Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
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.
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...
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 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.
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.
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.
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
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)
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.
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.
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.
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 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.).
Analytical solution of one dimensional temporally dependent ...
African Journals Online (AJOL)
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The models involve the one-site, two-site, and two-region ... (2005) presented an analytical solution to advection-dispersion equation ... transfer of heat in fluids, flow through porous media, and the spread of contaminants in fluids and in ...
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.
US Fish and Wildlife Service, Department of the Interior — This contaminant report is created for Hailstone National Wildlife Refuge in Montana. Sections of the report include weight, percent moisture, contaminant...
Analytic Solutions of Special Functional Equations
Directory of Open Access Journals (Sweden)
Octav Olteanu
2013-07-01
Full Text Available We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem. All these considerations work in the real case, for functions and operators. Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis. Some consequences are given. An approximating formula for the analytic form of the solution is also given. Finally, one illustrates the preceding results by an application to a concrete functional and operatorial equation. Some related examples are given.
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.
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.
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.
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.
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.
Analytic structure of solutions to multiconfiguration equations
Energy Technology Data Exchange (ETDEWEB)
Fournais, Soeren [Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, Building 1530, DK-8000 Arhus C (Denmark); Hoffmann-Ostenhof, Maria [Fakultaet fuer Mathematik, Universitaet Wien, Nordbergstrasse 15, A-1090 Vienna (Austria); Hoffmann-Ostenhof, Thomas [Institut fuer Theoretische Chemie, Waehringerstrasse 17, Universitaet Wien, A-1090 Vienna (Austria); Soerensen, Thomas Oestergaard [Department of Mathematics, Imperial College London, Huxley Building, 180 Queen' s Gate, London SW7 2AZ (United Kingdom)], E-mail: fournais@imf.au.dk, E-mail: Maria.Hoffmann-Ostenhof@univie.ac.at, E-mail: thoffman@esi.ac.at, E-mail: t.sorensen@imperial.ac.uk
2009-08-07
We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree-Fock) of Coulomb systems. We prove the following: let {l_brace}{psi}{sub 1}, ..., {psi}{sub M}{r_brace} be any solution to the rank-M multiconfiguration equations for a molecule with L fixed nuclei at R{sub 1},...,R{sub L} element of R{sup 3}. Then, for any j in {l_brace}1, ..., M{r_brace}, k in {l_brace}1, ..., L{r_brace}, there exists a neighborhood U{sub j,k} subset or equal R{sup 3} of R{sub k}, and functions {psi}{sup (1)}{sub j,k}, {psi}{sup (2)}{sub j,k}, real analytic in U{sub j,k}, such that {phi}{sub j}(x)={phi}{sub j,k}{sup (1)}(x)+|x-R{sub k}|{phi}{sub j,k}{sup (2)}(x), x element of U{sub j,k}. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo-Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schroedinger operator of atoms and molecules near two-particle coalescence points.
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.
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 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.
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.
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.
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.
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.
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.
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.
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…
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.
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 of strongly nonlinear Duffing oscillators
Directory of Open Access Journals (Sweden)
A.M. El-Naggar
2016-06-01
Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.
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.
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.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
Keywords: Burger-Huxley equation, iteration method, analytical solution, ... dynamics, chemical kinetics and mathematical biology (Albowitz and Clarkson, ... numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor theory, ...
Analytical solutions for the recovery tests after constant-discharge ...
African Journals Online (AJOL)
Received 11 April 2014; accepted in revised form 3 September 2014. Analytical solutions for the recovery ... ABSTRACT ... the analysis of residual drawdown data after a pumping test with step-wise or intermittently changing discharge rates is.
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.)
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.
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.
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...
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.
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 ...
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.
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...
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.
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.
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.
Analytic Solution to Shell Boundary – Value Problems
Directory of Open Access Journals (Sweden)
Yu. I. Vinogradov
2015-01-01
Full Text Available Object of research is to find analytical solution to the shell boundary – value problems, i.e. to consider the solution for a class of problems concerning the mechanics of hoop closed shells strain.The objective of work is to create an analytical method to define a stress – strain state of shells under non-axisymmetric loading. Thus, a main goal is to derive the formulas – solutions of the linear ordinary differential equations with variable continuous coefficients.The partial derivative differential equations of mechanics of shells strain by Fourier's method of variables division are reduced to the system of the differential equations with ordinary derivatives. The paper presents the obtained formulas to define solutions of the uniform differential equations and received on their basis formulas to define a particular solution depending on a type of the right parts of the differential equations.The analytical algorithm of the solution of a boundary task uses an approach to transfer the boundary conditions to the randomly chosen point of an interval of changing independent variable through the solution of the canonical matrix ordinary differential equation with the subsequent solution of system of algebraic equations for compatibility of boundary conditions at this point. Efficiency of algorithm is based on the fact that the solution of the ordinary differential equations is defined as the values of Cauchy – Krylova functions, which meet initial arbitrary conditions.The results of researches presented in work are useful to experts in the field of calculus mathematics, dealing with solution of systems of linear ordinary differential equations and creation of effective analytical computing methods to solve shell boundary – value problems.
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.
Analytical solution for Van der Pol-Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Kimiaeifar, A. [Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman (Iran, Islamic Republic of); Saidi, A.R. [Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman (Iran, Islamic Republic of)], E-mail: saidi@mail.uk.ac.ir; Bagheri, G.H.; Rahimpour, M. [Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman (Iran, Islamic Republic of); Domairry, D.G. [Department of Mechanical Engineering, Noshirvani Institute of Technology, Babol (Iran, Islamic Republic of)
2009-12-15
In this paper, the problem of single-well, double-well and double-hump Van der Pol-Duffing oscillator is studied. Governing equation is solved analytically using a new kind of analytic technique for nonlinear problems namely the 'Homotopy Analysis Method' (HAM), for the first time. Present solution gives an expression which can be used in wide range of time for all domain of response. Comparisons of the obtained solutions with numerical results show that this method is effective and convenient for solving this problem. This method is a capable tool for solving this kind of nonlinear problems.
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.
The analytical solution to the problem of statistical induction
Directory of Open Access Journals (Sweden)
Rodolfo de Cristofaro
2007-10-01
Full Text Available This article is a somewhat personal review of the history and substance of the problem of statistical induction. The main approaches proposed for solving this problem have been examined according to their merits, whit special reference to the analytical solution supported by Carnap. This solution has been re-examined in view of certain results, and is proposed again to the attention of the statisticians.
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)
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
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
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 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 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.
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.
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.
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.
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.
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)
Quantifying risks with exact analytical solutions of derivative pricing distribution
Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin
2017-04-01
Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.
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)
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.
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.
ADVAN-style analytical solutions for common pharmacokinetic models.
Abuhelwa, Ahmad Y; Foster, David J R; Upton, Richard N
2015-01-01
The analytical solutions to compartmental pharmacokinetic models are well known, but have not been presented in a form that easily allows for complex dosing regimen and changes in covariate/parameter values that may occur at discrete times within and/or between dosing intervals. Laplace transforms were used to derive ADVAN-style analytical solutions for 1, 2, and 3 compartment pharmacokinetic linear models of intravenous and first-order absorption drug administration. The equations calculate the change in drug amounts in each compartment of the model over a time interval (t; t = t2 - t1) accounting for any dose or covariate events acting in the time interval. The equations were coded in the R language and used to simulate the time-course of drug amounts in each compartment of the systems. The equations were validated against commercial software [NONMEM (Beal, Sheiner, Boeckmann, & Bauer, 2009)] output to assess their capability to handle both complex dosage regimens and the effect of changes in covariate/parameter values that may occur at discrete times within or between dosing intervals. For all tested pharmacokinetic models, the time-course of drug amounts using the ADVAN-style analytical solutions were identical to NONMEM outputs to at least four significant figures, confirming the validity of the presented equations. To our knowledge, this paper presents the ADVAN-style equations for common pharmacokinetic models in the literature for the first time. The presented ADVAN-style equations overcome obstacles to implementing the classical analytical solutions in software, and have speed advantages over solutions using differential equation solvers. The equations presented in this paper fill a gap in the pharmacokinetic literature, and it is expected that these equations will facilitate the investigation of useful open-source software for modelling pharmacokinetic data. Copyright © 2015 Elsevier Inc. All rights reserved.
Analytical solution of linear ordinary differential equations by differential transfer matrix method
Directory of Open Access Journals (Sweden)
Sina Khorasani
2003-08-01
Full Text Available We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the $n$th-order differential equation to a system of $n$ linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
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.
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.
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 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 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.
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.
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.
Analytical Chemistry Core Capability Assessment - Preliminary Report
Energy Technology Data Exchange (ETDEWEB)
Barr, Mary E. [Los Alamos National Laboratory; Farish, Thomas J. [Los Alamos National Laboratory
2012-05-16
The concept of 'core capability' can be nebulous one. Even at a fairly specific level, where core capability equals maintaining essential services, it is highly dependent upon the perspective of the requestor. Samples are submitted to analytical services because the requesters do not have the capability to conduct adequate analyses themselves. Some requests are for general chemical information in support of R and D, process control, or process improvement. Many analyses, however, are part of a product certification package and must comply with higher-level customer quality assurance requirements. So which services are essential to that customer - just those for product certification? Does the customer also (indirectly) need services that support process control and improvement? And what is the timeframe? Capability is often expressed in terms of the currently utilized procedures, and most programmatic customers can only plan a few years out, at best. But should core capability consider the long term where new technologies, aging facilities, and personnel replacements must be considered? These questions, and a multitude of others, explain why attempts to gain long-term consensus on the definition of core capability have consistently failed. This preliminary report will not try to define core capability for any specific program or set of programs. Instead, it will try to address the underlying concerns that drive the desire to determine core capability. Essentially, programmatic customers want to be able to call upon analytical chemistry services to provide all the assays they need, and they don't want to pay for analytical chemistry services they don't currently use (or use infrequently). This report will focus on explaining how the current analytical capabilities and methods evolved to serve a variety of needs with a focus on why some analytes have multiple analytical techniques, and what determines the infrastructure for these analyses. This
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.
Approximate analytical solutions to the condensation-coagulation equation of aerosols
DEFF Research Database (Denmark)
Smith, Naftali R.; Shaviv, Nir J.; Svensmark, Henrik
2016-01-01
We present analytical solutions to the steady state nucleation-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...... of sulfuric acid....
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.
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.
Analytical solutions for tsunami runup on a plane beach
DEFF Research Database (Denmark)
Madsen, Per A.; Schäffer, Hemming Andreas
2010-01-01
In the literature it has so far been common practice to consider solitary waves N-waves (composed of solitary waves) as the appropriate model of tsunamis approaching the shoreline. Unfortunately, this approach is based on a tie between the nonlinearity and the horizontal length scale (or duration......) of the wave, which is not realistic for geophysical tsunamis. To resolve this problem, we first derive analytical solutions to the nonlinear shallow-water (NSW) equations for the runup/rundown of single waves, where the duration and the wave height can be specified separately. The formulation is then extended...
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.
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.
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
Analytical Solutions for Corrosion-Induced Cohesive Concrete Cracking
Directory of Open Access Journals (Sweden)
Hua-Peng Chen
2012-01-01
Full Text Available The paper presents a new analytical model to study the evolution of radial cracking around a corroding steel reinforcement bar embedded in concrete. The concrete cover for the corroding rebar is modelled as a thick-walled cylinder subject to axisymmetrical displacement constraint at the internal boundary generated by expansive corrosion products. A bilinear softening curve reflecting realistic concrete property, together with the crack band theory for concrete fracture, is applied to model the residual tensile stress in the cracked concrete. A governing equation for directly solving the crack width in cover concrete is established for the proposed analytical model. Closed-form solutions for crack width are then obtained at various stages during the evolution of cracking in cover concrete. The propagation of crack front with corrosion progress is studied, and the time to cracking on concrete cover surface is predicted. Mechanical parameters of the model including residual tensile strength, reduced tensile stiffness, and radial pressure at the bond interface are investigated during the evolution of cover concrete cracking. Finally, the analytical predictions are examined by comparing with the published experimental data, and mechanical parameters are analysed with the progress of reinforcement corrosion and through the concrete cover.
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....
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.
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.
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.
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.
Maximum likelihood Jukes-Cantor triplets: analytic solutions.
Chor, Benny; Hendy, Michael D; Snir, Sagi
2006-03-01
Maximum likelihood (ML) is a popular method for inferring a phylogenetic tree of the evolutionary relationship of a set of taxa, from observed homologous aligned genetic sequences of the taxa. Generally, the computation of the ML tree is based on numerical methods, which in a few cases, are known to converge to a local maximum on a tree, which is suboptimal. The extent of this problem is unknown, one approach is to attempt to derive algebraic equations for the likelihood equation and find the maximum points analytically. This approach has so far only been successful in the very simplest cases, of three or four taxa under the Neyman model of evolution of two-state characters. In this paper we extend this approach, for the first time, to four-state characters, the Jukes-Cantor model under a molecular clock, on a tree T on three taxa, a rooted triple. We employ spectral methods (Hadamard conjugation) to express the likelihood function parameterized by the path-length spectrum. Taking partial derivatives, we derive a set of polynomial equations whose simultaneous solution contains all critical points of the likelihood function. Using tools of algebraic geometry (the resultant of two polynomials) in the computer algebra packages (Maple), we are able to find all turning points analytically. We then employ this method on real sequence data and obtain realistic results on the primate-rodents divergence time.
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...
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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;...
Microgenetic Learning Analytics Methods: Workshop Report
Aghababyan, Ani; Martin, Taylor; Janisiewicz, Philip; Close, Kevin
2016-01-01
Learning analytics is an emerging discipline and, as such, benefits from new tools and methodological approaches. This work reviews and summarizes our workshop on microgenetic data analysis techniques using R, held at the second annual Learning Analytics Summer Institute in Cambridge, Massachusetts, on 30 June 2014. Specifically, this paper…
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.
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.
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.
Xie, Dexuan; Volkmer, Hans W.; Ying, Jinyong
2016-04-01
The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.
Xie, Dexuan; Volkmer, Hans W; Ying, Jinyong
2016-04-01
The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.
Report: Analytical Chemistry in a Changing World.
Laitinen, H. A.
1980-01-01
Examines some of the changes that have occurred in the field of analytic chemistry, with emphasis on how the field has adapted to changes in science and technology. Current trends also are identified and discussed. (CS)
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.
Analytical solution for facilitated transport across a membrane
Marzouqi, Mohamed Hassan Al-; Hogendoorn, Kees J.A.; Versteeg, Geert F.
2002-01-01
An analytical expression for the facilitation factor of component A across a liquid membrane is derived in case of an instantaneous reaction A(g) + B(l) ⇔ AB(l) inside the liquid membrane. The present expression has been derived based on earlier analytical results obtained for the enhancement factor
Analytical Solution for facilitated transport across a membrane
Al-marzouqi, M.; Hogendoorn, Kees; Versteeg, Geert
2002-01-01
An analytical expression for the facilitation factor of component A across a liquid membrane is derived in case of an instantaneous reaction A(g)+B(l)AB(l) inside the liquid membrane. The present expression has been derived based on the analytical results of Olander (A.I.Ch.E. J. 6(2) (1960) 233)
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.
Hilpert, Markus
2010-04-01
We derive new analytical solutions for liquid infiltration into a gas-filled capillary tube, whose inlet is connected to a liquid reservoir held at a constant pressure. We generalize the Lucas-Washburn theory to account for a model for dynamic contact angle that assumes the nonequilibrium Young force to depend linearly on the velocity of the gas-liquid interface. Like Lucas and Washburn, we neglect inertial forces. Using the Lambert function, we derive explicit analytical solutions for the interface position, velocity, and acceleration as a function of time. Consistent with previous work, which used more general models for dynamic contact angle, we can distinguish between five infiltration scenarios: horizontal infiltration, upward infiltration (capillary rise), as well as steady-state, accelerating, and decelerating downward infiltration. We determine the mutually exclusive conditions for the different infiltration scenarios to occur in terms of the nondimensional parameters that define the problem. Moreover, we develop 2D and 3D diagrams that show which parameter combination results in which infiltration scenario. Our analytical solutions are also valid in the limit where the dynamic contact angle becomes constant. For a constant contact angle, accelerating downward infiltration occurs only if the initial interface is not located at the tube inlet but further down the tube. For the special case in which the contact angle is constant, the liquid pressure at the tube inlet is equal to the gas pressure, and the interface is initially located at the tube inlet, our solution for upward infiltration is identical to a solution previously reported in the literature.
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
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
Characterizing mammography reports for health analytics.
Rojas, Carlos C; Patton, Robert M; Beckerman, Barbara G
2011-10-01
As massive collections of digital health data are becoming available, the opportunities for large-scale automated analysis increase. In particular, the widespread collection of detailed health information is expected to help realize a vision of evidence-based public health and patient-centric health care. Within such a framework for large scale health analytics we describe the transformation of a large data set of mostly unlabeled and free-text mammography data into a searchable and accessible collection, usable for analytics. We also describe several methods to characterize and analyze the data, including their temporal aspects, using information retrieval, supervised learning, and classical statistical techniques. We present experimental results that demonstrate the validity and usefulness of the approach, since the results are consistent with the known features of the data, provide novel insights about it, and can be used in specific applications. Additionally, based on the process of going from raw data to results from analysis, we present the architecture of a generic system for health analytics from clinical notes.
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.
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...
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.
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.
Analytical solution based on stream-aquifer interactions in partially penetrating streams
Directory of Open Access Journals (Sweden)
Yong Huang
2010-09-01
Full Text Available An analytical solution of drawdown caused by pumping is developed in an aquifer hydraulically connected to a finite-width stream on the condition of two streams. The proposed analytical solution modified Hunt’s analytical solution and not only considers the effect of stream width on drawdown, but also takes the distribution of drawdown on the interaction of two streams into account. Advantages of the solution include its simple structure, consisting of the Theis well function, parameters of aquifer and streambed semipervious material. The calculated results show that the proposed analytical solution agrees well with the previous solution and the errors between the two solutions are equal to zero on the condition of a stream without considering the effect of stream width. Also, deviations between the two analytical solutions increase with the increase of stream width. Furthermore, four cases are studied to discuss the effect of two streams on drawdown. It assumes that some parameters are changeable, and other parameters are constant, such as stream width, the distance between stream and pumping well, stream recharge rate, and the leakance coefficient of streambed semipervious material, etc. The analytical solution may provide estimates for parameters of aquifer and streambed semipervious material using the Type Curve Method through the data of field test.
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
Reporting low-level analytical data
African Journals Online (AJOL)
Meyer
negative, or zero, as the best estimate of the measured characteristic, usually concentration. ... This manner of reporting data near the limits of measurement can be independent ... Some common practices for reporting low-level results include:.
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.
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.
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.
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
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.
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.
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.
Analytical Solution of Smoluchowski Equations in Aggregation–Fragmentation Processes
Sekiyama, Makoto; Ohtsuki, Toshiya; Yamamoto, Hiroshi
2017-10-01
The z-transform technique is used to analyze Smoluchowski equations of aggregation-fragmentation processes where the selection of aggregation clusters, a decomposed cluster and a generated cluster is entirely random and independent of cluster size. An analytic form of asymptotic behavior for a cluster size distribution function is derived on the basis of approximation where lower-order terms in the average cluster size are neglected. The obtained results agree well with numerical ones.
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.
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)
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.
Commercial Lighting Solutions, Webtool Peer Review Report
Energy Technology Data Exchange (ETDEWEB)
Jones, Carol C.; Meyer, Tracy A.
2009-06-17
The Commercial Lighting Solutions (CLS) project directly supports the U.S. Department of Energy’s Commercial Building Energy Alliance efforts to design high performance buildings. CLS creates energy efficient best practice lighting designs for widespread use, and they are made available to users via an interactive webtool that both educates and guides the end user through the application of the Lighting Solutions. This report summarizes the peer review of the beta version of the CLS webtool, which contains retail box lighting solutions. The methodology for the peer review process included data collection (stakeholder input), analysis of the comments, and organization of the input into categories for prioritization of the comments against a set of criteria. Based on this process, recommendations were developed about which feedback should be addressed for the release of version 1.0 of the webtool at the Lightfair conference in New York City in May 2009. Due to the volume of data (~500 comments) the methodology for addressing the peer review comments was central to the success of the ultimate goal of improving the tool. The comments were first imported into a master spreadsheet, and then grouped and organized in several layers. Solutions to each comment were then rated by importance and feasibility to determine the practicality of resolving the concerns of the commenter in the short-term or long-term. The rating system was used as an analytical tool, but the results were viewed thoughtfully to ensure that they were not the sole the factor in determining which comments were recommended for near-term resolution. The report provides a list of the top ten most significant and relevant improvements that will be made within the webtool for version 1.0 as well as appendices containing the short-term priorities in additional detail. Peer review comments that are considered high priority by the reviewers and the CLS team but cannot be completed for Version 1.0 are listed as
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.
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.
The analytic continuation of solutions of the generalized axially symmetric Helmholtz equation
Millar, R. F.
1983-12-01
The analytic continuation of a solution of the generalized axially symmetric Helmholtz equation u xx + u yy + (2α/ x) u x + k 2 u = 0is examined. A representation in terms of boundary data and the complex Riemann function is given for the continuation of the solution to an analytic boundary value problem; this also provides the solution of the analytic Cauchy problem on an analytic arc. Integral representations are found for the Riemann function, and the axial behaviour of the Riemann function is determined and used to recover a representation for the solution in terms of analytic axial data, as given originally by Henrici. For an exterior boundary value problem in which the axial values of the solution are defined on two disjoint, semi-infinite segments of the axis, it is shown that the two functions are not analytic continuations of one an-other and that a certain linear combination of them is an entire function. As an example, for α = 1/2 it is shown that the continuation of an exterior solution for a prolate spheroidal boundary is logarithmically infinite on the interfocal segment. A further special case, one that involves wave scattering by slender bodies of revolution for which the solution may be represented as a superposition over axial singularities, is briefly examined; properties of the axial values which are forced by this representation are determined and, where comparison is possible, shown to be consistent with the present work.
Analytical Chemistry Laboratory progress report for FY 1985
Energy Technology Data Exchange (ETDEWEB)
Green, D.W.; Heinrich, R.R.; Jensen, K.J.
1985-12-01
The Analytical Chemistry Laboratory is a full-cost-recovery service center, with the primary mission of providing a broad range of technical support services to the scientific and engineering programs at ANL. In addition, ACL conducts a research program in analytical chemistry, works on instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL handles a wide range of analytical problems, from routine standard analyses to unique problems that require significant development of methods and techniques. The purpose of this report is to summarize the technical and administrative activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year 1985 (October 1984 through September 1985). This is the second annual report for the ACL. 4 figs., 1 tab.
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.
Lunin, Andrei; Grudiev, Alexej
2011-01-01
Analytical solutions are derived for transient and steady state gradient distributions in the travelling wave accelerating structures with arbitrary variation of parameters over the structure length. The results of both the unloaded and beam loaded cases are presented.
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.
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.
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.
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.
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.
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.
General scalar-tensor cosmology: analytical solutions via noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-02-15
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. (orig.)
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.
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.
An analytical approach to the solution of the transport equation for photons
Energy Technology Data Exchange (ETDEWEB)
Reichert, Janice Teresinha, E-mail: janice.reichert@gmail.com [Universidade Tecnologica Federal do Parana (UTFPR), Pato Branco, PR (Brazil); Barichello, Liliane Basso, E-mail: lbaric@mat.ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil)
2011-07-01
An analytical solution is developed to the one-dimensional transport equation for photons, for the case which includes spectral dependence. The Klein-Nishina kernel for Compton scattering is considered and an analytical discrete ordinates method, the ADO method, is used to solve the resulting angular dependent problem. Numerical simulations are performed to evaluate the buildup factor. (author)
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Silva, Milena W. Da; Vilhena, Marco T. de; Bodmann, Bardo E., E-mail: milena.wollmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardobodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Leite, Sergio B., E-mail: bogado@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RS (Brazil)
2013-07-01
In this work, we report on an analytical representation for the solution of the neutron point kinetics equation, free of stiffness and assuming that the reactivity is a continuous or sectionally continuous function of time. To this end, we cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix into a diagonal matrix plus a matrix that contains the remaining terms. Expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, allows one to construct a recursive system, in form of a first order matrix differential equation with source. The initialization of the recursion procedure is of diagonal form and has no source, but satisfies the initial conditions. The remaining equations are subject to null initial conditions and include the time dependent diagonal elements together with the off diagonal elements as a source term. The solution is obtained in analytical representation which may be evaluated for any time value, because it is free of stiffness. We present numerical simulations and comparisons against results from the literature, for a constant, a step, a ramp, a quadratic and sine shaped reactivity function. (author)
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
Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.
Building a SEM Analytics Reporting Portfolio
Goff, Jay W.; Williams, Brian G.; Kilgore, Wendy
2016-01-01
Effective strategic enrollment management (SEM) efforts require vast amounts of internal and external data to ensure that meaningful reporting and analysis systems can assist managers in decision making. A wide range of information is integral for leading effective and efficient student recruitment and retention programs. This article is designed…
Building a SEM Analytics Reporting Portfolio
Goff, Jay W.; Williams, Brian G.; Kilgore, Wendy
2016-01-01
Effective strategic enrollment management (SEM) efforts require vast amounts of internal and external data to ensure that meaningful reporting and analysis systems can assist managers in decision making. A wide range of information is integral for leading effective and efficient student recruitment and retention programs. This article is designed…
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.
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.
Engineering report (conceptual design) PFP solution stabilization
Energy Technology Data Exchange (ETDEWEB)
Witt, J.B.
1997-07-17
This Engineering Report (Conceptual Design) addresses remediation of the plutonium-bearing solutions currently in inventory at the Plutonium Finishing Plant (PFP). The recommendation from the Environmental Impact Statement (EIS) is that the solutions be treated thermally and stabilized as a solid for long term storage. For solutions which are not discardable, the baseline plan is to utilize a denitration process to stabilize the solutions prior to packaging for storage.
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.
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.
Analytical solution and meaning of feasible regions in two-component three-way arrays.
Omidikia, Nematollah; Abdollahi, Hamid; Kompany-Zareh, Mohsen; Rajkó, Róbert
2016-10-01
Although many efforts have been directed to the development of approximation methods for determining the extent of feasible regions in two- and three-way data sets; analytical determination (i.e. using only finite-step direct calculation(s) instead of the less exact numerical ones) of feasible regions in three-way arrays has remained unexplored. In this contribution, an analytical solution of trilinear decomposition is introduced which can be considered as a new direct method for the resolution of three-way two-component systems. The proposed analytical calculation method is applied to the full rank three-way data array and arrays with rank overlap (a type of rank deficiency) loadings in a mode. Close inspections of the analytically calculated feasible regions of rank deficient cases help us to make clearer the information gathered from multi-way problems frequently emerged in physics, chemistry, biology, agricultural, environmental and clinical sciences, etc. These examinations can also help to answer, e.g., the following practical question: "Is two-component three-way data with proportional loading in a mode actually a three-way data array?" By the aid of the additional information resulted from the investigated feasible regions of two-component three-way data arrays with proportional profile in a mode, reasons for the inadequacy of the seemingly trilinear data treatment methods published in the literature (e.g., U-PLS/RBL-LD that was used for extraction of quantitative and qualitative information reported by Olivieri et al. (Anal. Chem. 82 (2010) 4510-4519)) could be completely understood.
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.
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.
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.
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).
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...
Analytical Lie-algebraic solution of a 3D sound propagation problem in the ocean
Energy Technology Data Exchange (ETDEWEB)
Petrov, P.S., E-mail: petrov@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Prants, S.V., E-mail: prants@poi.dvo.ru [Il' ichev Pacific Oceanological Institute, 43 Baltiyskaya str., Vladivostok, 690041 (Russian Federation); Petrova, T.N., E-mail: petrova.tn@dvfu.ru [Far Eastern Federal University, 8 Sukhanova str., 690950, Vladivostok (Russian Federation)
2017-06-21
The problem of sound propagation in a shallow sea with variable bottom slope is considered. The sound pressure field produced by a time-harmonic point source in such inhomogeneous 3D waveguide is expressed in the form of a modal expansion. The expansion coefficients are computed using the adiabatic mode parabolic equation theory. The mode parabolic equations are solved explicitly, and the analytical expressions for the modal coefficients are obtained using a Lie-algebraic technique. - Highlights: • A group-theoretical approach is applied to a problem of sound propagation in a shallow sea with variable bottom slope. • An analytical solution of this problem is obtained in the form of modal expansion with analytical expressions of the coefficients. • Our result is the only analytical solution of the 3D sound propagation problem with no translational invariance. • This solution can be used for the validation of the numerical propagation models.
Analytical Chemistry Laboratory, progress report for FY 1993
Energy Technology Data Exchange (ETDEWEB)
1993-12-01
The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year (FY) 1993 (October 1992 through September 1993). This annual report is the tenth for the ACL and describes continuing effort on projects, work on new projects, and contributions of the ACL staff to various programs at ANL. The Analytical Chemistry Laboratory is a full-cost-recovery service center, with the primary mission of providing a broad range of analytical chemistry support services to the scientific and engineering programs at ANL. The ACL also has research programs in analytical chemistry, conducts instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL handles a wide range of analytical problems. Some routine or standard analyses are done, but it is common for the Argonne programs to generate unique problems that require development or modification of methods and adaption of techniques to obtain useful analytical data. The ACL is administratively within the Chemical Technology Division (CMT), its principal ANL client, but provides technical support for many of the technical divisions and programs at ANL. The ACL has four technical groups--Chemical Analysis, Instrumental Analysis, Organic Analysis, and Environmental Analysis--which together include about 45 technical staff members. Talents and interests of staff members cross the group lines, as do many projects within the ACL.
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.
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.
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.
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.
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.
Analytical Chemistry Laboratory progress report for FY 1999
Energy Technology Data Exchange (ETDEWEB)
Green, D. W.; Boparai, A. S.; Bowers, D. L.; Graczyk, D. G.
2000-06-15
This report summarizes the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year (FY) 1999 (October 1998 through September 1999). This annual progress report, which is the sixteenth in this series for the ACL, describes effort on continuing projects, work on new projects, and contributions of the ACL staff to various programs at ANL.
Analytical Chemistry Laboratory progress report for FY 1998.
Energy Technology Data Exchange (ETDEWEB)
Boparai, A. S.; Bowers, D. L.; Graczyk, D. G.; Green, D. W.; Lindahl, P. C.
1999-03-29
This report summarizes the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year (FY) 1998 (October 1997 through September 1998). This annual progress report, which is the fifteenth in this series for the ACL, describes effort on continuing projects, work on new projects, and contributions of the ACL staff to various programs at ANL.
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.
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)
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.
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...
Sanskrityayn, Abhishek; Suk, Heejun; Kumar, Naveen
2017-04-01
In this study, analytical solutions of one-dimensional pollutant transport originating from instantaneous and continuous point sources were developed in groundwater and riverine flow using both Green's Function Method (GFM) and pertinent coordinate transformation method. Dispersion coefficient and flow velocity are considered spatially and temporally dependent. The spatial dependence of the velocity is linear, non-homogeneous and that of dispersion coefficient is square of that of velocity, while the temporal dependence is considered linear, exponentially and asymptotically decelerating and accelerating. Our proposed analytical solutions are derived for three different situations depending on variations of dispersion coefficient and velocity, respectively which can represent real physical processes occurring in groundwater and riverine systems. First case refers to steady solute transport situation in steady flow in which dispersion coefficient and velocity are only spatially dependent. The second case represents transient solute transport in steady flow in which dispersion coefficient is spatially and temporally dependent while the velocity is spatially dependent. Finally, the third case indicates transient solute transport in unsteady flow in which both dispersion coefficient and velocity are spatially and temporally dependent. The present paper demonstrates the concentration distribution behavior from a point source in realistically occurring flow domains of hydrological systems including groundwater and riverine water in which the dispersivity of pollutant's mass is affected by heterogeneity of the medium as well as by other factors like velocity fluctuations, while velocity is influenced by water table slope and recharge rate. Such capabilities give the proposed method's superiority about application of various hydrological problems to be solved over other previously existing analytical solutions. Especially, to author's knowledge, any other solution doesn
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.
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.
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.
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.
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.
Analytical Chemistry Laboratory. Progress report for FY 1996
Energy Technology Data Exchange (ETDEWEB)
Green, D.W.; Boparai, A.S.; Bowers, D.L.
1996-12-01
The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year (FY) 1996. This annual report is the thirteenth for the ACL. It describes effort on continuing and new projects and contributions of the ACL staff to various programs at ANL. The ACL operates in the ANL system as a full-cost-recovery service center, but has a mission that includes a complementary research and development component: The Analytical Chemistry Laboratory will provide high-quality, cost-effective chemical analysis and related technical support to solve research problems of our clients -- Argonne National Laboratory, the Department of Energy, and others -- and will conduct world-class research and development in analytical chemistry and its applications. Because of the diversity of research and development work at ANL, the ACL handles a wide range of analytical chemistry problems. Some routine or standard analyses are done, but the ACL usually works with commercial laboratories if our clients require high-volume, production-type analyses. It is common for ANL programs to generate unique problems that require significant development of methods and adaption of techniques to obtain useful analytical data. Thus, much of the support work done by the ACL is very similar to our applied analytical chemistry research.
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.
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.
Analytical Chemistry Laboratory Progress Report for FY 1994
Energy Technology Data Exchange (ETDEWEB)
Green, D.W.; Boparai, A.S.; Bowers, D.L. [and others
1994-12-01
The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year (FY) 1994 (October 1993 through September 1994). This annual report is the eleventh for the ACL and describes continuing effort on projects, work on new projects, and contributions of the ACL staff to various programs at ANL. The Analytical Chemistry Laboratory is a full-cost-recovery service center, with the primary mission of providing a broad range of analytical chemistry support services to the scientific and engineering programs at ANL. The ACL also has a research program in analytical chemistry, conducts instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL handles a wide range of analytical problems. Some routine or standard analyses are done, but it is common for the Argonne programs to generate unique problems that require significant development of methods and adaption of techniques to obtain useful analytical data. The ACL has four technical groups -- Chemical Analysis, Instrumental Analysis, Organic Analysis, and Environmental Analysis -- which together include about 45 technical staff members. Talents and interests of staff members cross the group lines, as do many projects within the ACL. The Chemical Analysis Group uses wet- chemical and instrumental methods for elemental, compositional, and isotopic determinations in solid, liquid, and gaseous samples and provides specialized analytical services. Major instruments in this group include an ion chromatograph (IC), an inductively coupled plasma/atomic emission spectrometer (ICP/AES), spectrophotometers, mass spectrometers (including gas-analysis and thermal-ionization mass spectrometers), emission spectrographs, autotitrators, sulfur and carbon determinators, and a kinetic phosphorescence uranium analyzer.
Energy Technology Data Exchange (ETDEWEB)
St. John, C.M.
1977-04-01
An underground repository containing heat generating, High Level Waste or Spent Unreprocessed Fuel may be approximated as a finite number of heat sources distributed across the plane of the repository. The resulting temperature, displacement and stress changes may be calculated using analytical solutions, providing linear thermoelasticity is assumed. This report documents a computer program based on this approach and gives results that form the basis for a comparison between the effects of disposing of High Level Waste and Spent Unreprocessed Fuel.
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.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
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.
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.
Finite analytic numerical solution of heat transfer and flow past a square channel cavity
Chen, C.-J.; Obasih, K.
1982-01-01
A numerical solution of flow and heat transfer characteristics is obtained by the finite analytic method for a two dimensional laminar channel flow over a two-dimensional square cavity. The finite analytic method utilizes the local analytic solution in a small element of the problem region to form the algebraic equation relating an interior nodal value with its surrounding nodal values. Stable and rapidly converged solutions were obtained for Reynolds numbers ranging to 1000 and Prandtl number to 10. Streamfunction, vorticity and temperature profiles are solved. Local and mean Nusselt number are given. It is found that the separation streamlines between the cavity and channel flow are concave into the cavity at low Reynolds number and convex at high Reynolds number (Re greater than 100) and for square cavity the mean Nusselt number may be approximately correlated with Peclet number as Nu(m) = 0.365 Pe exp 0.2.
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.
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.
Analytical Chemistry Laboratory progress report for FY 1984
Energy Technology Data Exchange (ETDEWEB)
Green, D.W.; Heinrich, R.R.; Jensen, K.J.; Stetter, J.R.
1985-03-01
Technical and administrative activities of the Analytical Chemistry Laboratory (ACL) are reported for fiscal year 1984. The ACL is a full-cost-recovery service center, with the primary mission of providing a broad range of technical support services to the scientific and engineering programs at ANL. In addition, ACL conducts a research program in analytical chemistry, works on instrumental and methods development, and provides analytical services for governmental, educational, and industrial organizations. The ACL is administratively within the Chemical Technology Division, the principal user, but provides technical support for all of the technical divisions and programs at ANL. The ACL has three technical groups - Chemical Analysis, Instrumental Analysis, and Organic Analysis. Under technical activities 26 projects are briefly described. Under professional activities, a list is presented for publications and reports, oral presentations, awards and meetings attended. 6 figs., 2 tabs.
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 $\\ell=0$.
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.
On the Approximate Analytical Solution to Non-Linear Oscillation Systems
Directory of Open Access Journals (Sweden)
Mahmoud Bayat
2013-01-01
Full Text Available This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation of the Variational Approach (VA is presented to obtain highly accurate analytical solutions to free vibration of conservative oscillators with inertia and static type cubic nonlinearities. In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods.
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....
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 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.
Analytical self-dual solutions in a nonstandard Yang–Mills–Higgs scenario
Energy Technology Data Exchange (ETDEWEB)
Casana, R.; Ferreira, M.M. [Departamento de Física, Universidade Federal do Maranhão, 65085-580 São Luís, Maranhão (Brazil); Hora, E. da, E-mail: edahora.ufma@gmail.com [Departamento de Física, Universidade Federal do Maranhão, 65085-580 São Luís, Maranhão (Brazil); Santos, C. dos [Centro de Física e Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, 4169-007 Porto (Portugal)
2013-05-13
We have found analytical self-dual solutions within the generalized Yang–Mills–Higgs model introduced in R. Casana et al. (2012) [1]. 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.
Analytical self-dual solutions in a nonstandard Yang-Mills-Higgs scenario
Casana, R.; Ferreira, M. M.; da Hora, E.; dos Santos, C.
2013-05-01
We have found analytical self-dual solutions within the generalized Yang-Mills-Higgs model introduced in R. Casana et al. (2012) [1]. 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.
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.
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.
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.
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.
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.
Romano, Marcello
2012-01-01
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any...
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.
Analytical chemistry laboratory. Progress report for FY 1997
Energy Technology Data Exchange (ETDEWEB)
Green, D.W.; Boparai, A.S.; Bowers, D.L. [and others
1997-12-01
The purpose of this report is to summarize the activities of the Analytical Chemistry Laboratory (ACL) at Argonne National Laboratory (ANL) for Fiscal Year (FY) 1997 (October 1996 through September 1997). This annual progress report is the fourteenth in this series for the ACL, and it describes continuing effort on projects, work on new projects, and contributions of the ACL staff to various programs at ANL.
Hackmann, Eva
2015-01-01
The complete set of analytic solutions of the geodesic equation in a Schwarzschild--(anti-)de Sitter space--time is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. Using the analytical solution, the question whether the cosmological constant could be a cause of the Pioneer Anomaly is addressed. The periastron shift and its post--Schwarzschild limit is derived. The developed method can also be applied to the geodesic equation in higher dimensional Schwarzschild space--times.
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.
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.
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.
Gazzillo, Domenico; Giacometti, Achille
2004-03-08
We discuss structural and thermodynamical properties of Baxter's adhesive hard sphere model within a class of closures which includes the Percus-Yevick (PY) one. The common feature of all these closures is to have a direct correlation function vanishing beyond a certain range, each closure being identified by a different approximation within the original square-well region. This allows a common analytical solution of the Ornstein-Zernike integral equation, with the cavity function playing a privileged role. A careful analytical treatment of the equation of state is reported. Numerical comparison with Monte Carlo simulations shows that the PY approximation lies between simpler closures, which may yield less accurate predictions but are easily extensible to multicomponent fluids, and more sophisticate closures which give more precise predictions but can hardly be extended to mixtures. In regimes typical for colloidal and protein solutions, however, it is found that the perturbative closures, even when limited to first order, produce satisfactory results.
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.
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.
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)
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.
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.
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.
Analytical solutions for radiation-driven winds in massive stars. I. The fast regime
Energy Technology Data Exchange (ETDEWEB)
Araya, I.; Curé, M. [Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso Av. Gran Bretaña 1111, Casilla 5030, Valparaíso (Chile); Cidale, L. S., E-mail: ignacio.araya@uv.cl [Departamento de Espectroscopía, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata (UNLP), and Instituto de Astrofísica La Plata, CCT La Plata, CONICET-UNLP Paseo del Bosque S/N, 1900 La Plata (Argentina)
2014-11-01
Accurate mass-loss rate estimates are crucial keys in the study of wind properties of massive stars and for testing different evolutionary scenarios. From a theoretical point of view, this implies solving a complex set of differential equations in which the radiation field and the hydrodynamics are strongly coupled. The use of an analytical expression to represent the radiation force and the solution of the equation of motion has many advantages over numerical integrations. Therefore, in this work, we present an analytical expression as a solution of the equation of motion for radiation-driven winds in terms of the force multiplier parameters. This analytical expression is obtained by employing the line acceleration expression given by Villata and the methodology proposed by Müller and Vink. On the other hand, we find useful relationships to determine the parameters for the line acceleration given by Müller and Vink in terms of the force multiplier parameters.
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.
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.
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.
Bibi, Sameena; Qamar, Shamsul; Seidel-Morgenstern, Andreas
2015-03-13
This work is concerned with the analysis of models for linear reactive chromatography describing irreversible A→B and reversible A↔B reactions. In contrast to previously published results rectangular reactant pulses are injected into initially empty or pre-equilibrated columns assuming both Dirichlet and Danckwerts boundary conditions. The models consist of two partial differential equations, accounting for convection, longitudinal dispersion and first order chemical reactions. Due to the effect of involved mechanisms on solute transport, analytical and numerical solutions of the models could be helpful to understand, design and optimize chromatographic reactors. The Laplace transformation is applied to solve the model equations analytically for linear adsorption isotherms. Statistical temporal moments are derived from solutions in the Laplace domain. Analytical results are compared with numerical predictions generated using a high-resolution finite volume scheme for two sets of boundary conditions. Several case studies are carried out to analyze reactive liquid chromatographic processes for a wide range of mass transfer and reaction kinetics. Good agreements in the results validate the correctness of the analytical solutions and accuracy of the proposed numerical algorithm.
Analytical Solution of Coupled Laminar Heat-Mass Transfer in a Tube with Uniform Heat Flux
Institute of Scientific and Technical Information of China (English)
无
1992-01-01
Analytical solution is obtained of coupled laminar heat-mass transfer in a tube with uniform heat flux.This corresponds to the case when a layer of sublimable material is coated on the inner surface of a tube with its outer surface heated by uniform heat flux and this coated material will sublime as gas flows throught the tube.
Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method
Directory of Open Access Journals (Sweden)
De-Gang Wang
2012-01-01
Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.
Tang, Liguo; Wu, Zhaojun; Liu, Shengxing; Yang, Wuyi
2012-08-01
The objective of this study is to investigate the three-dimensional (3-D) analytical solution for transient guided wave propagation in liquid-filled pipe systems using the eigenfunction expansion method (EEM). The eigenfunctions corresponding to finite liquid-filled pipe systems with a traction-free lateral boundary and rigid smooth end boundaries are obtained. Additionally, the orthogonality of the eigenfunctions is proved in detail. Subsequently, the exact 3-D analytical transient response of finite liquid-filled pipe systems to external body forces is constructed using the EEM, based on which, the approximate 3-D analytical transient response of the systems to external surface forces is derived. Furthermore, the analytical solution for transient guided wave propagation in finite liquid-filled pipe systems is extended explicitly and concisely to infinite liquid-filled pipe systems. Several numerical examples are given to illustrate the analysis of the spatial and frequency distributions of the radial and axial displacement amplitudes of various guided wave modes; the numerical examples also simulate the transient displacement of the pipe wall and the transient pressure of the internal liquid from the present solution. The present solution can provide some theoretical guidelines for the guided wave nondestructive evaluation of liquid-filled pipes and the guided wave technique for downhole data transfer.
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
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...
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
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.
DEFF Research Database (Denmark)
Dinca, Andreea; Miclea, P. T.; Lupei, V.;
1998-01-01
The paper describes the application of the complete-admittance matching in the design of two dichroic mirrors. The matching stacks were analytically synthesized and all solutions with 1, 2 and 3 periods were investigated in order to obtain a large transmission band and preserve the high reflectan...
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.
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.
Hilpert, Markus
2009-09-01
We generalize Washburn's analytical solution for capillary flow in a horizontally oriented tube by accounting for a dynamic contact angle. We consider two general models for dynamic contact angle: the uncompensated Young force on the contact line depends on the capillary number in the form of either (1) a power law with exponent beta or (2) a power series. By considering the ordinary differential equation (ODE) for the velocity of the gas-liquid interface instead of the ODE for the interface position, we are able to derive new analytical solutions. For both dynamic contact angle models, we derive analytical solutions for the travel time of the gas-liquid interface as a function of interface velocity. The interface position as a function of time can be obtained through numerical integration. For the power law and beta=1 (an approximation of Cox's model for dynamic contact angle), we obtain an analytical solution for both interface position and velocity as a function of time. For the power law and beta=3, we can express the interface velocity as a function of time.
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.
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…
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…
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
Application of an analytical method for solution of thermal hydraulic conservation equations
Energy Technology Data Exchange (ETDEWEB)
Fakory, M.R. [Simulation, Systems & Services Technologies Company (S3 Technologies), Columbia, MD (United States)
1995-09-01
An analytical method has been developed and applied for solution of two-phase flow conservation equations. The test results for application of the model for simulation of BWR transients are presented and compared with the results obtained from application of the explicit method for integration of conservation equations. The test results show that with application of the analytical method for integration of conservation equations, the Courant limitation associated with explicit Euler method of integration was eliminated. The results obtained from application of the analytical method (with large time steps) agreed well with the results obtained from application of explicit method of integration (with time steps smaller than the size imposed by Courant limitation). The results demonstrate that application of the analytical approach significantly improves the numerical stability and computational efficiency.
Xu, Xiaonong; Lu, Dingwei; Xu, Xibin; Yu, Yang; Gu, Min
2017-09-01
The Halbach type hollow cylindrical permanent magnet array (HCPMA) is a volume compact and energy conserved field source, which have attracted intense interests in many practical applications. Here, using the complex variable integration method based on the Biot-Savart Law (including current distributions inside the body and on the surfaces of magnet), we derive analytical field solutions to an ideal multipole HCPMA in entire space including the interior of magnet. The analytic field expression inside the array material is used to construct an analytic demagnetization function, with which we can explain the origin of demagnetization phenomena in HCPMA by taking into account an ideal magnetic hysteresis loop with finite coercivity. These analytical field expressions and demagnetization functions provide deeper insight into the nature of such permanent magnet array systems and offer guidance in designing optimized array system.
Analytic solutions for seismic travel time and ray path geometry through simple velocity models.
Energy Technology Data Exchange (ETDEWEB)
Ballard, Sanford
2007-12-01
The geometry of ray paths through realistic Earth models can be extremely complex due to the vertical and lateral heterogeneity of the velocity distribution within the models. Calculation of high fidelity ray paths and travel times through these models generally involves sophisticated algorithms that require significant assumptions and approximations. To test such algorithms it is desirable to have available analytic solutions for the geometry and travel time of rays through simpler velocity distributions against which the more complex algorithms can be compared. Also, in situations where computational performance requirements prohibit implementation of full 3D algorithms, it may be necessary to accept the accuracy limitations of analytic solutions in order to compute solutions that satisfy those requirements. Analytic solutions are described for the geometry and travel time of infinite frequency rays through radially symmetric 1D Earth models characterized by an inner sphere where the velocity distribution is given by the function V (r) = A-Br{sup 2}, optionally surrounded by some number of spherical shells of constant velocity. The mathematical basis of the calculations is described, sample calculations are presented, and results are compared to the Taup Toolkit of Crotwell et al. (1999). These solutions are useful for evaluating the fidelity of sophisticated 3D travel time calculators and in situations where performance requirements preclude the use of more computationally intensive calculators. It should be noted that most of the solutions presented are only quasi-analytic. Exact, closed form equations are derived but computation of solutions to specific problems generally require application of numerical integration or root finding techniques, which, while approximations, can be calculated to very high accuracy. Tolerances are set in the numerical algorithms such that computed travel time accuracies are better than 1 microsecond.
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo;
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which ...... is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....
Energy Technology Data Exchange (ETDEWEB)
Moawad, S. M., E-mail: smmoawad@hotmail.com [Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef (Egypt)
2015-02-15
In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.
A study of nonlinear radiation damping by matching analytic and numerical solutions
Anderson, J. L.; Hobill, D. W.
1988-04-01
In the present use of a mixed analytic-numerical matching scheme to study a linear oscillator that is coupled to a nonlinear field, the approximate causal solution constructed in the radiation zone was matched to a finite-differencing scheme-derived numerical solution in the inner zone. The required agreement of the two solutions in the overlap region permitted the extension of the numerical scheme arbitrarily into the future. The late time behavior of the system in all studied cases was independent of initial conditions. The linearized 'monopole energy loss' formula breaks down in cases of either fast motions or strong nonlinearities.
Institute of Scientific and Technical Information of China (English)
刘林; C.K.Shum
2000-01-01
The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for0< e< 1, where e is the orbital eccentricity of the orbiter. in the solution, it is as-sumed that the rotation of the central body is slow, and its astronomical background is clear. Examples for such planets in the solar system are Ven黶 and Mercury. The perturbation solution is tested numer-ically on two Venusian orbiters with eccentric orbits, PVO and Magellan, and found to be effective.
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
2008-01-01
Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.
A New Homotopy Analysis Method for Approximating the Analytic Solution of KdV Equation
Directory of Open Access Journals (Sweden)
Vahid Barati
2014-01-01
Full Text Available In this study a new technique of the Homotopy Analysis Method (nHAM is applied to obtain an approximate analytic solution of the well-known Korteweg-de Vries (KdV equation. This method removes the extra terms and decreases the time taken in the original HAM by converting the KdV equation to a system of first order differential equations. The resulted nHAM solution at third order approximation is then compared with that of the exact soliton solution of the KdV equation and found to be in excellent agreement.
Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
El-Amin, Mohamed
2017-07-06
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0＜e＜1,where e is the orbital eccentricity of the orbiter.In the solution,it is assumed that the rotation of the central body is slow,and its astronomical background is clear.Examples for such planets in the solar system are Venus and Mercury.The perturbation solution is tested numerically on two Venusian orbiters with eccentric orbits,PVO and Magellan,and found to be effective.
Directory of Open Access Journals (Sweden)
Mohsen Alipour
2013-01-01
Full Text Available We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs. In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD, and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI. The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Institute of Scientific and Technical Information of China (English)
G. Darmani; S. Setayeshi; H. Ramezanpour
2012-01-01
In this paper an efficient computational method based on extending the sensitivity approach （SA） is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations （DDEs）, the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach.
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 solution and optimal design for galloping-based piezoelectric energy harvesters
Tan, T.; Yan, Z.
2016-12-01
The performance of the galloping-based piezoelectric energy harvester is usually investigated numerically. Instead of performing case studies by numerical simulations, analytical solutions of the nonlinear distributed parameter model are derived to capture the intrinsic effects of the physical parameters on the performance of such energy harvesters. The analytical solutions are confirmed with the numerical solutions. Optimal performance of such energy harvesters is therefore revealed theoretically. The electric damping due to the electromechanical coupling is defined. The design at the optimal electrical damping with smaller onset speed to galloping, higher harvested power, and acceptable tip displacement is superior than the design at the maximal electrical damping, as long as the optimal electrical damping can be achieved. Otherwise, the design at the maximal electrical damping should be then adopted. As the wind speed and aerodynamic empirical coefficients increase, the tip displacement and harvested power increase. This study provides a theoretical design and optimization procedure for galloping-based piezoelectric energy harvesters.
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.
Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport
Energy Technology Data Exchange (ETDEWEB)
Litvinenko, Yuri E.; Effenberger, Frederic, E-mail: yuril@waikato.ac.nz [Department of Mathematics, University of Waikato, P.B. 3105 Hamilton (New Zealand)
2014-12-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Baseline configuration for GNSS attitude determination with an analytical least-squares solution
Chang, Guobin; Xu, Tianhe; Wang, Qianxin
2016-12-01
The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however an analytical solution can exist for specific baseline configurations. The main aim of this work is to design this class of configurations. Both single and double difference measurements are treated which refer to the dedicated and non-dedicated receivers respectively. More realistic error models are employed in which the correlations between different measurements are given full consideration. The desired configurations are worked out. The configurations are rotation and scale equivariant and can be applied to both the dedicated and non-dedicated receivers. For these configurations, the analytical and optimal solution for the attitude is also given together with its error variance-covariance matrix.
An analytical solution for transient radial flow through unsaturated fractured porous media
Energy Technology Data Exchange (ETDEWEB)
Wu, Yu-Shu; Pan, Lehua
2004-02-13
This paper presents analytical solutions for one-dimensional radial transient flow through horizontal, unsaturated fractured rock formation. In these solutions, unsaturated flow through fractured media is described by a linearized Richards' equation, while fracture-matrix interaction is handled using the dual-continuum concept. Although linearizing Richards' equation requires a specially correlated relationship between relative permeability and capillary pressure functions for both fractures and matrix, these specially formed relative permeability and capillary pressure functions are still physically meaningful. These analytical solutions can thus be used to describe the transient behavior of unsaturated flow in fractured media under the described model conditions. They can also be useful in verifying numerical simulation results, which, as demonstrated in this paper, are otherwise difficult to validate.
Lindén, Fredrik; Zettergren, Henning
2016-01-01
We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.
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.
An Analytical Solution by HAM for Nonlinear Simulation of Deepwater SCR Installation
Directory of Open Access Journals (Sweden)
Yi Wang
2014-01-01
Full Text Available Steel catenary riser (SCR is a cost-effective riser system that is widely used in deepwater offshore oilfields development. During SCR J-lay installation, the movement of pull-head must be carefully controlled to ensure riser safety. Since the SCR installation path calculation through numerical simulation software is usually time-consuming, this paper has established a mechanical model for SCR installation by making use of homotopy analysis method (HAM to simplify its analytical solution, and dimensional analysis was considered in making initial guess solution. Based on this analytical solution, a program within the framework of MATLAB was developed to predict the two-dimensional riser behavior during installation, and a sensitivity analysis for different values of the control variables was carried out. Engineers may efficiently optimize the installation path by the application of this technique.
Caciotta, G
2016-01-01
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem, due to the intrinsic hyperbolicity of the Einstein equations. The magnitude of this region depends only on suitable $H_s$ Sobolev norms of the initial data for a fixed $s\\leq 7$ and if the initial data are sufficiently small the analytic solution is global. In a previous paper, hereafter "I", we have described a geometric way of writing the vacuum Einstein equations for the characteristic problems we are considering and a local solution in a suitable "double null cone gauge" characterized by the use of a double null cone foliation of the spacetime.
A transversely localized light in a waveguide: the analytical solution and its potential application
Arslanov, Narkis M.; Moiseev, Sergey A.; Kamli, Ali A.
2017-02-01
Investigation of light in waveguide structures is a topical modern problem that has long-standing historical roots. A parallel-plate waveguide is a basic model in these studies and is intensively used in numerous investigations of nano-optics, integrated circuits and nanoplasmonics. In this letter we have first found an approximate analytical solution which describes the light modes with high accuracy in the subwavelength waveguides. The solution provides a way of obtaining a clear understanding of the light properties within the broadband spectral range in the waveguide with various physical parameters. The potential of the analytical solution for studies of light fields in the waveguides of nano-optics and nanoplasmonics has also been discussed.
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...
A fractional model to describe the Brownian motion of particles and its analytical solution
Directory of Open Access Journals (Sweden)
Jing-Jing Yao
2015-12-01
Full Text Available In this article, we apply a relatively modified analytic iterative method for solving a time-fractional Fokker–Planck equation subject to given constraints. The utilized method is a numerical technique based on the generalization of residual error function and then applying the generalized Taylor series formula. This method can be used as an alternative to obtain analytic solutions of different types of fractional partial differential equations such as Fokker–Planck equation applied in mathematics, physics, and engineering. The solutions of our equation are calculated in the form of a rapidly convergent series with easily computable components. The validity, potentiality, and practical usefulness of the proposed method have been demonstrated by applying it to several numerical examples. The results reveal that the proposed methodology is very useful and simple in determination of solution of the Fokker–Planck equation of fractional order.
Jin, Congrui; Davoodabadi, Ali; Li, Jianlin; Wang, Yanli; Singler, Timothy
2017-03-01
Due to the development of novel micro-fabrication techniques to produce ultra-thin materials and increasing interest in thin biological membranes, in recent years, the mechanical characterization of thin films has received a significant amount of attention. To provide a more accurate solution for the relationship among contact radius, load and deflection, the fundamental and widely applicable problem of spherical indentation of a freestanding circular membrane have been revisited. The work presented here significantly extends the previous contributions by providing an exact analytical solution to the governing equations of Föppl-Hecky membrane indented by a frictionless spherical indenter. In this study, experiments of spherical indentation has been performed, and the exact analytical solution presented in this paper is compared against experimental data from existing literature as well as our own experimental results.
Kostanyan, Artak E
2015-08-07
In closed-loop recycling (CLR) chromatography, the effluent from the outlet of a column is directly returned into the column through the sample feed line and continuously recycled until the required separation is reached. To select optimal operating conditions for the separation of a given feed mixture, an appropriate mathematical description of the process is required. This work is concerned with the analysis of models for the CLR separations. Due to the effect of counteracting mechanisms on separation of solutes, analytical solutions of the models could be helpful to understand and optimize chromatographic processes. The objective of this work was to develop analytical expressions to describe the CLR counter-current (liquid-liquid) chromatography (CCC). The equilibrium dispersion and cell models were used to describe the transport and separation of solutes inside a CLR CCC column. The Laplace transformation is applied to solve the model equations. Several possible CLR chromatography methods for the binary and complex mixture separations are simulated.
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
Full Text Available Though methods and algorithms in numerical analysis are not new, they have become increasingly popular with the development of high speed computing capabilities. Indeed, the ready availability of high speed modern digital computers and easy-to-employ powerful software packages has had a major impact on science, engineering education and practice in the recent past. Researchers in the past had to depend on analytical skills to solve significant engineering problems but, nowadays, researchers have access to tremendous amount of computation power under their fingertips, and they mostly require understanding the physical nature of the problem and interpreting the results. For some problems, several approximate analytical solutions already exist for simple cases but finding new solution to complex problems by designing and developing novel techniques and algorithms are indeed a great challenging task to give approximate solutions and sufficient accuracy especially for engineering purposes. In particular, it is frequently assumed that deriving an analytical solution for any problem is simpler than obtaining a numerical solution for the same problem. But in most of the cases relationships between numerical and analytical solutions complexities are exactly opposite to each other. In addition, analytical solutions are limited to relatively simple problems while numerical ones can be obtained for complex realistic situations. Indeed, analytical solutions are very useful for testing (benchmarking numerical codes and for understanding principal physical controls of complex processes that are modeled numerically. During the recent past, in order to overcome some numerical difficulties a variety of numerical approaches were introduced, such as the finite difference methods (FDM, the finite element methods (FEM, and other alternative methods. Numerical methods typically include material on such topics as computer precision, root finding techniques, solving
Castro López, R.; Sun, Guo-Hua; Camacho-Nieto, O.; Yáñez-Márquez, C.; Dong, Shi-Hai
2017-09-01
We present analytical matter-wave solutions to a generalized Gross-Pitaevskii (GGP) equation with several new time and space varying nonlinearity coefficients and external fields. This is realized by taking a suitable similarity transformation to the GGP equation which makes the original partial differential equation into a stationary and ordinary differential equation. We report a few families of analytical solutions of the GGP equation with several new time and space varying nonlinearity interactions, in which some physically relevant soliton solutions are found. The profile features of the evolution wave functions depend on the different choices of the composite functions ξ.
Analytical Solutions of a Nonlinear Convection-Diﬀusion Equation With Polynomial Sources
Directory of Open Access Journals (Sweden)
N. A. Kudryashov
2016-01-01
Full Text Available Nonlinear convection–diﬀusion equations are widely used for the description of various processes and phenomena in physics, mechanics and biology. In this work we consider a family of nonlinear ordinary diﬀerential equations which is a traveling wave reduction of a nonlinear convection–diﬀusion equation with a polynomial source. We study a question about integrability of this family of nonlinear ordinary diﬀerential equations. We consider both stationary and non–stationary cases of this equation with and without convection. In order to construct general analytical solutions of equations from this family we use an approach based on nonlocal transformations which generalize the Sundman transformations. We show that in the stationary case without convection the general analytical solution of the considered family of equations can be constructed without any constraints on its parameters and can be expressed via the Weierstrass elliptic function. Since in the general case this solution has a cumbersome form we ﬁnd some correlations on the parameters which allow us to construct the general solution in the explicit form. We show that in the non–stationary case both with and without convection we can ﬁnd a general analytical solution of the considered equation only imposing some correlation on the parameters. To this aim we use criteria for the integrability of the Lienard equation which have recently been obtained. We ﬁnd explicit expressions in terms of exponential and elliptic functions for the corresponding analytical solutions.
Energy Technology Data Exchange (ETDEWEB)
Finger, S.M.; De Avila, J.C.; Keith, V.F.
1996-08-01
The Road Transportable Analytical Laboratory (RTAL) provides a portabler laboratory for the analysis of soils, ground water, and surface water. This report presents data from a soils sample TCLP VOA and SVOA report, aqueous sample RCRA metals report, soils sample total and isotopic uranium report, SVOA sample analytical performance report, and and RCRA metal sample analytical performance report.
An analytical dynamo solution for large-scale magnetic fields of galaxies
Chamandy, Luke
2016-11-01
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, parametrized 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 α-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 on to galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure data sets. Further, we explore the properties of our numerical solutions, and their dependence on certain parameter values. We illustrate and assess the degree to which numerical solutions based on various levels of approximation, common in the dynamo literature, agree with one another.
Comparison of input parameters regarding rock mass in analytical solution and numerical modelling
Yasitli, N. E.
2016-12-01
Characteristics of stress redistribution around a tunnel excavated in rock are of prime importance for an efficient tunnelling operation and maintaining stability. As it is a well known fact that rock mass properties are the most important factors affecting stability together with in-situ stress field and tunnel geometry. Induced stresses and resultant deformation around a tunnel can be approximated by means of analytical solutions and application of numerical modelling. However, success of these methods depends on assumptions and input parameters which must be representative for the rock mass. However, mechanical properties of intact rock can be found by laboratory testing. The aim of this paper is to demonstrate the importance of proper representation of rock mass properties as input data for analytical solution and numerical modelling. For this purpose, intact rock data were converted into rock mass data by using the Hoek-Brown failure criterion and empirical relations. Stress-deformation analyses together with yield zone thickness determination have been carried out by using analytical solutions and numerical analyses by using FLAC3D programme. Analyses results have indicated that incomplete and incorrect design causes stability and economic problems in the tunnel. For this reason during the tunnel design analytical data and rock mass data should be used together. In addition, this study was carried out to prove theoretically that numerical modelling results should be applied to the tunnel design for the stability and for the economy of the support.
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.
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.
Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
Camporeale, E; MacDonald, E A
2015-01-01
We study the steady-state expansion of a collisionless, electrostatic, quasi-neutral plasma plume into vacuum, with a fluid model. We analyze approximate semi-analytical solutions, that can be used in lieu of much more expensive numerical solutions. In particular, we focus on the earlier studies presented in Parks and Katz (1979), Korsun and Tverdokhlebova (1997), and Ashkenazy and Fruchtman (2001). By calculating the error with respect to the numerical solution, we can judge the range of validity for each solution. Moreover, we introduce a generalization of earlier models that has a wider range of applicability, in terms of plasma injection profiles. We conclude by showing a straightforward way to extend the discussed solutions to the case of a plasma plume injected with non-null azimuthal velocity.
El-Ajou, Ahmad; Arqub, Omar Abu; Momani, Shaher
2015-07-01
In this paper, explicit and approximate solutions of the nonlinear fractional KdV-Burgers equation with time-space-fractional derivatives are presented and discussed. The solutions of our equation are calculated in the form of rabidly convergent series with easily computable components. The utilized method is a numerical technique based on the generalized Taylor series formula which constructs an analytical solution in the form of a convergent series. Five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method. Graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution. The results reveal that the method is very effective and simple in determination of solution of the fractional KdV-Burgers equation.
Commercial Lighting Solutions Webtool Peer Review Report, Office Solutions
Energy Technology Data Exchange (ETDEWEB)
Beeson, Tracy A.; Jones, Carol C.
2010-02-01
The Commercial Lighting Solutions (CLS) project directly supports the U.S. Department of Energy’s Commercial Building Energy Alliance efforts to design high performance buildings. CLS creates energy efficient best practice lighting designs for widespread use, and they are made available to users via an interactive webtool that both educates and guides the end user through the application of the Lighting Solutions. This report summarizes the peer review of the CLS webtool for offices. The methodology for the peer review process included data collection (stakeholder input), analysis of the comments, and organization of the input into categories for prioritization of the comments against a set of criteria. Based on this process, recommendations were developed for the release of version 2.0 of the webtool at the Lightfair conference in Las Vegas in May 2010. The report provides a list of the top ten most significant and relevant improvements that will be made within the webtool for version 2.0 as well as appendices containing the comments and short-term priorities in additional detail. Peer review comments that are considered high priority by the reviewers and the CLS team but cannot be completed for Version 2.0 are listed as long-term recommendations.
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.
Akbar, Fathan
2016-01-01
In this paper we examine more deeply about the bending mechanism of rod-shaped fireworks which burned from the free end. We derived new analytic equations. Surprisingly, we obtained the bending patterns are similar to the cornu spiral. With a few simple steps we proved that positions of points throughout the fireworks are given by Fresnel integrals, C(x) and S(x), which are generally found in phenomena of electromagnetic wave diffraction. Although we deeply discussed bending of fireworks rods, however the proposed method is likely to explain any phenomena in nature related to an evolving length scale associated with some material that becomes progressively stiff or dry, such as the growth of resin exuded from trees.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
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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.
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.
Optomechanically induced carrier-envelope-phase-dependent effects and their analytical solutions
Ma, Jinyong; Gan, Jinghui; Guccione, Giovanni; Campbell, Geoff T.; Buchler, Ben C.; Lü, Xinyou; Wu, Ying; Lam, Ping Koy
2017-06-01
To date, investigations of carrier-envelope-phase (CEP)-dependent effects have been limited to optical pulses with few cycles and high intensity and have not been reported for other types of pulses. Optomechanical systems are shown to have the potential to go beyond these limits. We present an approach using optomechanics to extend the concept of the traditional CEP in the few-cycle regime to mechanical pulses and develop a two-step model to give a physical insight. By adding an auxiliary continuous optical field, we show that a CEP-dependent effect appears even in the multicycle regime of mechanical pulses. We obtain the approximated analytical solutions providing full understanding for these optomechanically induced CEP-dependent effects. In addition, our findings show that one can draw on the optomechanical interaction to revive the CEP-dependent effects on optical pulses with an arbitrary number of cycles and without specific intensity requirements. The effects of CEP, broadly extended to encompass few- and multicycle optical and mechanical pulses, may stimulate a variety of applications in the preparation of a CEP-stabilized pulse, the generation of ultrasonic pulses with a desired shape, the linear manipulation of optical combs, and more.
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.
ANALYTICAL SOLUTION FOR BENDING BEAM SUBJECT TO LATERAL FORCE WITH DIFFERENT MODULUS
Institute of Scientific and Technical Information of China (English)
姚文娟; 叶志明
2004-01-01
A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.
Mathias, S. A.; Hardisty, P. E.; Trudell, M. R.; Zimmerman, R. W.
2008-12-01
If geo-sequestration of CO2 is to be employed as a key greenhouse gas reduction method in the global effort to mitigate climate change, simple yet robust methods must be available to help design and monitor injection into saline aquifers. There has been significant development of simple analytical and semi-analytical techniques to support screening analysis and performance assessment for potential carbon sequestration sites. These techniques have generally been used to estimate the size of CO2 plumes for the purpose of leakage rate estimation. A common assumption of previous has been that both the fluids and the geological formation are incompressible. Consequently, calculation of pressure distribution requires the specification of an arbitrary radius of influence. In the present work, we relax this restriction by incorporating fluid and formation compressibility into our governing equations. These equations are transformed into ordinary differential equations using a similarity transformation, and are then solved using the method of matched asymptotic expansions. By allowing for compressibility in the fluids and formation, the solutions improve on previous work by not requiring the specification of an arbitrary radius of influence. Our solution is also capable of accounting for non-Darcy inertial effects modeled by the Forchheimer equation. These analytical solutions are validated by comparison with finite difference solutions. Our analysis leads to a simple yet highly accurate algebraic equation for estimating the evolution of a CO2 plume, and the associated pressure buildup, as a function of time.
New Analytic Solution to the Lane-Emden Equation of Index 2
Directory of Open Access Journals (Sweden)
S. S. Motsa
2012-01-01
Full Text Available We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986 which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.
Analytic solutions for links and triangles distributions in finite Barabási-Albert networks
Ferreira, Ricardo M.; de Almeida, Rita M. C.; Brunnet, Leonardo G.
2017-01-01
Barabási-Albert model describes many different natural networks, often yielding sensible explanations to the subjacent dynamics. However, finite size effects may prevent from discerning among different underlying physical mechanisms and from determining whether a particular finite system is driven by Barabási-Albert dynamics. Here we propose master equations for the evolution of the degrees, links and triangles distributions, solve them both analytically and by numerical iteration, and compare with numerical simulations. The analytic solutions for all these distributions predict the network evolution for systems as small as 100 nodes. The analytic method we developed is applicable for other classes of networks, representing a powerful tool to investigate the evolution of natural networks.
Two dimensional analytical solution for a partially vegetated compound channel flow
Institute of Scientific and Technical Information of China (English)
HUAI Wen-xin; XU Zhi-gang; YANG Zhong-hua; ZENG Yu-hong
2008-01-01
The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item. The compound channel is di- vided into 3 sub-regions in the transverse direction, and the coefficients in every region's differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vege- tated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical so- lution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.
Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem
Younis, Mohammad I.
2014-08-17
We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a 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 in the literature 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 approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.
Indian Academy of Sciences (India)
Jianping Shi; Jibin Li; Shumin Li
2013-11-01
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations.
Pauritsch, Marcus; Birk, Steffen; Hergarten, Stefan; Kellerer-Pirklbauer, Andreas; Winkler, Gerfried
2014-05-01
Rock glaciers as aquifer systems in alpine catchments may strongly influence the hydrological characteristics of these catchments. Thus, they have a high impact on the ecosystem and potential natural hazards such as for example debris flow. Therefore, knowledge of the hydrodynamic processes, internal structure and properties of these aquifers is important for resource management and risk assessment. The investigation of such aquifers often turns out to be expensive and technically complicated because of their strongly limited accessibility. Analytical solutions of discharge recession provide a quick and easy way to estimate aquifer parameters. However, due to simplifying assumptions the validity of the interpretation is often questionable. In this study we compared results of an analytical solution of discharge recessions with results based on a numerical model. This was done in order to analyse the range of uncertainties and the applicability of the analytical method in alpine catchment areas. The research area is a 0.76 km² large catchment in the Seckauer Tauern Range, Austria. The dominant aquifer in this catchment is a rock glacier, namely the Schöneben Rock Glacier. This relict rock glacier (i.e. containing no permafrost at present) covers an area of 0.11 km² and is drained by one spring at the rock glacier front. The rock glacier consists predominantly of gneissic sediments (mainly coarse-grained, blocky at the surface) and extends from 1720 to 1905 m a.s.l.. Discharge of the rock glacier spring is automatically measured since 2002. Electric conductivity and water temperature is monitored since 2008. An automatic weather station was installed in 2011 in the central part of the catchment. Additionally data of geophysical surveys (refraction seismic and ground penetrating radar) have been used to analyse the base slope and inner structure of the rock glacier. The measured data are incorporated into a numerical model implemented in MODFLOW. The numerical
Analytical Solution for the Size of the Minimum Dominating Set in Complex Networks
Nacher, Jose C
2016-01-01
Domination is the fastest-growing field within graph theory with a profound diversity and impact in real-world applications, such as the recent breakthrough approach that identifies optimized subsets of proteins enriched with cancer-related genes. Despite its conceptual simplicity, domination is a classical NP-complete decision problem which makes analytical solutions elusive and poses difficulties to design optimization algorithms for finding a dominating set of minimum cardinality in a large network. Here we derive for the first time an approximate analytical solution for the density of the minimum dominating set (MDS) by using a combination of cavity method and Ultra-Discretization (UD) procedure. The derived equation allows us to compute the size of MDS by only using as an input the information of the degree distribution of a given network.
Sakamoto, Y.; Vodenska, I.
2016-09-01
We investigate the Japanese banking crisis in the late 1990s with a simple network based mathematical model, which allows us to simulate the crisis as well as to obtain new perspective through analytic solution of our network model. We effectively identify the actual bankrupted banks and the robustness of the banking system using a simulation model based on properties of a bi-partite bank-asset network. We show the mean time property and analytical solution of the model revealing aggregate time dynamics of bank asset prices throughout the banking crisis. The results disclose simple but fundamental property of asset growth, instrumental for understanding the bank crisis. We also estimate the selling pressure for each asset type, derived from a Cascading Failure Model (CFM), offering new perspective for investigating the phenomenon of banking crisis.
An analytical solution for VOCs emission from multiple sources/sinks in buildings
Institute of Scientific and Technical Information of China (English)
DENG BaoQing; YU Bo; Chang Nyung KIM
2008-01-01
An analytical solution is presented to describe the emission/sorption of volatile organic compounds (VOCs) from/on multiple single-layer materials coexisting in buildings. The diffusion of VOCs within each material is described by a transient diffusion equation. All diffusion equations are coupled with each other through the equation of mass conservation in the air. The analytical solution is validated by the experimental data in literature, Compared to the one-material case, the coexistence of multiple materials may decrease the emission rate of VOCs from each material. The smaller the diffusion coef-ficient is, the more the emission rate decreases. Whether a material is a source or a sink in the case of multiple materials coexisting is not affected by the diffusion coefficient. For the case of multiple mate-rials with different partition coefficients, a material with a high partition coefficient may become a sink. This may promote the emission of VOCs from other materials.
An analytical solution for the model of drug distribution and absorption in small intestine
Mingyu, Xu
1990-11-01
According to the physiological and anatomical characteristics of small intestine, neglecting the effect of its motility on the distribution and absorption of drug and nutrient, Y. Miyamoto et al.[1] proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drug by numerical analysis. In this paper, we give a steady state analytical solution of the above model including deactivation term. The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence provides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.
An analytical solution describing the shape of a yield stress material subjected to an overpressure
DEFF Research Database (Denmark)
Hovad, Emil; Spangenberg, Jon; Larsen, P.;
2016-01-01
Many fluids and granular materials are able to withstand a limited shear stress without flowing. These materials are known as yields stress materials. Previously, an analytical solution was presented to quantify the yield stress for such materials. The yields stress is obtained based on the density...... as well as the spread length and height of the material when deformed in a box due to gravity. In the present work, the analytical solution is extended with the addition of an overpressure that acts over the entire body of the material. This extension enables finding the shape of a yield stress material...... with known density and yield stress when for instance deformed under water or subjected to a forced air pressure....
Modeling of the anode side of a direct methanol fuel cell with analytical solutions
Mosquera, Martín A
2010-01-01
In this work, analytical solutions were derived (for any methanol oxidation reaction order) for the profiles of methanol concentration and proton current density by assuming diffusion mass transport mechanism, Tafel kinetics, and fast proton transport in the anodic catalyst layer of a direct methanol fuel cell. An expression for the Thiele modulus that allows to express the anodic overpotential as a function of the cell current, and kinetic and mass transfer parameters was obtained. For high cell current densities, it was found that the Thiele modulus ($\\phi^2$) varies quadratically with cell current density; yielding a simple correlation between anodic overpotential and cell current density. Analytical solutions were derived for the profiles of both local methanol concentration in the catalyst layer and local anodic current density in the catalyst layer. Under the assumptions of the model presented here, in general, the local methanol concentration in the catalyst layer cannot be expressed as an explicit fun...
Axially symmetric static sources: A general framework and some analytical solutions
Herrera, L; Ibañez, J; Ospino, J
2013-01-01
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed with axial symmetry. The structure scalars are calculated and the inhomogeneity factors are identified. Finally some exact analytical solutions were found. One of these solutions describes an incompressible spheroid with isotropic pressure and becomes the well known interior Schwarzschild solution in the spherically symmetric limit, however it cannot be matched smoothly to any Weyl exterior metric. Another family of solutions was found that corresponds to an anisotropic fluid distribution and can in principle be matched to a Weyl exterior.
Unified Analytical Solution for Radial Flow to a Well in a Confined Aquifer
Mishra, Phoolendra Kumar
2011-01-01
Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper [1967]; Hantush [1964] when the pumping well has no wellbore storage; Theis [1935] when both conditions are fulfilled and Yang et.al. [2006] when the pumping well is partially penetrating, has finite radius but lacks storage. We use our solution to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells.
Institute of Scientific and Technical Information of China (English)
CHEN Jiang-ying; CHEN Wei-qiu
2007-01-01
The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media.The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.
AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION
Directory of Open Access Journals (Sweden)
Giorgio Baiamonte
2010-03-01
Full Text Available This paper deals with the analytical solution of kinematic wave equations for overland flow occurring in an infiltrating hillslope. The infiltration process is described by the Green-Ampt model. The solution is derived only for the case of an intermediate flow regime between laminar and turbulent ones. A transitional regime can be considered a reliable flow condition when, to the laminar overland flow, is also associated the effect of the additional resistance due to raindrop impact. With reference to the simple case of an impervious hillslope, a comparison was carried out between the present solution and the non-linear storage model. Some applications of the present solution were performed to investigate the effect of main parameter variability on the hillslope response. Particularly, the effect of hillslope geometry and rainfall intensity on the time to equilibrium is shown.
Solitary waves and their stability in colloidal media: semi-analytical solutions
Marchant, T R
2012-01-01
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas compressibility. Semi-analytical solutions, for both one and two spatial dimensions, are derived using an averaged Lagrangian and suitable trial functions for the solitary waves. Power versus propagation constant curves and neutral stability curves are obtained for both cases, which illustrate that multiple solution branches occur for both the one and two dimensional geometries. For the one-dimensional case it is found that three solution branches (with a bistable regime) occur, while for the two-dimensional case two solution branches (with a single stable branch) occur in the limit of low background packing fractions. For high background packing fractions the power versus propagation constant curves are monotonic and the solitary waves stable for all parameter values. Comparisons are mad...
Analytic rotating black-hole solutions in N-dimensional f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Nashed, G.G.L. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Cairo (Egypt); Ain Shams University, Faculty of Science, Mathematics Department, Cairo (Egypt); Egyptian Relativity Group (ERG), Cairo (Egypt); El Hanafy, W. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, Cairo (Egypt); Egyptian Relativity Group (ERG), Cairo (Egypt)
2017-02-15
A non-diagonal vielbein ansatz is applied to the N-dimension field equations of f(T) gravity. An analytical vacuum solution is derived for the quadratic polynomial f(T)=T+εT{sup 2} and an inverse relation between the coupling constant ε and the cosmological constant Λ. Since the induced metric has off-diagonal components, it cannot be removed by a mere coordinate transformation, the solution has a rotating parameter. The curvature and torsion scalars invariants are calculated to study the singularities and horizons of the solution. In contrast to general relativity, the Cauchy horizon differs from the horizon which shows the effect of the higher order torsion. The general expression of the energy-momentum vector of f(T) gravity is used to calculate the energy of the system. Finally, we have shown that this kind of solution satisfies the first law of thermodynamics in the framework of f(T) gravitational theories. (orig.)
Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits
Sochi, Taha
2015-01-01
In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.
Analytic rotating black-hole solutions in N-dimensional f( T) gravity
Nashed, G. G. L.; El Hanafy, W.
2017-02-01
A non-diagonal vielbein ansatz is applied to the N-dimension field equations of f( T) gravity. An analytical vacuum solution is derived for the quadratic polynomial f(T)=T+ɛ T^2 and an inverse relation between the coupling constant ɛ and the cosmological constant Λ . Since the induced metric has off-diagonal components, it cannot be removed by a mere coordinate transformation, the solution has a rotating parameter. The curvature and torsion scalars invariants are calculated to study the singularities and horizons of the solution. In contrast to general relativity, the Cauchy horizon differs from the horizon which shows the effect of the higher order torsion. The general expression of the energy-momentum vector of f( T) gravity is used to calculate the energy of the system. Finally, we have shown that this kind of solution satisfies the first law of thermodynamics in the framework of f( T) gravitational theories.
Yan, Xin; Liang, Lan-Ju; Ding, Xin; Yao, Jian-Quan
2017-02-01
A high-sensitivity sensing technique was demonstrated based on a flexible terahertz dual-band metamaterial absorber. The absorber has two perfect absorption peaks, one with a fundamental resonance (f1) of the structure and another with a high-order resonance (f2) originating from the interactions of adjacent unit cells. The quality factor (Q) and figure of merit of f2 are 6 and 14 times larger than that of f1, respectively. For the solid analyte, the changes in resonance frequency are monitored upon variation of analyte thickness and index; a linear relation between the amplitude absorption with the analyte thickness is achieved for f2. The sensitivity (S) is 31.2% refractive index units (RIU-1) for f2 and 13.7% RIU-1 for f1. For the aqueous solutions, the amplitude of absorption decreases linearly with increasing the dielectric constant for the ethanol-water mixture of f1. These results show that the designed absorber cannot only identify a solid analyte but also characterize aqueous solutions through the frequency shift and amplitude absorption. Therefore, the proposed absorber is promising for future applications in high-sensitivity monitoring biomolecular, chemical, ecological water systems, and aqueous biosystems.
Benchmark of ASTRA with Analytical Solution for the Longitudinal Plasma Oscillation Problem
Geloni, Gianluca; Schneidmiller, Evgeny A; Yurkov, Mikhail V
2004-01-01
During the design of X-FELs, space-charge codes are required to simulate the evolution of longitudinal plasma oscillation within an electron beam in connection with LSC microbunching instability [1] and certain pump-probe synchronization schemes [2]. In the paper [3] we presented an analytical solution to the initial value problem for longitudinal plasma oscillation in an electron beam. Such a result, besides its theoretical importance, allows one to benchmark space-charge simulation programs against a self-consistent solution of the evolution problem. In this paper we present a comparison between our results [3] and the outcomes of the simulation code ASTRA.
Analytic Solution for Tachyon Condensation in Berkovits' Open Superstring Field Theory
Erler, Theodore
2013-01-01
We present an analytic solution for tachyon condensation on a non-BPS D-brane in Berkovits' open superstring field theory. The solution is presented as a product of $2\\times 2$ matrices in two distinct $GL_2$ subgroups of the open string star algebra. All string fields needed for for computation of the nonpolynomial action can be derived in closed form, and the action produces the expected non-BPS D-brane tension in accordance with Sen's conjecture. We also comment on how D-brane charges may be encoded in the topology of the tachyon vacuum gauge orbit.
Functions of diffraction correction and analytical solutions in nonlinear acoustic measurement
Alliès, Laurent; Nadi, M
2008-01-01
This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction applied to fundamental, makes it possible to obtain simple solutions for the second harmonic of the average acoustic pressure, but sufficiently precise for measuring the parameter of nonlinearity B/A in a finite amplitude method. Comparison with other expressions requiring numerical integration, show the solutions are precise in the nearfield.
Semi analytical solution of second order fuzzy Riccati equation by homotopy perturbation method
Jameel, A. F.; Ismail, Ahmad Izani Md
2014-07-01
In this work, the Homotopy Perturbation Method (HPM) is formulated to find a semi-analytical solution of the Fuzzy Initial Value Problem (FIVP) involving nonlinear second order Riccati equation. This method is based upon homotopy perturbation theory. This method allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily calculated. The effectiveness of the algorithm is demonstrated by solving nonlinear second order fuzzy Riccati equation. The results indicate that the method is very effective and simple to apply.
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.
A new analytic solution for 2nd-order Fermi acceleration
Mertsch, Philipp
2011-01-01
A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments.
Analytical solution to the Riemann problem of 1D elastodynamics with general constitutive laws
Berjamin, H; Chiavassa, G; Favrie, N
2016-01-01
Under the hypothesis of small deformations, the equations of 1D elastodynamics write as a 2 x 2 hyperbolic system of conservation laws. Here, we study the Riemann problem for convex and nonconvex constitutive laws. In the convex case, the solution can include shock waves or rarefaction waves. In the nonconvex case, compound waves must also be considered. In both convex and nonconvex cases, a new existence criterion for the initial velocity jump is obtained. Also, admissibility regions are determined. Lastly, analytical solutions are completely detailed for various constitutive laws (hyperbola, tanh and polynomial), and reference test cases are proposed.
Analytical solution for a class of linear quadratic open-loop Nash game with multiple players
Institute of Scientific and Technical Information of China (English)
Xiaohong NIAN; Zhisheng DUAN; Wenyan TANG
2006-01-01
In this paper, the Nash equilibria for differential games with multiple players is studied. A method for solving the Riccati-type matrix differential equations for open-loop Nash strategy in linear quadratic game with multiple players is presented and analytical solution is given for a type of differential games in which the system matrixcan be diagonalizable. As the special cases, the Nash equilibria for some type of differential games with particular structure is studied also, and some results in previous literatures are extended. Finally, a numerical example is given to illustrate the effectiveness of the solution procedure.
Indian Academy of Sciences (India)
Ali S Wadi; Mourad F Dimian; Fayez N Ibrahim
2014-08-01
We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0. The variation of (, ) with the time from = 0 up to → ∞ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.
An analytical solution to contaminant transport through composite liners with geomembrane defects
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
To investigate the performance of landfill composite liner system,a one-dimensional model was developed for solute transport through composite liners containing geomembrane defects.An analytical solution to the model was obtained by the method of Laplace transformation.The results obtained by the presented solution agree well with those obtained by the numerical method.Results show that leachate head and construction quality of geomembrane(GM) have significant influences on the performance of the composite liners for heavy metal ions.The breakthrough time of lead decreases from 50 a to 19 a when the leachate head increases from 0.3 m to 10 m.It is also indicated that the contaminant mass flux of volatile organic compounds(VOCs) induced by leakage can not be neglected in case of poor construction quality of the landfill barrier system.It is shown that diffusion coefficient and partition coefficient of GM have great influences on solute transport through composite liners for VOCs.The breakthrough time of heavy metal ions will be greatly overestimated if the effects of diffusion and adsorption of clay and geosynthetic clay liner(GCL) are neglected.The composite liner consisting of a geomembrane and a GCL provides a poor barrier for VOCs.The presented analytical solution is relatively simple to apply and can be used for preliminary design of composite liners,evaluating experimental results,and verifying more complex numerical models.
Analytical solution for the vertical profile of daily production in the ocean
Kovač, Žarko; Platt, Trevor; Sathyendranath, Shubha; Morović, Mira
2016-05-01
Photosynthesis parameters are routinely estimated from in vitro measurements of primary production under constant light reaching each incubation bottle, by fitting a photosynthesis-irradiance function to the measurements. Here we take one such function and integrate it in time for variable light input, similar to natural conditions, to obtain the analytical solution for the vertical profile of daily phytoplankton production in the field. This solution is then fitted to in situ measurements of primary production profiles in the same manner as a photosynthesis-irradiance function is fitted to in vitro measurements under controlled and constant light conditions to retrieve the photosynthesis-irradiance parameters. The method is tested on the Hawaii Ocean Time-series data set. The solution explained 97.88% of the variance in measured normalized production at individual depths. The recovered parameters were then used to model the normalized daily water-column production. The model explained 99.21% of variance in normalized watercolumn production of the entire data set. The seasonal cycle of the photosynthesis parameters recovered with the analytical solution was further studied for the Hawaii Ocean Time-series. With respect to the photosynthesis parameter determination, the solution bridges the gap between classical photosynthesis-irradiance measurements under controlled light conditions and in situ measurements which are made under natural, variable light conditions. It presents a new tool for the estimation of photosynthesis parameters from in situ measurements of primary production.
Huang, Junqi; Goltz, Mark N.
2017-06-01
To greatly simplify their solution, the equations describing radial advective/dispersive transport to an extraction well in a porous medium typically neglect molecular diffusion. While this simplification is appropriate to simulate transport in the saturated zone, it can result in significant errors when modeling gas phase transport in the vadose zone, as might be applied when simulating a soil vapor extraction (SVE) system to remediate vadose zone contamination. A new analytical solution for the equations describing radial gas phase transport of a sorbing contaminant to an extraction well is presented. The equations model advection, dispersion (including both mechanical dispersion and molecular diffusion), and rate-limited mass transfer of dissolved, separate phase, and sorbed contaminants into the gas phase. The model equations are analytically solved by using the Laplace transform with respect to time. The solutions are represented by confluent hypergeometric functions in the Laplace domain. The Laplace domain solutions are then evaluated using a numerical Laplace inversion algorithm. The solutions can be used to simulate the spatial distribution and the temporal evolution of contaminant concentrations during operation of a soil vapor extraction well. Results of model simulations show that the effect of gas phase molecular diffusion upon concentrations at the extraction well is relatively small, although the effect upon the distribution of concentrations in space is significant. This study provides a tool that can be useful in designing SVE remediation strategies, as well as verifying numerical models used to simulate SVE system performance.
Directory of Open Access Journals (Sweden)
Constantin Bota
2014-01-01
Full Text Available The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.
ANALYTICAL SOLUTION OF THE K-TH ORDER AUTONOMOUS ORDINARY DIFFERENTIAL EQUATION
Directory of Open Access Journals (Sweden)
Ronald Orozco López
2017-04-01
Full Text Available The main objective of this paper is to find the analytical solution of the autonomous equation y(k = f (y and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.
Analytical solution of precessional switching in nanomagnets driven by hard-axis field pulses
Energy Technology Data Exchange (ETDEWEB)
D' Aquino, M., E-mail: daquino@uniparthenope.it [Engineering Department, University of Naples “Parthenope”, 80143 Naples (Italy); Perna, S.; Serpico, C. [DIETI, University of Naples Federico II, 80125 Naples (Italy); Bertotti, G. [Istituto Nazionale di Ricerca Metrologica, 10135 Torino (Italy); Mayergoyz, I.D. [ECE Department and UMIACS, University of Maryland, College Park, MD, 20742 (United States); Quercia, A. [DIETI, University of Naples Federico II, 80125 Naples (Italy)
2016-04-01
The precessional switching process of a magnetic nanoparticle subject to external field pulses applied along the hard-axis is considered. The critical field pulse amplitude necessary to realize the switching is determined. Then, the analytical solution of magnetization switching dynamics is derived in the lossless limit by using elliptic functions. Moreover, expressions for the field pulse duration tolerances which guarantee successful switching are also obtained. The theoretical predictions are verified by macrospin numerical simulations of ultra-fast magnetization switching.
A multigroup radiation diffusion test problem: Comparison of code results with analytic solution
Energy Technology Data Exchange (ETDEWEB)
Shestakov, A I; Harte, J A; Bolstad, J H; Offner, S R
2006-12-21
We consider a 1D, slab-symmetric test problem for the multigroup radiation diffusion and matter energy balance equations. The test simulates diffusion of energy from a hot central region. Opacities vary with the cube of the frequency and radiation emission is given by a Wien spectrum. We compare results from two LLNL codes, Raptor and Lasnex, with tabular data that define the analytic solution.
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.
Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits
Sochi, Taha
2015-01-01
In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing th...
Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A
2016-03-01
Additive manufacturing (AM) has enabled fabrication of open-cell porous biomaterials based on repeating unit cells. The micro-architecture of the porous biomaterials and, thus, their physical properties could then be precisely controlled. Due to their many favorable properties, porous biomaterials manufactured using AM are considered as promising candidates for bone substitution as well as for several other applications in orthopedic surgery. The mechanical properties of such porous structures including static and fatigue properties are shown to be strongly dependent on the type of the repeating unit cell based on which the porous biomaterial is built. In this paper, we study the mechanical properties of porous biomaterials made from a relatively new unit cell, namely truncated cube. We present analytical solutions that relate the dimensions of the repeating unit cell to the elastic modulus, Poisson's ratio, yield stress, and buckling load of those porous structures. We also performed finite element modeling to predict the mechanical properties of the porous structures. The analytical solution and computational results were found to be in agreement with each other. The mechanical properties estimated using both the analytical and computational techniques were somewhat higher than the experimental data reported in one of our recent studies on selective laser melted Ti-6Al-4V porous biomaterials. In addition to porosity, the elastic modulus and Poisson's ratio of the porous structures were found to be strongly dependent on the ratio of the length of the inclined struts to that of the uninclined (i.e. vertical or horizontal) struts, α, in the truncated cube unit cell. The geometry of the truncated cube unit cell approaches the octahedral and cube unit cells when α respectively approaches zero and infinity. Consistent with those geometrical observations, the analytical solutions presented in this study approached those of the octahedral and cube unit cells when
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
Analytical Solutions of Ionic Diffusion and Heat Conduction in Multilayered Porous Media
Directory of Open Access Journals (Sweden)
Yu Bai
2015-01-01
Full Text Available Ionic diffusion and heat conduction in a multiple layered porous medium have many important engineering applications. One of the examples is the chloride ions from deicers penetrating into concrete structures such as bridge decks. Different overlays can be placed on top of concrete surface to slowdown the chloride penetration. In this paper, the chloride ion diffusion equations were established for concrete structures with multiple layers of protective system. By using Laplace transformation, an analytical solution was developed first for chloride concentration profiles in two-layered system and then extended to multiple layered systems with nonconstant boundary conditions, including the constant boundary and linear boundary conditions. Because ionic diffusion in saturated media and heat conduction are governed by the same form of partial differential equations with different materials parameters, the analytical solution was further extended to handle heat conduction in a multiple layered system under nonconstant boundary conditions. The numerical results were compared with available test data. The basic trends of the analytical solution and the test data agreed quite well.
An explicit closed-form analytical solution for European options under the CGMY model
Chen, Wenting; Du, Meiyu; Xu, Xiang
2017-01-01
In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump Le´vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This "globalness" of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.
Directory of Open Access Journals (Sweden)
Santosh Soni
2011-12-01
Full Text Available OnTARGET and MAP are examples of analytics-based solutions that were designed from the outset to address specific business challenges in the broad area of sales force productivity. Although they address different underlying issues, these solutions implement a common approach that is generally applicable to a broad class of operational challenges. Both solutions rely on rigorously defined data models that integrate all relevant data into a common database. Choices of the data to be included in the data model are driven both by end-user requirements as well as the need for relevant inputs to analytical models. Both business problems have a natural mapping to applications of predictive modeling: predicting the probability to purchase in the case of OnTARGET, and estimating the realistic revenue opportunity in the case of MAP. Delivering the underlying data and the analytic insights directly to frontline decision makers (sales representatives for OnTARGET and sales executives for MAP is crucial to driving business impact, and a significant effort has been invested in developing efficient web-based tools with the necessary supporting infrastructure. In this paper we discuss several aspects and analyze them.
Directory of Open Access Journals (Sweden)
Santosh Soni
2011-09-01
Full Text Available OnTARGET and MAP are examples of analytics-based solutions that were designed from the outset to address specific business challenges in the broad area of sales force productivity. Although they address different underlying issues, these solutions implement a common approach that is generally applicable to a broad class of operational challenges. Both solutions rely on rigorously defined data models that integrate all relevant data into a common database. Choices of the data to be included in the data model are driven both by end-user requirements as well as the need for relevant inputs to analytical models. Both business problems have a natural mapping to applications of predictive modeling: predicting the probability to purchase in the case of OnTARGET, and estimating the realistic revenue opportunity in the case of MAP. Delivering the underlying data and the analytic insights directly to frontline decision makers (sales representatives for OnTARGET and sales executives for MAP is crucial to driving business impact, and a significant effort has been invested in developing efficient web-based tools with the necessary supporting infrastructure. In this paper we discuss several aspects and analyze them.
Cubic autocatalysis in a reaction-diffusion annulus: semi-analytical solutions
Alharthi, M. R.; Marchant, T. R.; Nelson, M. I.
2016-06-01
Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction-diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feature of this geometry is the effect, of varying the width of the annulus, on the static and dynamic multiplicity. The results show that for a thicker annulus, Hopf bifurcations and multiple steady-state solutions occur in a larger portion of parameter space. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with numerical solutions of the governing partial differential equations.
Big data analytics as a service infrastructure: challenges, desired properties and solutions
Martín-Márquez, Manuel
2015-12-01
CERN's accelerator complex generates a very large amount of data. A large volumen of heterogeneous data is constantly generated from control equipment and monitoring agents. These data must be stored and analysed. Over the decades, CERN's researching and engineering teams have applied different approaches, techniques and technologies for this purpose. This situation has minimised the necessary collaboration and, more relevantly, the cross data analytics over different domains. These two factors are essential to unlock hidden insights and correlations between the underlying processes, which enable better and more efficient daily-based accelerator operations and more informed decisions. The proposed Big Data Analytics as a Service Infrastructure aims to: (1) integrate the existing developments; (2) centralise and standardise the complex data analytics needs for CERN's research and engineering community; (3) deliver real-time, batch data analytics and information discovery capabilities; and (4) provide transparent access and Extract, Transform and Load (ETL), mechanisms to the various and mission-critical existing data repositories. This paper presents the desired objectives and properties resulting from the analysis of CERN's data analytics requirements; the main challenges: technological, collaborative and educational and; potential solutions.
Hayek, Mohamed; Kosakowski, Georg; Jakob, Andreas; Churakov, Sergey V.
2012-03-01
One of the challenging problems in mathematical geosciences is the determination of analytical solutions of nonlinear partial differential equations describing transport processes in porous media. We are interested in diffusive transport coupled with precipitation-dissolution reactions. Several numerical computer codes that simulate such systems have been developed. Analytical solutions, if they exist, represent an important tool for verification of numerical solutions. We present a methodology for deriving such analytical solutions that are exact and explicit in space and time variables. They describe transport of several aqueous species coupled to precipitation and dissolution of a single mineral in one, two, and three dimensions. As an application, we consider explicit analytical solutions for systems containing one or two solute species that describe the evolution of solutes and solid concentrations as well as porosity. We use one of the proposed analytical solutions to test numerical solutions obtained from two conceptually different reactive transport codes. Both numerical implementations could be verified with the help of the analytical solutions and show good agreement in terms of spatial and temporal evolution of concentrations and porosities.
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
Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil
2012-10-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.
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.
An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures
Amadei, B.; Savage, W.Z.
2001-01-01
We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.
Danish, Mohammad; Kumar, Shashi; Kumar, Surendra
2012-03-01
Exact analytical solutions for the velocity profiles and flow rates have been obtained in explicit forms for the Poiseuille and Couette-Poiseuille flow of a third grade fluid between two parallel plates. These exact solutions match well with their numerical counter parts and are better than the recently developed approximate analytical solutions. Besides, effects of various parameters on the velocity profile and flow rate have been studied.
Hilpert, Markus
2010-11-01
In a preceding paper, we derived analytical solutions for the displacement of a gas by a liquid in horizontal and inclined capillary tubes where the tube inlet is connected to a liquid reservoir of constant pressure. We considered quite general models for the dynamic contact angle and were able to derive implicit equations for the velocity of the gas-liquid interface. These solutions allowed us to identify five different flow scenarios for liquid withdrawal that differed in the direction of flow and the sign of the acceleration of the gas-liquid interface. In this paper, we consider the special case where the dynamic contact angle is determined by a nonequilibrium Young force that depends linearly on the capillary number. Thus we can derive explicit and the more traditional implicit analytical solutions for both the position and the velocity of the gas-liquid interface. We also construct diagrams that allow us to predict which of the five flow scenarios will occur depending on the nondimensional parameters that define the problem. The diagrams can be combined with diagrams previously obtained for infiltration and the entire parameter space subdivided into regions that are associated with either liquid withdrawal, liquid infiltration, or metastable and stable equilibrium states. Our solutions are also valid within the limit where the contact angle is constant.
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...
Allen, Jeffrey S
2003-05-15
An analytical solution to the capillary equation of Young and Laplace is derived that allows determination of the static contact angle based on the volume of a sessile drop and the wetted area of the substrate. This solution does not require numerical integration to determine the drop profile and accounts for surface deformation due to gravitational effects. Calculation of the static contact angle by this method is remarkably simple and accurate when the contact angle is less than 30 degrees. A natural scaling arises in the solution, which provides indication of when a drop is small enough so as to neglect gravitational influences on the surface shape which, for small contact angles, is generally less than 1 microl. The technique described has the simplicity of the spherical cap approximation but remains accurate for any size of sessile drop.
Real analytic solutions for marginal deformations in open superstring field theory
Okawa, Yuji
2007-09-01
We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction.
Real analytic solutions for marginal deformations in open superstring field theory
Okawa, Yuji
2007-01-01
We construct analytic solutions for marginal deformations satisfying the reality condition in open superstring field theory formulated by Berkovits when operator products made of the marginal operator and the associated superconformal primary field are regular. Our strategy is based on the recent observation by Erler that the problem of finding solutions for marginal deformations in open superstring field theory can be reduced to a problem in the bosonic theory of finding a finite gauge parameter for a certain pure-gauge configuration labeled by the parameter of the marginal deformation. We find a gauge transformation generated by a real gauge parameter which infinitesimally changes the deformation parameter and construct a finite gauge parameter by its path-ordered exponential. The resulting solution satisfies the reality condition by construction.
Adhesive-bonded double-lap joints. [analytical solutions for static load carrying capacity
Hart-Smith, L. J.
1973-01-01
Explicit analytical solutions are derived for the static load carrying capacity of double-lap adhesive-bonded joints. The analyses extend the elastic solution Volkersen and cover adhesive plasticity, adherend stiffness imbalance and thermal mismatch between the adherends. Both elastic-plastic and bi-elastic adhesive representations lead to the explicit result that the influence of the adhesive on the maximum potential bond strength is defined uniquely by the strain energy in shear per unit area of bond. Failures induced by peel stresses at the ends of the joint are examined. This failure mode is particularly important for composite adherends. The explicit solutions are sufficiently simple to be used for design purposes
Analytical solution of the problem of the rise of a Taylor bubble
Zudin, Yuri B.
2013-05-01
In the classical works of Prandtl and Taylor devoted to the analysis of the problem of the rise of a Taylor bubble in a round tube, a solution of the Laplace equation is used, which contains divergent infinite series. The present paper outlines a method for the correct analysis of the mentioned problem. Using the method of superposition of "elementary flows," a solution was obtained for flow of an ideal fluid over a body of revolution in a pipe. Satisfying the free surface condition in the vicinity of the stagnation point and using the limiting transition with respect to the main parameter lead to the relation for the rise velocity of a Taylor bubble expressed in terms of the Froude number. In order to validate the method of superposition, it was applied to the problem of the rise of a plane Taylor bubble in a flat gap, which also has an exact analytical solution obtained with the help of the complex variable theory.
Directory of Open Access Journals (Sweden)
Essam R. El-Zahar
2016-01-01
Full Text Available A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM. First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.
Solved problems in classical mechanics analytical and numerical solutions with comments
de Lange, O L
2010-01-01
Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...
Hilpert, Markus
2009-09-01
In a recent paper, we generalized Washburn's analytical solution for capillary flow in a horizontally oriented tube by accounting for a dynamic contact angle. In this paper, we derive solutions for flow in inclined tubes that account for gravity. We again consider two general models for dynamic contact angle: the uncompensated Young force on the contact line depends on the capillary number in the form of (1) a power law with exponent beta, or (2) a polynomial. A dimensional analysis shows that, aside from the parameters for the model for the uncompensated Young force, the problem is defined through four nondimensional parameters: (1) the advancing equilibrium contact angle, (2) the initial contact angle, (3) a Bond number, and (4) nondimensional liquid pressure at the tube inlet relative to the constant gas pressure. For both contact angle models, we derive analytical solutions for the travel time of the gas-liquid interface as a function of interface velocity. The interface position as a function of travel time can be obtained through numerical integration. For the power law and beta=1 (an approximation of Cox's model for dynamic contact angle), we obtain an analytical solution for travel time as a function of interface position, as Washburn did for constant contact angle. Four different flow scenarios may occur: the interface moves (1) upward and approaches the height of capillary rise, (2) downward with the steady-state velocity, (3) downward while approaching the steady-state velocity from an initially higher velocity, or (4) downward while approaching the steady-state velocity from an initially smaller velocity.
Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals
Indian Academy of Sciences (India)
X Wang; E Pan
2008-05-01
We study some typical defect problems in one-dimensional (1D) hexagonal and two-dimensional (2D) octagonal quasicrystals. The first part of this investigation addresses in detail a uniformly moving screw dislocation in a 1D hexagonal piezoelectric quasicrystal with point group 6. A general solution is derived in terms of two functions 1, 2, which satisfy wave equations, and another harmonic function 3. Elementary expressions for the phonon and phason displacements, strains, stresses, electric potential, electric fields and electric displacements induced by the moving screw dislocation are then arrived at by employing the obtained general solution. The derived solution is verified by comparison with existing solutions. Also obtained in this part of the investigation is the total energy of the moving screw dislocation. The second part of this investigation is devoted to the study of the interaction of a straight dislocation with a semi-infinite crack in an octagonal quasicrystal. Here the crack penetrates through the solid along the period direction and the dislocation line is parallel to the period direction. We first derive a general solution in terms of four analytic functions for plane strain problem in octagonal quasicrystals by means of differential operator theory and the complex variable method. All the phonon and phason displacements and stresses can be expressed in terms of the four analytic functions. Then we derive the exact solution for a straight dislocation near a semi-infinite crack in an octagonal quasicrystal, and also present the phonon and phason stress intensity factors induced by the straight dislocation and remote loads.
Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals
Wang, X.; Pan, E.
2008-05-01
We study some typical defect problems in one-dimensional (1D) hexagonal and two-dimensional (2D) octagonal quasicrystals. The first part of this investigation addresses in detail a uniformly moving screw dislocation in a 1D hexagonal piezoelectric quasicrystal with point group 6mm. A general solution is derived in terms of two functions \\varphi_1, \\varphi_2, which satisfy wave equations, and another harmonic function \\varphi_3. Elementary expressions for the phonon and phason displacements, strains, stresses, electric potential, electric fields and electric displacements induced by the moving screw dislocation are then arrived at by employing the obtained general solution. The derived solution is verified by comparison with existing solutions. Also obtained in this part of the investigation is the total energy of the moving screw dislocation. The second part of this investigation is devoted to the study of the interaction of a straight dislocation with a semi-infinite crack in an octagonal quasicrystal. Here the crack penetrates through the solid along the period direction and the dislocation line is parallel to the period direction. We first derive a general solution in terms of four analytic functions for plane strain problem in octagonal quasicrystals by means of differential operator theory and the complex variable method. All the phonon and phason displacements and stresses can be expressed in terms of the four analytic functions. Then we derive the exact solution for a straight dislocation near a semi-infinite crack in an octagonal quasicrystal, and also present the phonon and phason stress intensity factors induced by the straight dislocation and remote loads.
Schulreich, Michael Mathias
2011-01-01
Aims: Bow shock waves are a common feature of groups and clusters of galaxies since they are generated as a result of supersonic motion of galaxies through the intergalactic medium. The goal of this work is to present an analytical solution technique for such astrophysical hypersonic blunt body problems. Methods: A method, developed by Schneider (1968, JFM, 31, 397) in the context of aeronautics, allows calculation of the galaxy's shape as long as the shape of the bow shock wave is known (so-called inverse method). In contrast to other analytical models, the solution is valid in the whole flow region (from the stagnation point up to the bow shock wings) and in particular takes into account velocity gradients along the streamlines. We compare our analytical results with two-dimensional hydrodynamical simulations carried out with an extended version of the VH-1 hydrocode which is based on the piecewise parabolic method with a Lagrangian remap. Results: It is shown that the applied method accurately predicts the...
Catalytic mechanism in cyclic voltammetry at disc electrodes: an analytical solution.
Molina, Angela; González, Joaquín; Laborda, Eduardo; Wang, Yijun; Compton, Richard G
2011-08-28
The theory of cyclic voltammetry at disc electrodes and microelectrodes is developed for a system where the electroactive reactant is regenerated in solution using a catalyst. This catalytic process is of wide importance, not least in chemical sensing, and it can be characterized by the resulting peak current which is always larger than that of a simple electrochemical reaction; in contrast the reverse peak is always relatively diminished in size. From the theoretical point of view, the problem involves a complex physical situation with two-dimensional mass transport and non-uniform surface gradients. Because of this complexity, hitherto the treatment of this problem has been tackled mainly by means of numerical methods and so no analytical expression was available for the transient response of the catalytic mechanism in cyclic voltammetry when disc electrodes, the most popular practical geometry, are used. In this work, this gap is filled by presenting an analytical solution for the application of any sequence of potential pulses and, in particular, for cyclic voltammetry. The induction principle is applied to demonstrate mathematically that the superposition principle applies whatever the geometry of the electrode, which enabled us to obtain an analytical equation valid whatever the electrode size and the kinetics of the catalytic reaction. The theoretical results obtained are applied to the experimental study of the electrocatalytic Fenton reaction, determining the rate constant of the reduction of hydrogen peroxide by iron(II).
Analytic solutions for colloid transport with time- and depth-dependent retention in porous media
Leij, Feike J.; Bradford, Scott A.; Sciortino, Antonella
2016-12-01
Elucidating and quantifying the transport of industrial nanoparticles (e.g. silver, carbon nanotubes, and graphene oxide) and other colloid-size particles such as viruses and bacteria is important to safeguard and manage the quality of the subsurface environment. Analytic solutions were derived for aqueous and solid phase colloid concentrations in a porous medium where colloids were subject to advective transport and reversible time and/or depth-dependent retention. Time-dependent blocking and ripening retention were described using a Langmuir-type equation with a rate coefficient that respectively decreased and increased linearly with the retained concentration. Depth-dependent retention was described using a rate coefficient that is a power-law function of distance. The stream tube modeling concept was employed to extend these analytic solutions to transport scenarios with two different partitioning processes (i.e., two types of retention sites). The sensitivity of concentrations was illustrated for the various time- and/or depth-dependent retention model parameters. The developed analytical models were subsequently used to describe breakthrough curves and, in some cases, retention profiles from several published column studies that employed nanoparticle or pathogenic microorganisms. Simulations results provided valuable insights on causes for many observed complexities associated with colloid transport and retention, including: increasing or decreasing effluent concentrations with continued colloid application, delayed breakthrough, low concentration tailing, and retention profiles that are hyper-exponential, exponential, linear, or non-monotonic with distance.
Similarity solutions of vertical plane wall plume based on finite analytic method
Institute of Scientific and Technical Information of China (English)
HUAI Wen-xin; ZENG Yu-hong
2007-01-01
The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.
Analytical solutions for reactive transport under an infiltration-redistribution cycle.
Severino, Gerardo; Indelman, Peter
2004-05-01
Transport of reactive solute in unsaturated soils under an infiltration-redistribution cycle is investigated. The study is based on the model of vertical flow and transport in the unsaturated zone proposed by Indelman et al. [J. Contam. Hydrol. 32 (1998) 77], and generalizes it by accounting for linear nonequilibrium kinetics. An exact analytical solution is derived for an irreversible desorption reaction. The transport of solute obeying linear kinetics is modeled by assuming equilibrium during the redistribution stage. The model which accounts for nonequilibrium during the infiltration and assumes equilibrium at the redistribution stage is termed partial equilibrium infiltration-redistribution model (PEIRM). It allows to derive approximate closed form solutions for transport in one-dimensional homogeneous soils. These solutions are further applied to computing the field-scale concentration by adopting the Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979) 461] column model. The effect of soil heterogeneity on the solute spread is investigated by modeling the hydraulic saturated conductivity as a random function of horizontal coordinates. The quality of the PEIRM is illustrated by calculating the critical values of the Damköhler number which provide the achievable accuracy in estimating the solute mass in the mobile phase. The distinguishing feature of transport during the infiltration-redistribution cycle as compared to that of infiltration only is the finite depth of solute penetration. For irreversible desorption, the maximum solute penetration W/theta(r) is determined by the amount of applied water W and the residual water content theta(r). For sorption-desorption kinetics, the maximum depth of penetration z(r)(e, infinity ) also depends on the ratio between the rate of application and the column-saturated conductivity. It is shown that z(r)(e, infinity ) is bounded between the depths W/(theta(r)+K(d)) and W/theta(r) corresponding to the maximum solute
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
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.
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.
Kia, T.; Longuski, J. M.
1984-01-01
Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
Barna, I. F.; Mátyás, L.
2015-09-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
Analytic self-similar solutions of the Oberbeck-Boussinesq equations
Barna, I F
2015-01-01
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection
Anglin, J. R.; Schulz, A.
2017-01-01
Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for noninteracting fermions on a two-dimensional lattice [Qiao, Jung, and MacDonald, Nano Lett. 11, 3453 (2011), 10.1021/nl201941f; Qiao et al., Phys. Rev. Lett. 112, 206601 (2014), 10.1103/PhysRevLett.112.206601]. Here we confirm this result analytically in the corresponding continuum k .p model, by solving the associated two-dimensional Dirac equation, in the presence of a "checkerboard" potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.
Analytical solution of diffusion model for nutrient release from controlled release fertilizer
Ameenuddin Irfan, Sayed; Razali, Radzuan; KuShaari, KuZilati; Mansor, Nurlidia; Azeem, Babar
2017-09-01
An analytical method has been developed to solve the initial value problem which arises from Fick’s diffusion equation encountered in the modelling of the Controlled Release Fertilizers. The proposed analytical solution is developed using the modified Adomian decomposition method. This method does not require the discretization method, reliability and efficiency of this method is more and it also reduces the calculation time. The model has predicted the effect of granule radius and diffusion coefficient on the nutrient release and total release time of Controlled Release Fertilizer. Model has predicted that increase in the radius of granule reduces the release and vice versa in case of diffusion coefficient. Detailed understanding of these parameters helps in improved designing of Controlled Release Fertilizer.
Analytical Solution of Flow and Heat Transfer over a Permeable Stretching Wall in a Porous Medium
Directory of Open Access Journals (Sweden)
M. Dayyan
2013-01-01
Full Text Available Boundary layer flow through a porous medium over a stretching porous wall has seen solved with analytical solution. It has been considered two wall boundary conditions which are power-law distribution of either wall temperature or heat flux. These are general enough to cover the isothermal and isoflux cases. In addition to momentum, both first and second laws of thermodynamics analyses of the problem are investigated. The governing equations are transformed into a system of ordinary differential equations. The transformed ordinary equations are solved analytically using homotopy analysis method. A comprehensive parametric study is presented, and it is shown that the rate of heat transfer increases with Reynolds number, Prandtl number, and suction to the surface.
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.
Technology report on Railway Embedded Network solutions
Wahl, M; BERNOCCHI, M; Just, P.; WEISS, AH; GOIKOETXEA, J; BILLION, J; NEMORIN, J
2007-01-01
Deliverable D3D.3.1 Technology report on Railway Embedded Network solutions is a deliverable of Work Package SP3D_WP3 ICOM Specification & Telecom Interfaces of Onboard and Train Train Networks. It takes place within the InteGRail Task 3D_03.1 State of the Art in Embedded Networks. The objectives of this deliverable are: - to consider which embedded communication network technologies are already into ser-vice within the trains; - to analyse Ethernet-based technologies; - to evaluate how Ethe...
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Two-component jet simulations: I. Topological stability of analytical MHD outflow solutions
Matsakos, T; Vlahakis, N; Massaglia, S; Mignone, A; Trussoni, E
2007-01-01
Observations of collimated outflows in young stellar objects indicate that several features of the jets can be understood by adopting the picture of a two-component outflow, wherein a central stellar component around the jet axis is surrounded by an extended disk-wind. The precise contribution of each component may depend on the intrinsic physical properties of the YSO-disk system as well as its evolutionary stage. In this context, the present article starts a systematic investigation of two-component jet models via time-dependent simulations of two prototypical and complementary analytical solutions, each closely related to the properties of stellar-outflows and disk-winds. These models describe a meridionally and a radially self-similar exact solution of the steady-state, ideal hydromagnetic equations, respectively. By using the PLUTO code to carry out the simulations, the study focuses on the topological stability of each of the two analytical solutions, which are successfully extended to all space by remo...
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.
Bars, Itzhak; Steinhardt, Paul J; Turok, Neil
2012-01-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null energy condition. There is a special subset of geodesically complete non-generic solutions which perform zero-size bounces without ever entering the antigravit...
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
Directory of Open Access Journals (Sweden)
Takibayev N.Zh.
2010-04-01
Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two ﬁxed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two ﬁxed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei ﬁxed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.
Analytical Solution of the Blast Wave Problem in a Non-Ideal Gas
Institute of Scientific and Technical Information of China (English)
L. P. Singh; S. D. Ram; D. B. Singh
2011-01-01
An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium. It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave. Also, an analytical expression for the total energy in a non-ideal medium is derived.%An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium.It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave.Also,an analytical expression for the total energy in a non-ideal medium is derived.Blast waves are common occurrences in the Earth's atmosphere.They result from a sudden release of a relatively large amount of energy.Typical examples are lightening and chemical or nuclear explosions.Assume that we have an explosion,following which there may exist a very small region filled with hot matter at high pressure in a duration,which starts to expand outwards with its front headed by a strong shock.The process generally takes place in a very short time after which a forward-moving shock wave develops,which continuously assimilates the ambient air into the blast wave.Although some of the explosive material may still remain near the center,the amount of the air absorbed increases with time,and the later behavior of the blast wave may well be represented by the model of the shock wave at the front and a purely gasdynamic treatment for the motion of the air inside,which may be assumed to have ideal and non-viscous adiabatic heat exponent.
Zharkova, V. V.; Dobranskis, R. R.
2016-06-01
In this paper we consider simultaneous analytical solutions of continuity equations for electron beam precipitation (a) in collisional losses and (b) in ohmic losses, or mixed energy losses (MEL) by applying the iterative method to calculate the resulting differential densities at given precipitation depth. The differential densities of precipitating electrons derived from the analytical solutions for MELs reveal increased flattening at energies below 10-30 keV compared to a pure collisional case. This flattening becomes stronger with an increasing precipitation depth turning into a positive slope at greater precipitation depths in the chromosphere resulting in a differential density distribution with maximum that shifts towards higher energies with increase in column depth, while the differential densities combining precipitating and returning electrons are higher at lower energies than those for a pure collisional case. The resulting hard X-ray (HXR) emission produced by the beams with different initial energy fluxes and spectral indices is calculated using the MEL approach for different ratios between the differential densities of precipitating and returning electrons. The number of returning electrons can be even further enhanced by a magnetic mirroring, not considered in the present model, while dominating at lower atmospheric depths where the magnetic convergence and magnitude are the highest. The proposed MEL approach provides an opportunity to account simultaneously for both collisional and ohmic losses in flaring events, which can be used for a quick spectral fitting of HXR spectra and evaluation of a fraction of returning electrons versus precipitating ones. The semi-analytical MEL approach is used for spectral fitting to Reuven High Energy Solar Spectroscopic Imager observations of nine C, M and X class flares revealing a close fit to the observations and good resemblance to numerical FP solutions.
Lin, Yezhi; Liu, Yinping; Li, Zhibin
2012-01-01
The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_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.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.
Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system
Sedghi, Mohammad M.; Samani, Nozar
2015-09-01
Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.
Smyth, Katherine; Bathurst, Stephen; Sammoura, Firas; Kim, Sang-Gook
2013-08-01
In this work, the deflection equation of a piezoelectrically-driven micromachined ultrasonic transducer (PMUT) is analytically determined using a Green's function approach. With the Green's function solution technique, the deflection of a circular plate with an arbitrary circular/ring electrode geometry is explicitly solved for axisymmetric vibration modes. For a PMUT with one center electrode covering ≈60% of the plate radius, the Green's function solution compares well with existing piece-wise and energy-based solutions with errors of less than 1%. The Green's function solution is also simpler than them requiring no numerical integration, and applies to any number of axisymmetric electrode geometries. Experimentally measured static deflection data collected from a fabricated piezoelectric micro ultrasonic transducer (PMUT) is further used to validate the Green's function model analysis. The center deflection and deflection profile data agree well with the Green's function solution over a range of applied bias voltages (5 to 21 V) with the average error between the experimental and Green's function data less than 9%.
Benchmarking the invariant embedding method against analytical solutions in model transport problems
Directory of Open Access Journals (Sweden)
Wahlberg Malin
2006-01-01
Full Text Available The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.
Kazempour, Sobhan; Soroushfar, Saheb
2016-01-01
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes.
Original analytic solution of a half-bridge modelled as a statically indeterminate system
Oanta, Emil M.; Panait, Cornel; Raicu, Alexandra; Barhalescu, Mihaela
2016-12-01
The paper presents an original computer based analytical model of a half-bridge belonging to a circular settling tank. The primary unknown is computed using the force method, the coefficients of the canonical equation being calculated using either the discretization of the bending moment diagram in trapezoids, or using the relations specific to the polygons. A second algorithm based on the method of initial parameters is also presented. Analyzing the new solution we came to the conclusion that most of the computer code developed for other model may be reused. The results are useful to evaluate the behavior of the structure and to compare with the results of the finite element models.
Analytic, piecewise solution to the Lane-Emden equation for stars with complex density profiles
Miller, Jeff; Bogdanovic, Tamara
2017-01-01
The polytropic models of stars are used for a variety of applications in computational astrophysics. These are typically obtained by numerically solving the Lane-Emden equation for a star in hydrostatic equilibrium under assumption that the pressure and density within the star obey the polytropic equation of state. We present an efficient analytic, piecewise differentiable solution to the Lane-Emden equation which allows “stitching” of different polytropes to represent complex pressure and density profiles. This approach can be used to model stars with distinct properties in their cores and envelopes, such as the evolved red giant and horizontal branch stars.
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.
Analytical Solution for Wave-Induced Response of Seabed with Variable Shear Modulus
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A plane strain analysis based on the generalized Biot's equation is utilized to investigate the wave-induced response of a poro-elastic seabed with variable shear modulus. By employing integral transform and Frobenius methods, the transient and steady solutions for the wave-induced pore water pressure, effective stresses and displacements are analytically derived in detail. Verification is available through the reduction to the simple case of homogeneous seabed. The numerical results indicate that the inclusion of variable shear modulus significantly affects the wave-induced seabed response.
Colantoni, A; Boubaker, K
2014-01-30
In this paper Enhanced Variational Iteration Method, EVIM is proposed, along with the BPES, for solving Bratu equation which appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers, with diameters less than 1/4 microns have been used in non-wovens and filtration industries for a broad range of filtration applications in the last decade. Electro-spinning process has been associated to Bratu equation through thermo-electro-hydrodynamics balance equations. Analytical solutions have been proposed, discussed and compared.
Analytical Solutions of Time Periodic Electroosmotic Flow in a Semicircular Microchannel
Directory of Open Access Journals (Sweden)
Shaowei Wang
2015-01-01
Full Text Available The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.
SWASHES: a library of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies
Delestre, Olivier; Pierre-Antoine, Ksinant; Darboux, Frédéric; Christian, Laguerre; Vo, Thi Ngoc Tuoi; James, Francois; Cordier, Stephane
2013-01-01
A significant number of analytic solutions to the Shallow Water equations is discribed in a unified formalism. They encompass a wide variety of flow conditions (supercritical, subcritical, shock, etc.), in 1 or 2 space dimensions, with or without rain and soil friction, for transitory flow or steady state. An original feature is that the corresponding source codes are made available to the community (http://www.univ-orleans.fr/mapmo/soft/SWASHES), so that users of Shallow Water based models can easily find an adaptable benchmark library to validate numerical methods.
Analytical solutions for the fractional diffusion-advection equation describing super-diffusion
Directory of Open Access Journals (Sweden)
Gómez Francisco
2016-01-01
Full Text Available This paper presents the alternative construction of the diffusion-advection equation in the range (1; 2. The fractional derivative of the Liouville-Caputo type is applied. Analytical solutions are obtained in terms of Mittag-Leffler functions. In the range (1; 2 the concentration exhibits the superdiffusion phenomena and when the order of the derivative is equal to 2 ballistic diffusion can be observed, these behaviors occur in many physical systems such as semiconductors, quantum optics, or turbulent diffusion. This mathematical representation can be applied in the description of anomalous complex processes.
Analytic solution for fluxons in a long Josephson junction with surface losses
DEFF Research Database (Denmark)
Sakai, S.; Pedersen, Niels Falsig
1986-01-01
Analytic solutions for a fluxon in a long Josephson junction in the presence of surface losses (β term) as well as shunt losses (α term) are obtained by assuming a triangular current-phase relation. This theoretical result provides exact information on fluxon properties (e.g., the line shape, vel......, velocity, etc.), independent of the magnitude of α and β. We find that if β is smaller than a critical value, the fluxon behavior is similar to that of the β=0 case, but if β is larger, quite different behavior is observed, particularly in the high-velocity region....
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.
The Analytical Solution of the Schr\\"odinger Particle in Multiparameter Potential
Taş, Ahmet
2016-01-01
In this study, we present analytical solutions of the Schr\\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type approximation to the centrifugal potential. For any n and l (states) quantum numbers, we get the bound state energy eigenvalues numerically and the corresponding eigenfunctions.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.
Analytical solution of the Klein Gordon equation for a quadratic exponential-type potential
Ezzatpour, Somayyeh; Akbarieh, Amin Rezaei
2016-07-01
In this research study, analytical solutions of the Klein Gordon equation by considering the potential as a quadratic exponential will be presented. However, the potential is assumed to be within the framework of an approximation for the centrifugal potential in any state. The Nikiforov-Uvarov method is used to calculate the wave function, as well as corresponding exact energy equation, in bound states. We finally concluded that the quadratic exponential-type potential under which the results were deduced, led to outcomes that were comparable to the results obtained from the well-known potentials in some special cases.
Soroushfar, Saheb; Saffari, Reza; Sahami, Ehsan
2016-07-01
In this paper, we consider the timelike and null geodesics around the static (GMGHS, magnetically charged GMGHS, electrically charged GMGHS) and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained results we study astrophysical applications.
Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
Cebeci, Hakan; Özdemir, Nülifer; Şentorun, Seçil
2016-05-01
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits and their stabilities. Furthermore, we obtain the analytical solutions of the equations of motion and express them in terms of Jacobian and Weierstrass elliptic functions. Finally, we discuss the observables of the bound motion and calculate the perihelion shift and Lense-Thirring effect for the bound orbits.
Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
Cebeci, Hakan; Şentorun, Seçil
2015-01-01
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits and their stabilities. Furthermore, we obtain the analytical solutions of the equations of motion and express them in terms of Jacobian and Weierstrass elliptic functions. Finally, we discuss the observables of the bound motion and calculate the perihelion shift and Lense-Thirring effect for three dimensional bound orbits.
An Explicit,Totally Analytic Solution of Laminar Viscous FLow over a Semi—Infinite Flat Plate
Institute of Scientific and Technical Information of China (English)
Shi－JunLIAO
1998-01-01
In this paper,a new kind of analytic technique for nonlinear problems,namely the Homotopy Analysis Method,is applied to give an explicit,totally analytic solution of the Blasius' flow.i.e.,the two dimensional (2D) laminar viscous flow over a semi-infinite flat plate.This analytic solution is valid in the whole region having physical meanings.To our knowledge,it is the first time in history that such a kind of explicit,totally analytic solution is given.This fact well verifies the great potential and validity of the Honmotopy Analysis Method as a kind of powerful analytic tool for nonlinear problems in science and engineering.
A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions.The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions,and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on (2+1)-dimensional dispersive long-wave equation.
Analytical general solutions for static wormholes in f(R,T) gravity
Moraes, P. H. R. S.; Correa, R. A. C.; Lobato, R. V.
2017-07-01
Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f(R,T) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T-dependence in f(R,T) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f(R,T) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.
Analytical quality-by-design approach for sample treatment of BSA-containing solutions
Institute of Scientific and Technical Information of China (English)
Lien Taevernier; Evelien Wynendaele; Matthias D’Hondt; Bart De Spiegeleer
2015-01-01
The sample preparation of samples containing bovine serum albumin (BSA), e.g., as used in transdermal Franz diffusion cell (FDC) solutions, was evaluated using an analytical quality-by-design (QbD) approach. Traditional precipitation of BSA by adding an equal volume of organic solvent, often successfully used with conventional HPLC-PDA, was found insufficiently robust when novel fused-core HPLC and/or UPLC-MS methods were used. In this study, three factors (acetonitrile (%), formic acid (%) and boiling time (min)) were included in the experimental design to determine an optimal and more suitable sample treatment of BSA-containing FDC solutions. Using a QbD and Derringer desirability (D) approach, combining BSA loss, dilution factor and variability, we constructed an optimal working space with the edge of failure defined as Do0.9. The design space is modelled and is confirmed to have an ACN range of 8373%and FA content of 170.25%.
Analytical solution of laminar-laminar stratified two-phase flows with curved interfaces
Energy Technology Data Exchange (ETDEWEB)
Brauner, N.; Rovinsky, J.; Maron, D.M. [Tel-Aviv Univ. (Israel)
1995-09-01
The present study represents a complete analytical solution for laminar two-phase flows with curved interfaces. The solution of the Navier-Stokes equations for the two-phases in bipolar coordinates provides the `flow monograms` describe the relation between the interface curvature and the insitu flow geometry when given the phases flow rates and viscosity ratios. Energy considerations are employed to construct the `interface monograms`, whereby the characteristic interfacial curvature is determined in terms of the phases insitu holdup, pipe diameter, surface tension, fluids/wall adhesion and gravitation. The two monograms are then combined to construct the system `operational monogram`. The `operational monogram` enables the determination of the interface configuration, the local flow characteristics, such as velocity profiles, wall and interfacial shear stresses distribution as well as the integral characteristics of the two-phase flow: phases insitu holdup and pressure drop.
Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating
Abbas, Ibrahim A.; Marin, Marin
2017-03-01
In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written in the form of a vector-matrix differential equation, which is then solved by an eigenvalue approach. The exact analytical solution is adopted for the temperature, the components of displacement and stresses. The results obtained are presented graphically for the effect of laser pulse to display the phenomena physical meaning. The graphical results indicate that the thermal relaxation time has a great effect on the temperature, the components of displacement and the components of stress.
On the analytical solution for the Pütter-Bertalanffy growth equation.
Ohnishi, Shuhei; Yamakawa, Takashi; Akamine, Tatsuro
2014-02-21
This study develops the basic idea of Pütter and Bertalanffy addressing the allometric scaling of anabolism and catabolism on somatic growth dynamics. We proposed a standardized form of the Pütter-Bertalanffy equation (PBE), which is given as the extended model of Richards function, and subsequently solved it. The analytical solution of the PBE was defined by an incomplete beta function and can take a wide range of shapes in its growth curve. The mathematical behavior of PBE due to the change in parameter values was briefly discussed. Most forms of solution consistently hold the implicit functional type with respect to the variable of body size. © 2013 Published by Elsevier Ltd.
Deriving Coarse-Grained Charges from All-Atom Systems: An Analytic Solution.
McCullagh, Peter; Lake, Peter T; McCullagh, Martin
2016-09-13
An analytic method to assign optimal coarse-grained charges based on electrostatic potential matching is presented. This solution is the infinite size and density limit of grid-integration charge-fitting and is computationally more efficient by several orders of magnitude. The solution is also minimized with respect to coarse-grained positions which proves to be an extremely important step in reproducing the all-atom electrostatic potential. The joint optimal-charge optimal-position coarse-graining procedure is applied to a number of aggregating proteins using single-site per amino acid resolution. These models provide a good estimate of both the vacuum and Debye-Hückel screened all-atom electrostatic potentials in the vicinity and in the far-field of the protein. Additionally, these coarse-grained models are shown to approximate the all-atom dimerization electrostatic potential energy of 10 aggregating proteins with good accuracy.
Malkov, M A
2016-01-01
An analytic solution for a Fokker-Planck equation that describes propagation of energetic particles through a scattering medium is obtained. The solution is found in terms of an infinite series of mixed moments of particle distribution. The spatial dispersion of a particle cloud released at t=0 evolves through three phases, ballistic (t>Tc), where Tc is the collision time.The ballistic phase is characterized by a decelerating expansion of the initial point source in form of "box" distribution with broadening walls. The next, transdiffusive phase is marked by the box walls broadened to its size and a noticeable slow down of expansion. Finally, the evolution enters the conventional diffusion phase.
Institute of Scientific and Technical Information of China (English)
Wang Teng; Wang Kuihua; Xie Kanghe
2001-01-01
The vibration problem of a pile of arbitrary segments with variable modulus under exciting force is established, in which the influence of the soil under pile toe and the surroundings is taken into account. With Laplace transforms, the transmit functions for velocity and displacement of pile are derived. Furthermore, in terms of the convolution theorem and inversed Laplace transform, an analytical solution for the time domain response of a pile subjected to a semi-sine impulse is developed,which is the theoretical basis of the sonic method in pile integrity testing. Based on the solution, the vibration properties of pile with sharp or continuous modulus are studied. The validity of this approach is verified through fidd dynamic tests on some engineering piles. It shows that the theoretical prediction and the response of the pile are in good agreement.
A nonlinear model arising in the buckling analysis and its new analytic approximate solution
Energy Technology Data Exchange (ETDEWEB)
Khan, Yasir [Zhejiang Univ., Hangzhou, ZJ (China). Dept. of Mathematics; Al-Hayani, Waleed [Univ. Carlos III de Madrid, Leganes (Spain). Dept. de Matematicas; Mosul Univ. (Iraq). Dept. of Mathematics
2013-05-15
An analytical nonlinear buckling model where the rod is assumed to be an inextensible column and prismatic is studied. The dimensionless parameters reduce the constitutive equation to a nonlinear ordinary differential equation which is solved using the Adomian decomposition method (ADM) through Green's function technique. The nonlinear terms can be easily handled by the use of Adomian polynomials. The ADM technique allows us to obtain an approximate solution in a series form. Results are presented graphically to study the efficiency and accuracy of the method. To the author's knowledge, the current paper represents a new approach to the solution of the buckling of the rod problem. The fact that ADM solves nonlinear problems without using perturbations and small parameters can be judged as a lucid benefit of this technique over the other methods. (orig.)
Directory of Open Access Journals (Sweden)
Md. Alal Hosen
2015-01-01
Full Text Available In the present paper, a complicated strongly nonlinear oscillator with cubic and harmonic restoring force, has been analysed and solved completely by harmonic balance method (HBM. Investigating analytically such kinds of oscillator is very difficult task and cumbersome. In this study, the offered technique gives desired results and to avoid numerical complexity. An excellent agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. It is remarkably important that, second-order approximate results are almost same with exact solutions. The advantage of this method is its simple procedure and applicable for many other oscillatory problems arising in science and engineering.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-01-15
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.
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.
An Analytical Solution Applied to Heat and Mass Transfer in a Vibrated Fluidised Bed Dryer
Energy Technology Data Exchange (ETDEWEB)
Picado, Apolinar
2011-07-01
A mathematical model for the drying of particulate solids in a continuous vibrated fluidised bed dryer was developed and applied to the drying of grain wetted with a single liquid and porous particles containing multicomponent liquid mixtures. Simple equipment and material models were applied to describe the process. In the plug-flow equipment model, a thin layer of particles moving forward and well mixed in the direction of the gas flow was regarded; thus, only the longitudinal changes of particle moisture content and composition as well as temperature along the dryer were considered. Concerning the material model, mass and heat transfer in a single isolated particle was studied. For grain wetted with a single liquid, mass and heat transfer within the particles was described by effective transfer coefficients. Assuming a constant effective mass transport coefficient and effective thermal conductivity of the wet particles, analytical solutions of the mass and energy balances were obtained. The variation of both transport coefficients along the dryer was taken into account by a stepwise application of the analytical solution in space intervals with non-uniform inlet conditions and averaged coefficients from previous locations in the dryer. Calculation results were verified by comparison with experimental data from the literature. There was fairly good agreement between experimental data and simulation but the results depend strongly on the correlation used to calculate heat and mass transfer coefficients. For the case of particles containing a multicomponent liquid mixture dried in the vibrated fluidised bed dryer, interactive diffusion and heat conduction were considered the main mechanisms for mass and heat transfer within the particles. Assuming a constant matrix of effective multicomponent diffusion coefficients and thermal conductivity of the wet particles, analytical solutions of the diffusion and conduction equations were obtained. The equations for mass
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.
Digital Repository Service at National Institute of Oceanography (India)
Shankar, D.; McCreary, J.P.; Han, W.; Shetye, S.R.
OF GEOPHYSICAL RESEARCH, VOL. 101, NO. C6, PAGES 13,975-13,991, JUNE 15, 1996 Dynamics of the East India Coastal Current 1. Analytic solutions forced by interior Ekman pumping and local alongshore winds D. Snankar Centre for Mathematical Modelling... linear, continuously stratified model is used to investigate how forcing by interior Ekman pumping and local alongshore winds affects the East India Coastal Current (EICC). Solutions are found analytically to an approximate version of the equations...
Gazzillo, Domenico; Munaò, Gianmarco; Prestipino, Santi
2016-06-01
We study a pure fluid of heteronuclear sticky Janus dumbbells, considered to be the result of complete chemical association between unlike species in an initially equimolar mixture of hard spheres (species A) and sticky hard spheres (species B) with different diameters. The B spheres are particles whose attractive surface layer is infinitely thin. Wertheim's two-density integral equations are employed to describe the mixture of AB dumbbells together with unbound A and B monomers. After Baxter factorization, these equations are solved analytically within the associative Percus-Yevick approximation. The limit of complete association is taken at the end. The present paper extends to the more general, heteronuclear case of A and B species with size asymmetry a previous study by Wu and Chiew [J. Chem. Phys. 115, 6641 (2001)], which was restricted to dumbbells with equal monomer diameters. Furthermore, the solution for the Baxter factor correlation functions qi j α β ( r ) is determined here in a fully analytic way, since we have been able to find explicit analytic expressions for all the intervening parameters.
Hrabe, J.; Lewis, D. P.
2004-03-01
A fairly general theoretical model for pulsed arterial spin labeling perfusion methods has been available for some time but analytical solutions were derived for only a small number of arterial blood input functions. These mostly assumed a sudden and simultaneous arrival of the tagged blood into the imaged region. More general cases had to be handled numerically. We present analytical solutions for two more realistic arterial input functions. They both allow the arrival times of the molecules of tagged arterial blood to be statistically distributed. We consider cases of (1) a uniform distribution on a finite time interval and (2) a normal distribution characterized by its mean and standard deviation. These models are physiologically meaningful because the statistical nature of the arrival times reflects the distribution of velocities and path lengths that the blood water molecules undertake from the tagging region to the imaged region. The model parameters can be estimated from the measured dependency of the perfusion signal on the tag inversion time.
Analytical Solution for Three-Dimensional Capture Zone of a Slanted Well
Zhou, Yu-Hui; Chen, Chia-Shyun
2016-04-01
It is rather impractical to install vertical wells inside a building for the sake of dealing with groundwater contamination under the building. Slant wells, however, provide an alternative because they can be drilled with a θ angle (with respect to the horizontal surface) from the edge of the building foundation to the target aquifer. Herein, a steady-state, analytical solution is developed for the three-dimensional (3D) capture zone created by a slant well pumping under the influence of a uniform regional flow field of a constant hydraulic gradient, i. The aquifer is assumed to be confined, homogeneous with a vertical anisotropy ratio, κ(Kx /Kz ≤ 1). The 3D capture zone is the largest when the slant well is in the same direction of +i, and the smallest when the slant well is in the direction at a right angle to +i; other conditions remain the same. Decreasingκ compresses the 3D capture zone in the vertical direction while elongates its horizontal extent. The stagnation point moves upward and closer to the slant well screen when i increases. Application of the linear superposition principle to this 3D analytical solution can yield information for various conditions that involve multiple slant wells with different orientation and θ angles, providing a useful understanding of how to employ slant wells to withdraw contaminated groundwater that cannot be done using the conventional vertical wells.
Application of the homotopy method for analytical solution of non-Newtonian channel flows
Energy Technology Data Exchange (ETDEWEB)
Roohi, Ehsan [Department of Aerospace Engineering, Sharif University of Technology, PO Box 11365-8639, Azadi Avenue, Tehran (Iran, Islamic Republic of); Kharazmi, Shahab [Department of Mechanical Engineering, Sharif University of Technology, PO Box 11365-8639, Azadi Avenue, Tehran (Iran, Islamic Republic of); Farjami, Yaghoub [Department of Computer Engineering, University of Qom, Qom (Iran, Islamic Republic of)], E-mail: roohi@sharif.edu
2009-06-15
This paper presents the homotopy series solution of the Navier-Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals 36 182-92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena observed in non-Newtonian channel flows. For example, it is observed that the velocity profile of non-Newtonian Couette flow is indistinctive from the velocity profile of the Newtonian one. Additionally, we observe flow separation in non-Newtonian Couette-Poiseuille flow even though the pressure gradient is negative (favorable). We provide physical reasoning for these unique phenomena.
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.
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.
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)
Analytical solutions of heat transfer for laminar flow in rectangular channels
Rybiński, Witold; Mikielewicz, Jarosław
2014-12-01
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.
New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods
S Saha, Ray
2016-04-01
In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.
Analytical solution to the circularity problem in the discounted cash flow valuation framework
Directory of Open Access Journals (Sweden)
Felipe Mejía-Peláez
2011-12-01
Full Text Available In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We present a general formulation without circularity for the equity value (E, cost of levered equity (Ke, levered firm value (V, and the weighted average cost of capital (WACC. We furthermore compare the results obtained from these formulas with the results of the application of the Adjusted Present Value approach (no circularity and the iterative solution of circularity based upon the iteration feature of a spreadsheet, concluding that all methods yield exactly the same answer. The advantage of this solution is that it avoids problems such as using manual methods (i.e., the popular “Rolling WACC” ignoring the circularity issue, setting a target leverage (usually constant with the inconsistencies that result from it, the wrong use of book values, or attributing the discrepancies in values to rounding errors.
Analytic solutions for Wheeler-Feynman interaction: Two bodies in straight-line motion
Stephas, Paul
1992-02-01
Analytic solutions are obtained for two point particles with any total energy that have charges of like sign and whose motions are confined to one dimension. These solutions are obtained by explicitly deriving the conserved quantities associated with Wheeler-Feynman interactions into forms that do not contain integrals but, rather, contain ``partial contributions'' to the momenta and potentials of particle two. The resulting conserved energy, momentum, and Lorentz momentum equations are separated in time to yield one set of equations with variables t1 and t2- (retarded) and another set with variables t1 and t1+ (advanced). These are solved to obtain auxiliary solutions x1r(t1) and x1a(t1), which are then combined for the case m1 = m2 to give the actual world lines x1(t1) and x2(t2). Comparison is made with a previous computer-generated exact solution for the same interaction and energy; good qualitative agreement is found, although some quantitative differences persist.
Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.
Suk, Heejun
2016-08-01
This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.
An analytical solution for a partially wetting puddle and the location of the static contact angle.
Elena Diaz, M; Fuentes, Javier; Cerro, Ramon L; Savage, Michael D
2010-08-01
A model is formulated for a static puddle on a horizontal substrate taking account of capillarity, gravity and disjoining pressure arising from molecular interactions. There are three regions of interest--the molecular, transition and capillary regions with characteristic film thickness, hm, ht and hc. An analytical solution is presented for the shape of the vapour-liquid interface outside the molecular region where interfacial tension can be assumed constant. This solution is used to shed new light on the static contact angle and, specifically, it is shown that. (i) There is no point in the vapour-liquid interface where the angle of inclination, theta, is identically equal to the static contact angle, theta(o), but the angle at the point of null curvature is the closest with the difference of O(epsilon2) where epsilon2 = ht/hc is a small parameter. (ii) The liquid film is to O(epsilon) a wedge of angle theta(o) extending from a few nanometers to a few micrometers of the contact line. A second analytical solution for the shape of interface within the molecular region reveals that cos theta has a logarithmic variation with film thickness, cos theta=cos theta-ln[1-h2(m)/2h2]. The case, hm = 0, is of special significance since it refers to a unique configuration in which the effect of molecular interactions vanishes, disjoining pressure is everywhere zero and the vapour-liquid interface is now described exactly by the Young-Laplace equation and includes a wedge of angle, theta(o), extending down to the solid substrate.
Estimating Fuel Cycle Externalities: Analytical Methods and Issues, Report 2
Energy Technology Data Exchange (ETDEWEB)
Barnthouse, L.W.; Cada, G.F.; Cheng, M.-D.; Easterly, C.E.; Kroodsma, R.L.; Lee, R.; Shriner, D.S.; Tolbert, V.R.; Turner, R.S.
1994-07-01
of complex issues that also have not been fully addressed. This document contains two types of papers that seek to fill part of this void. Some of the papers describe analytical methods that can be applied to one of the five steps of the damage function approach. The other papers discuss some of the complex issues that arise in trying to estimate externalities. This report, the second in a series of eight reports, is part of a joint study by the U.S. Department of Energy (DOE) and the Commission of the European Communities (EC)* on the externalities of fuel cycles. Most of the papers in this report were originally written as working papers during the initial phases of this study. The papers provide descriptions of the (non-radiological) atmospheric dispersion modeling that the study uses; reviews much of the relevant literature on ecological and health effects, and on the economic valuation of those impacts; contains several papers on some of the more complex and contentious issues in estimating externalities; and describes a method for depicting the quality of scientific information that a study uses. The analytical methods and issues that this report discusses generally pertain to more than one of the fuel cycles, though not necessarily to all of them. The report is divided into six parts, each one focusing on a different subject area.
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The Analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance Cylinders, and it is derived...... by transformation of the exact eigenfunction series solution. The transformation employs the Hankel function wave transformation to express the eigenfunction series of higher-order Hankel functions, with their singularities at the coordinate system origin as a superposition of zero-order Hankel functions...... with their singularities at different positions away from the origin. The transformation necessitates a truncation of the wave transformation but the inaccuracy introduced hereby is shown to be negligible. The analytical Method of Auxiliary Sources solution is employed as a reference to investigate the accuracy...
Energy Technology Data Exchange (ETDEWEB)
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
2014-07-01
This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.
General analytical solutions for DC/AC circuit-network analysis
Rubido, Nicolás; Grebogi, Celso; Baptista, Murilo S.
2017-06-01
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. This simplifies the treatment that could be done via Thévenin's theorem. Contrary to solving Kirchhoff's equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.
Galley, Chad R.; Rothstein, Ira Z.
2017-05-01
We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is v5ν Ω (t -t0) where t0 is the initial time, t is the time elapsed, and Ω and v are the angular orbital frequency and initial speed, respectively. ν is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second-order corrections of the leading radiation reaction force, which involves highly nontrivial checks of the formalism (i.e., its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging, we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.
Energy Technology Data Exchange (ETDEWEB)
Sharif, Ahmed
1997-12-31
The reservoir up-scaling problem has been receiving increased attention in recent years. Over the past decade or so, there has been increasing interest in development of computationally efficient methods to determine effective properties or permeability. Those properties were traditionally computed from detailed numerical solutions of the actual reservoir realization. This is an indirect approach requiring substantial computer resources particularly in 3D problems in which the number of grid-blocks often become impractically large. A contrasting strategy is the direct approach in which the effective properties are computed directly from the statistical description of the medium without the aid of an actual reservoir realization. This method will be particularly important for multiphase problems. Among the direct methods, a particularly promising one which motivated this study, is the self-consistent approximation for determining the electric conductivity of heterogeneous media and multiphase materials. In reservoir engineering context, the self-consistent approximation has been recently applied to determine effective permeabilities. This approximation needs analytical solutions for the fluctuation of pressure created in an otherwise homogeneous matrix of infinite dimensions by the submersion of inclusions. The existing solutions are based on models which have limitations on the orientation of permeability tensors and perhaps largely in the geometry of the inclusions. Mathematical models have been developed which strongly generalize the existing inclusion models serving as a basis for the self-consistent approximation. 21 refs., 9 figs., 2 tabs.
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 $r=2M$. ...
An analytical solution of the Fokker-Planck equation in the phase-locked loop transient analysis
Zhang, Weijian
1987-01-01
A probabilistic approach is used to obtain an analytical solution to the Fokker-Planck equation used in the transient analysis of the phase-locked loop phase error process of the first-order phase-locked loop. The solution procedure, which is based on the Girsanov transformation, is described.
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.
Directory of Open Access Journals (Sweden)
S. Sreenadh
2016-06-01
Full Text Available The Peristaltic transport of conducting nanofluids under the effect of slip condition in an asymmetric channel is reported in the present work. The mathematical modelling has been carried out under long wavelength and low Reynolds number approximations. The analytical solutions are obtained for pressure rise, nanoparticle concentration, temperature distribution, velocity profiles and stream function. Influence of various parameters on the flow characteristics has been discussed with the help of graphs. The results showed that the pressure rise increases with increasing magnetic effect and decreases with increasing slip parameter. The effects of thermophoresis parameter and Brownian motion parameter on the nanoparticle concentration and temperature distribution are studied. It is observed that the pressure gradient increases with increasing slip parameter and magnetic effect. The trapping phenomenon for different parameters is presented.
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