ junction with positively charged columnar grain boundaries with high defect density. These expressions apply to non-depleted grains with sufficiently high bulk hole mobilities. The accuracy of the formulas is verified by direct comparison to numerical simulations. Numerical simulations further show that the dark J(V) can be used to determine the open-circuit potential Voc of an illuminated junction for a given short-circuit current density Jsc . A precise relation between the grain boundary properties and Voc is provided, advancing the understanding of the influence of grain boundaries on the efficiency of thin film polycrystalline photovoltaics like CdTe and Cu(In,Ga)Se2 .
Directory of Open Access Journals (Sweden)
Nguyen Anh Dao
2016-11-01
Full Text Available We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.
Kabala, Z. J.
1997-08-01
Under the assumption that local solute dispersion is negligible, a new general formula (in the form of a convolution integral) is found for the arbitrary k-point ensemble moment of the local concentration of a solute convected in arbitrary m spatial dimensions with general sure initial conditions. From this general formula new closed-form solutions in m=2 spatial dimensions are derived for 2-point ensemble moments of the local solute concentration for the impulse (Dirac delta) and Gaussian initial conditions. When integrated over an averaging window, these solutions lead to new closed-form expressions for the first two ensemble moments of the volume-averaged solute concentration and to the corresponding concentration coefficients of variation (CV). Also, for the impulse (Dirac delta) solute concentration initial condition, the second ensemble moment of the solute point concentration in two spatial dimensions and the corresponding CV are demonstrated to be unbound. For impulse initial conditions the CVs for volume-averaged concentrations axe compared with each other for a tracer from the Borden aquifer experiment. The point-concentration CV is unacceptably large in the whole domain, implying that the ensemble mean concentration is inappropriate for predicting the actual concentration values. The volume-averaged concentration CV decreases significantly with an increasing averaging volume. Since local dispersion is neglected, the new solutions should be interpreted as upper limits for the yet to be derived solutions that account for local dispersion; and so should the presented CVs for Borden tracers. The new analytical solutions may be used to test the accuracy of Monte Carlo simulations or other numerical algorithms that deal with the stochastic solute transport. They may also be used to determine the size of the averaging volume needed to make a quasi-sure statement about the solute mass contained in it.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Quanlin; Birkholzer, Jens T.; Tsang, Chin-Fu
2008-07-15
A number of (semi-)analytical solutions are available to drawdown analysis and leakage estimation of shallow aquifer-aquitard systems. These solutions assume that the systems are laterally infinite. When a large-scale pumping from (or injection into) an aquifer-aquitard system of lower specific storativity occurs, induced pressure perturbation (or hydraulic head drawdown/rise) may reach the lateral boundary of the aquifer. We developed semi-analytical solutions to address the induced pressure perturbation and vertical leakage in a 'laterally bounded' system consisting of an aquifer and an overlying/underlying aquitard. A one-dimensional radial flow equation for the aquifer was coupled with a one-dimensional vertical flow equation for the aquitard, with a no-flow condition imposed on the outer radial boundary. Analytical solutions were obtained for (1) the Laplace-transform hydraulic head drawdown/rise in the aquifer and in the aquitard, (2) the Laplace-transform rate and volume of leakage through the aquifer-aquitard interface integrated up to an arbitrary radial distance, (3) the transformed total leakage rate and volume for the entire interface, and (4) the transformed horizontal flux at any radius. The total leakage rate and volume depend only on the hydrogeologic properties and thicknesses of the aquifer and aquitard, as well as the duration of pumping or injection. It was proven that the total leakage rate and volume are independent of the aquifer's radial extent and wellbore radius. The derived analytical solutions for bounded systems are the generalized solutions of infinite systems. Laplace-transform solutions were numerically inverted to obtain the hydraulic head drawdown/rise, leakage rate, leakage volume, and horizontal flux for given hydrogeologic and geometric conditions of the aquifer-aquitard system, as well as injection/pumping scenarios. Application to a large-scale injection-and-storage problem in a bounded system was demonstrated.
Nonlinear Whitham-Broer-Kaup Wave Equation in an Analytical Solution
Directory of Open Access Journals (Sweden)
S. A. Zahedi
2008-01-01
Full Text Available This study presented a new approach for the analysis of a nonlinear Whitham-Broer-Kaup equation dealing with propagation of shallow water waves with different dispersion relations. The analysis was based on a kind of analytical method, called Variational Iteration Method (VIM. To illustrate the capability of the approach, some numerical examples were given and the propagation and the error of solutions were shown in comparison to those of exact solution. In clear conclusion, the approach was efficient and capable to obtain the analytical approximate solution of this set of wave equations while these solutions could straightforwardly show some facts of the described process deeply such as the propagation. This method can be easily extended to other nonlinear wave equations and so can be found widely applicable in this field of science.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this study, a semi-analytical formulation based on the Scaled Boundary Finite Element Method (SBFEM) was proposed and used to obtain the solution for the characteristics of a two-dimensional dam-reservoir system with absorptive reservoir bottom in the frequency domain. For simplicity, the dam with arbitrary upstream faces was assumed to be rigid and was subjected to a horizontal ground acceleration, while the reservoir with absorptive bottom was assumed to be semi-infinite. The reservoir was divided into two sub-domains: a near-field sub-domain and a far-field sub-domain. The near-field sub-domain with arbitrary geometry was modelled by the Finite Element Method (FEM), while the effects of the far-field sub-domain which was assumed to be horizontal were described by a semi-analytical formation. The semi-analytical formulation involved the effect of absorptive reservoir bottom, as well as the radiation damping effect of a semi-infinite reservoir. A FEM/SBFEM coupling formulation was presented to solve dam-reservoir coupled problems. The accuracy and efficiency of the coupling formulation were demonstrated by computing some benchmark examples. Highly accurate results are produced even if the near-field sub-domain is very small.
Institute of Scientific and Technical Information of China (English)
HOU Bang-Pin; WANG Shun-Jin; YU Wan-Lun; SUN Wei-Li; WANG Gang
2004-01-01
@@ We obtain the analytical solution to the master equation in the photon number representation by using algebraic dynamical method in the nonautonomous case. Based on the solution we find that a two-mode coherent sate can be produced within dissipative background, and the averaged photon number for each mode is related to the damping constant, external field amplitude and coupling constant between two modes.
An approximate and an analytical solution to the carousel-pendulum problem
Energy Technology Data Exchange (ETDEWEB)
Vial, Alexandre [Pole Physique, Mecanique, Materiaux et Nanotechnologies, Universite de technologie de Troyes, 12, rue Marie Curie BP-2060, F-10010 Troyes Cedex (France)], E-mail: alexandre.vial@utt.fr
2009-09-15
We show that an improved solution to the carousel-pendulum problem can be easily obtained through a first-order Taylor expansion, and its accuracy is determined after the obtention of an unusable analytical exact solution, advantageously replaced by a numerical one. It is shown that the accuracy is unexpectedly high, even when the ratio length of the pendulum to carousel radius approaches unity. (letters and comments)
Exact Analytical Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length
Institute of Scientific and Technical Information of China (English)
CHEN Yong; LI Biao; ZHENG Yu
2007-01-01
In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.
Zhu, Changjiang; Duan, Renjun
2003-02-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation \\left\\{\\begin{array}{@{}l@{\\qquad}l@{}} u_t+\\big(\\frac{u^2}{2}\\big)_x=0 x\\gt0\\quad t\\gt0\\\\ u(x,0)=u_0(x) x\\geq0\\\\ u(0,t)=0 t\\geq0. \\end{array}\\right. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
Linear polymer aqueous solutions in soft lubrication:From boundary to mixed lubrication
Institute of Scientific and Technical Information of China (English)
LIU; ShuHai; TAN; GuiBin; WANG; DeGuo
2013-01-01
In order to better understand linear polymer aqueous solutions in soft lubrication from boundary to mixed lubrication,poly(ethylene glycol) and sodium hyaluronateare used as model polymers were investigated by using UMT-2 tribometer with the ball-on-disk mode. The relationship between the master Stribeck curves of the polymer aqueous solutions and the influence factors were investigated. Experimental results indicated that soft lubrication is determined by lubricant rheological properties and surface-lubricant interactions, e.g., wetting behavior of polymer aqueous solution on tribological surfaces.
On the analytical solution of Fornberg–Whitham equation with the new fractional derivative
Indian Academy of Sciences (India)
Olaniyi Samuel Iyiola; Gbenga Olayinka Ojo
2015-10-01
Motivated by the simplicity, natural and efficient nature of the new fractional derivative introduced by R Khalil et al in J. Comput. Appl. Math. 264, 65 (2014), analytical solution of space-time fractional Fornberg–Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM). The new fractional derivative makes it possible to introduce fractional order in space to the Fornberg–Whitham equation and be able to obtain its solution. This work displays the elegant nature of the application of q-HAM to solve strongly nonlinear fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for nonlinear differential equations. Comparisons are made on the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell
Directory of Open Access Journals (Sweden)
Rong Xiao
2014-01-01
Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.
Directory of Open Access Journals (Sweden)
Yanmei Sun
2012-01-01
Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.
Institute of Scientific and Technical Information of China (English)
Yi Yang; Jike Liu; Chengwu Cai
2008-01-01
The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods.For the problem with a rectangular hole,only approximate results are derived.This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions.By using the U-transformation technique and the finite element method,the analytical displacement solutions of the finite element equations are derived in the series form.Therefore,the stress concentration can then be discussed easily and conveniently.For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method.The stress concentration factors for various ratios of height to width of the hole are obtained.
Analytical solution of magnetothermoelastic interaction in a fiber-reinforced anisotropic material
Hobiny, Aatef D.; Abbas, Ibrahim A.
2016-12-01
The present paper is concerned with the investigation of the analytical solution of a fiber-reinforced anisotropic material under generalized magnetothermoelastic theory using the eigenvalue approach. Based on the Lord-Shulman theory, the formulation is applied to generalized magnetothermoelasticity with one relaxation time. Based on eigenvalue approach, exponential Fourier transform and Laplace techniques, the analytical solutions has been obtained. The inverses of Fourier transforms are obtained analytically. Numerical computations for a fiber-reinforced-like material have been performed and the results are presented graphically. The results of the temperature, displacement components and stress components have been verified numerically and are represented graphically. Comparisons are made with the results predicted by the presence and absence of reinforcement.
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields.
Kuru, S; Negro, J; Nieto, L M
2009-11-11
Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.
Analytical solutions to a hillslope-storage kinematic wave equation for subsurface flow
Troch, P.A.; Loon, van E.; Hilberts, A.
2002-01-01
Hillslope response has traditionally been studied by means of the hydraulic groundwater theory. Subsurface flow from a one-dimensional hillslope with a sloping aquifer can be described by the Boussinesq equation [Mem. Acad. Sci. Inst. Fr. 23 (1) (1877) 252–260]. Analytical solutions to Boussinesq's
Big Data Analytics Solutions: The Implementation Challenges in the Financial Services Industry
Ojo, Michael O.
2016-01-01
The challenges of Big Data (BD) and Big Data Analytics (BDA) have attracted disproportionately less attention than the overwhelmingly espoused benefits and game-changing promises. While many studies have examined BD challenges across multiple industry verticals, very few have focused on the challenges of implementing BDA solutions. Fewer of these…
Exact Analytical Solution of the Klein-Gordon Equation in the Generalized Woods-Saxon Potential
Bayrak, O.; Sahin, D.
2015-09-01
The exact analytical solution of the Klein-Gordon equation for the spin-0 particles in the generalized Woods-Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π0 particles.
Microchannel electrokinetics of charged analytes in buffered solutions near floating electrodes
DEFF Research Database (Denmark)
Andersen, Mathias Bækbo; Wolfcale, Trevor; Gregersen, Misha Marie;
We present both experimental and numerical studies of nonlinear electrokinetic flow of buffered solutions seeded with dilute analytes in a straight microchannel (0.6 μm high, 250 μm wide, and 9000 μm long) with a 0.15 μm high 60 μm wide electrode situated at the bottom center of the channel...
On the Analytical Solution of Non-Orthogonal Stagnation Point Flow towards a Stretching Sheet
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Bagheri, G. H.; Barari, Amin
2011-01-01
An analytical solution for non-orthogonal stagnation point for the steady flow of a viscous and incompressible fluid is presented. The governing nonlinear partial differential equations for the flow field are reduced to ordinary differential equations by using similarity transformations existed i...
Hilpert, Markus
2010-07-15
The displacement of a gas by a liquid in both horizontal and inclined capillary tubes where the tube inlet is connected to a liquid reservoir of constant pressure can be described by the Lucas-Washburn theory. One can also use the Lucas-Washburn theory to model the reverse flow, that is, liquid withdrawal, even though the latter case has received relatively little attention. In this paper, we derive analytical solutions for the travel time of the gas-liquid interface as a function of interface velocity. The interface position can be obtained by numerically integrating the numerically inverted interface velocity. Therefore we refer to these solutions as (semi)-analytical. We neglect inertial forces. However, we account for a dynamic contact angle where the nondimensional non-equilibrium Young force depends on the capillary number in the form of either a power law or a power series. We explore the entire nondimensional parameter space. The analytical solutions allow us to show that five different liquid withdrawal scenarios may occur that differ in the direction of flow and the sign of the acceleration of the gas-liquid interface: horizontal, upward, steady-state downward, accelerating downward, and decelerating downward flow. In the last case, the liquid is withdrawn from the tube either completely or partially. The (semi)-analytical solutions are also valid within the limit where the contact angle is constant.